case study based questions on number system

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.

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Class 8 Maths Chapter 1 Case Based Questions - Number System

Correct Answer is Option (a) Number system: A numeral system (or system of numeration) is a writing system for expressing numbers that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The number the numeral represents is called its value.

Correct Answer is Option (a) a p + q a p  . a q  = a p + q

Correct Answer is Option (b) r – s is rational number.

Reason  : This statement is false. The difference between a rational number (r) and an irrational number (s) can be either rational or irrational. There is no general rule that says the difference of a rational and an irrational number must be rational. Counterexamples can easily be constructed to show that the difference could be either rational or irrational.

Correct Answer is Option (a)

Q7:  In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. How many rational numbers are there between 5 and 7.

(a)  0 (b)  1 (c)  2 (d)  infinite

Correct Answer is Option (d) There are an infinite amount of irrational numbers between 5 and 7.

Q8: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. What fraction of the students participated in the campaign. (a)  2/7 (b) 5/7 (c)  4/7 (d)  7/7

Correct Answer is Option (b)

Number of students participated in campaign = 5

Number of total students = 7

Therefore, fraction of the students participated in the campaign. = 5/7

Q9: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. What kind of decimal expansion it has. (a) Terminating (b)  non terminating (c)  terminating repeating (d)  non terminating repeating

Correct Answer is Option (d) A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Non-terminating, non-repeating decimals can be easily created by using a pattern.

Q10: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. Every rational number is a _______ number. (a) Prime (b)  Composite (c)  real (d)  even

Correct Answer is Option (c) Every rational number is a real number. It can be defined as any number that can be expressed in the p/q form where q ≠ 0. We can also say that any fraction falls under the class of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero.

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CBSE Class 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

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Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

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CBSE Class 10 Maths Case Study Questions for Class 10 Maths Chapter 1 - Real Numbers (Published by CBSE)

Cbse class 10 maths cased study question bank for chapter 1 - real numbers is available here. this question bank is very useful to prepare for the class 10 maths exam 2021-2022..

The Central Board of Secondary Education has introduced the case study questions in class 10 exam pattern 2021-2022. The CBSE Class 10 questions papers of Board Exam 2022 will have questions based on case study. Therefore, students should get familiarised with these questions to do well in their board exam.

We have provided here case study questions for Class 10 Maths Chapter 1 - Real Numbers. These questions have been published by the CBSE board itself. Students must solve all these questions at the same time they finish with the chapter - Real numbers. 

Case Study Questions for Class 10 Maths Chapter 1 - Real Numbers

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

1. What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

Answer: c) 288

2. If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is

Answer: b) 4

3. 36 can be expressed as a product of its primes as

a) 2 2 × 3 2

b) 2 1 × 3 3

c) 2 3 × 3 1

d) 2 0 × 3 0

Answer: a) 2 2 × 3 2

4. 7 × 11 × 13 × 15 + 15 is a

a) Prime number

b) Composite number

c) Neither prime nor composite

d) None of the above

Answer: b) Composite number

5. If p and q are positive integers such that p = ab 2 and q= a 2 b, where a , b are prime numbers, then the LCM (p, q) is

Answer: b) a 2 b 2

CASE STUDY 2:

A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

1. In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are

Answer: b) 12

2. What is the minimum number of rooms required during the event?

Answer: d) 21

3. The LCM of 60, 84 and 108 is

Answer: a) 3780

4. The product of HCF and LCM of 60,84 and 108 is

Answer: d) 45360

5. 108 can be expressed as a product of its primes as

a) 2 3 × 3 2

b) 2 3 × 3 3

c) 2 2 × 3 2

d) 2 2 × 3 3

Answer: d) 2 2 × 3 3

CASE STUDY 3:

A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

1. What will be the value of x?

Answer: b) 13915

2. What will be the value of y?

Answer: c) 11

3. What will be the value of z?

Answer: b) 23

4. According to Fundamental Theorem of Arithmetic 13915 is a

a) Composite number

b) Prime number

d) Even number

Answer: a) Composite number

5. The prime factorisation of 13915 is

a) 5 × 11 3 × 13 2

b) 5 × 11 3 × 23 2

c) 5 × 11 2 × 23

d) 5 × 11 2 × 13 2

Answer: c) 5 × 11 2 × 23

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

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CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

Table of Contents

CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadrilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

RELATED STORIES

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)

1. Given two distinct points, there exists one and only one line through them. (Theorem)

2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES (15 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

3. (Motivate) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

5. (Prove) The angles opposite to equal sides of a triangle are equal.

6. (Motivate) The sides opposite to equal angles of a triangle are equal.

4. QUADRILATERALS (13 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.

2. (Motivate) In a parallelogram opposite sides are equal, and conversely.

3. (Motivate) In a parallelogram opposite angles are equal, and conversely.

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.

6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

5. CIRCLES (17 Periods)

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

5. (Motivate) Angles in the same segment of a circle are equal.

6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION 1.

1. AREAS (5 Periods)

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17 Periods)

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15 Periods)

 Bar graphs, histograms (with varying base lengths), and frequency polygons.

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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• Revision Notes
• Important Questions
• Previous Years Questions
• Case-Based Questions
• Assertion and Reason Questions

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Number System - An Introduction

Class 7 - apc understanding computer studies, choose the correct option.

In a decimal number system, the base of a number is represented by

• All of them

Reason — The decimal number system uses 10 digits (from 0 to 9) hence its has a base of 10.

The base of an octal number is represented by:

Reason — The octal number system uses 8 digits (from 0 to 7) hence its has a base of 8.

To convert an octal number to its binary equivalent, each octal digit is expressed as

• 3 bits form

4 bits form

• 8 bits form

Reason — Since the digits from 0 to 7 need a maximum of 3 bits to be represented in binary form hence in Octal to Binary conversion each octal digit is expressed as 3 bits form.

Sixteen raised to the power zero (16⁰) is equivalent to

Reason — Any number raised to the power of 0 is 1.

An octal number system uses the digits from

Reason — The octal number system is a base 8 number system as it uses the digits from 0 to 7.

The base of a hexa-decimal number is represented by

Reason — The hexa-decimal number system uses 16 digits (from 0 to 15) hence its has a base of 16.

In a hexa-decimal number system, 'B' represents the digit

Reason — In hexa-decimal number system, the digits 0 to 15 are represented by the letters A to F.

To express a hexa-decimal number to its binary equivalent, each hexa-decimal digit is expressed as

• 2 bits form

Reason — Since the digits from 0 to 15 need a maximum of 4 bits to be represented in binary form hence in Hexa-decimal to Binary conversion each hexa-decimal digit is expressed as 4 bits form.

The binary equivalent of a hexa-decimal digit 12(C) is represented by

Reason — The hexa-decimal digit 12(C) is represented as 1100.

Question 10

The hexa-decimal equivalent digit of 1011 (4 bits form) is

Reason — The hexa-decimal equivalent digit of 1011 (4 bits form) is 11.

Fill in the blanks

The binary system consists of two digits 0 and 1 .

A decimal number system uses the digits from 0 to 9 .

The base in the decimal number system is written as 10 .

A binary number system is written with 2 as the base.

In a decimal to binary conversion, the first remainder is known as Least Significant Bit (LSB) and the last remainder is Most Significant Bit (MSB) .

Complete the following tables

Case-Study Based Questions

Your teacher has assigned you a task to give a presentation on conversion of octal numbers into binary numbers and vice-versa. You are asked to create some aids to support your presentation. You have created two tables, Table 1 and Table 2, to demonstrate some examples.

In the above tables, some entries have either been missed or incorrect. Answer the following questions based on the above case:

(a) What will be filled in the blank space of Table 1?

(b) Find and rectify the incorrect binary equivalent in Table 1.

(c) Fill the appropriate octal equivalent in the blank space of Table 2.

(d) Find and rectify the incorrect octal equivalent in Table 2.

(b) In Table 1, the binary equivalent of octal number 3 is incorrect. The correct value is 011 .

(d) In Table 2, the octal equivalent of binary number 011 is incorrect. The correct value is 3 .

Convert the following to their binary equivalents

Therefore, (78) 10 = (1001110) 2

Therefore, (99) 10 = (1100011) 2

Therefore, (141) 10 = (10001101) 2

Therefore, (123) 10 = (1111011) 2

Convert the following to their decimal equivalents

Equivalent decimal number = 1 + 4 + 16 = 21

Therefore, (10101) 2 = (21) 10

Equivalent decimal number = 16

Therefore, (10000) 2 = (16) 10

Equivalent decimal number = 1 + 8 + 16 = 25

Therefore, (11001) 2 = (25) 10

Equivalent decimal number = 2 + 8 + 32 = 42

Therefore, (101010) 2 = (42) 10

Convert the following to Decimal numbers

Equivalent decimal number = 8 + 320 = 328

Therefore, (510) 8 = (328) 10

Equivalent decimal number = 12 + 176 + 2560 = 2748

Therefore, (ABC) 16 = (2748) 10

(1001011) 2

Equivalent decimal number = 1 + 2 + 8 + 64 = 75

Therefore, (1001011) 2 = (75) 10

Equivalent decimal number = 7 + 208 + 3072 = 3287

Therefore, (CD7) 16 = (3287) 10

Equivalent decimal number = 1 + 8 + 32 = 41

Therefore, (101001) 2 = (41) 10

(1100111) 2

Equivalent decimal number = 1 + 2 + 4 + 32 + 64 = 103

Therefore, (1100111) 2 = (103) 10

Convert the following to binary numbers

Therefore, (342) 8 = ( 011 undefined   100 undefined   010 undefined \bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{100}}\medspace\bold{\underlinesegment{010}} 011 ​ 100 ​ 010 ​ ) 2

Therefore, (203) 8 = ( 010 undefined   000 undefined   011 undefined \bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{011}} 010 ​ 000 ​ 011 ​ ) 2

Therefore, (9AD) 16 = ( 1001 undefined   1010 undefined   1101 undefined \bold{\underlinesegment{1001}}\medspace\bold{\underlinesegment{1010}}\medspace\bold{\underlinesegment{1101}} 1001 ​ 1010 ​ 1101 ​ ) 2

Therefore, (157) 8 = ( 001 undefined   101 undefined   111 undefined \bold{\underlinesegment{001}}\medspace\bold{\underlinesegment{101}}\medspace\bold{\underlinesegment{111}} 001 ​ 101 ​ 111 ​ ) 2

Therefore, (ABC) 16 = ( 1010 undefined   1011 undefined   1100 undefined \bold{\underlinesegment{1010}}\medspace\bold{\underlinesegment{1011}}\medspace\bold{\underlinesegment{1100}} 1010 ​ 1011 ​ 1100 ​ ) 2

Therefore, (DE) 16 = ( 1101 undefined   1110 undefined \bold{\underlinesegment{1101}}\medspace\bold{\underlinesegment{1110}} 1101 ​ 1110 ​ ) 2

Convert the following to their hexa-decimal equivalent

(110011101111) 2

Grouping in bits of 4:

1100 undefined 1110 undefined 1111 undefined \underlinesegment{1100} \quad \underlinesegment{1110} \quad \underlinesegment{1111} 1100 ​ 1110 ​ 1111 ​

Therefore, (110011101111) 2 = (CEF) 16

(11010111100) 2

0110 undefined 1011 undefined 1100 undefined \underlinesegment{0110} \quad \underlinesegment{1011} \quad \underlinesegment{1100} 0110 ​ 1011 ​ 1100 ​

Therefore, (11010111100) 2 = (6BC) 16

Therefore, (89392) 10 = (15D30) 16

(100101101110) 2

1001 undefined 0110 undefined 1110 undefined \underlinesegment{1001} \quad \underlinesegment{0110} \quad \underlinesegment{1110} 1001 ​ 0110 ​ 1110 ​

Therefore, (100101101110) 2 = (96E) 16

Therefore, (9894) 10 = (26A6) 16

Therefore, (4966) 10 = (1366) 16

Short Answer Questions

What are the different types of number systems that a computer deals with?

The different types of number systems are:

• Binary Number System
• Octal Number System
• Decimal Number System
• Hexadecimal Number System

What is meant by the following terms? Give an example of each.

(a) An octal number (b) A hexa-decimal number

(a) An Octal number — An octal number uses 8 types of digits — 0, 1, 2, 3, 4, 5, 6, 7. It is represented with base 8.

(b) A hexa-decimal number — A Hexa-decimal number uses 16 types of digits (0 to 15). To represent digits from 10 to 15 it uses letters from A to F respectively. It is represented with base 16.

Question 3a

Give two differences between Binary number and Decimal number

Question 3b

Give two differences between Octal number and Binary number

• Math Article

Number System Questions

Number systems questions are provided here with solutions. In Class 9, we will come across the Number System chapter where we learn the basics of different types of numbers and their applications. In number theory , you may have learned about the different classifications of numbers, such as whole and natural numbers, even and odd numbers, etc. Here, we will solve the problems based on rational and irrational numbers. Students can practice the questions and it would be helpful for the students to understand this chapter. Here, we have provided a variety of number system questions and some important questions for practice. Let us learn in brief about each concept covered in this chapter before we solve a question based on it.

Also, read: Number System For Class 9

Number System Questions with Solutions

1. What are the five rational numbers between 1 and 2?

Solution: We need to find 5 rational numbers between 1 and 2

Divide and multiply both the numbers by (5+1)

6/6 and 12/6 are rational numbers now.

Therefore, the required rational numbers between 1 and 2 are:

6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6.

2. Can we locate √3 on the number line?

Solution: Yes, we can locate it.

Follow the steps to locate it: Construct BD of unit length perpendicular to OB

Then using the Pythagoras theorem, we see that OD = √((√2) 2 +1 2 ) = √3

With centre O and radius OD, using a compass, draw an arc that cuts the number line at the point Q.

4. Show that 0.3333…, can be expressed in the form of rational number, i.e. p/q.

Solution: Let x = 0.33333

10 x = 10 × (0.333…) = 3.333…

We can write,

3.3333… = 3 + 0.3333… = 3 + x

10 x = 3 + x

5. Write the following in decimal form and mention what expansion it is.

(i) 36/100 = 0.36

It is terminating.

(ii) 1/11 = 0.09090909…

It is non-terminating and repeating

6. Add 2√2 + 5√3 and √2 – 3√3.

Solution: (2√2 + 5√3) + (√2 – 3√3)

= (2+1)√2+(5-3)√3

7. Multiply 6√2 by 2√2.

Solution: 6√2 x 2√2

6 x 2 x √2 x √2

8. Rationalise the denominator of 1/√3

Solution: To rationalise the denominator of 1/√3, we need to multiply the numerator and denominator by √3

1/√3 x (√3/√3) = √3/3

9. Rationalise the denominator of √2/(√3-√5).

Solution: Multiply both numerator and denominator by √3+√5

Numerator = √2(√3+√5)

Denominator = (√3-√5)(√3+√5) = (√3) 2 -(√5) 2 = 3-5 = -2

= [-√2(√3+√5)]/2

10. Simplify:

(i) 2 1/3 .2 2/3

(ii) (3 1/5 ) 4

(iii) 7 1/3 /7 1/5

(iv) 13 1/7 .17 1/7

(iii) (7 1/3 )/(7 1/5 )

= 7 ( 1/3)-(1/5)

= (13.17) 1/7

Video Lesson

Number system and factorisation.

Number System Questions for Practice

• If (p ×q) = 6p-4q+3pq, then find the value of [(6×3)+(4×3)]
• Find out which of the following numbers are prime numbers, given that “p” is a prime number.

(a) 2p  (b)p 2 (c)3p (d) p-2 (e) p-3

• Write down the five rational numbers between 6/5 and 7/5
• Express the decimal number 1.2343 in the form of a rational number (i.e p/q form)
• Simplify the expression (2 2 -3)x. (4+2 2 )

Frequently Asked Question on the Number System Questions

What is meant by number system.

In mathematics, a number system is defined as the way of expressing numbers. The number system provides a distinct way of expressing different types of numbers and it also provides the algebraic structure of the mathematical problem.

What are the different types of numbers?

The different types of numbers are: Natural Numbers Whole numbers Real Numbers Rational Numbers Irrational numbers Complex numbers

Why do we use numbers?

The numbers are used to count the surrounding thing. Numbers are used for expressing money, time, date, and so on. Without numbers, we could not be able to understand the value of many things

What are the four different types of number systems?

The four major types of number system are: Binary number system (base 2 number system) Octal number system (base 8 number system) Decimal number system (base 10 number system) Hexadecimal number system (base 16 number system)

What are the applications of the number system?

The most common application of the number system is found in computer technology. It uses the binary number system. The base 2 number system is used in the process of digital encoding

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Class 9 Maths Case Study Questions of Chapter 1 Real Numbers

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Case study Questions in Class 9 Mathematics Chapter 1  are very important to solve for your exam. Class 9 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 1 Real Numbers

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

1. What will be the value of x?

Answer: b) 13915

2. What will be the value of y?

Answer: c) 11

3. What will be the value of z?

Answer: b) 23

4. According to the Fundamental Theorem of Arithmetic 13915 is a

a) Composite number

b) Prime number

c) Neither prime nor composite

d) Even number

Answer: a) Composite number

5. The prime factorization of 13915 is

a) 5 × 11 3  × 13 2

b) 5 × 11 3  × 23 2

c) 5 × 11 2  × 23

d) 5 × 11 2  × 13 2

Answer: c) 5 × 112 × 23

Case Study 2: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (d) no value of n

Answer: (d) no value of n3

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, an is a rational number?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

Answer: (c) for all n > 1

(iii) If x and y are two odd positive integers, then which of the following is true?

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2   is odd (d) both (a) and (b)

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

(a) always true (b) always false (c) sometimes true (d) None of these

Answer:(a) always true

(v) If n is any odd integer, then n 2 – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

Answer: (d) 8

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Real Numbers Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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CBSE MCQ for Class 9 Maths Chapter 1 Number System Free PDF

Guys, we are working very hard to provide you with TOPIC-WISE MCQs (as listed below). Till then, attached below is the Master PDF having all the topics. Hope you understand. Enjoy your preparation! All the Best! 

CBSE MCQ for Class 9 Maths Chapter 1 Number System PDF

The CBSE MCQ for Class 9 Maths Chapter 1 Number System are provided above, in detailed and free to download PDF format. The solutions are latest , comprehensive , confidence inspiring , with easy to understand explanation . To download NCERT Class 9 Solutions PDF for Free, just click ‘ Download pdf ’.

Other MCQ Questions for Maths Class 9th CBSE

• CBSE MCQ for Class 9 Maths Chapter 2 Polynomials
• CBSE MCQ for Class 9 Maths: Chapter 3 Coordinate Geometry
• CBSE MCQ for Class 9 Maths: Chapter 4 Linear Equations in Two Variables
• CBSE MCQ for Class 9 Maths Chapter 5 Euclid’s Geometry

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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Case Study Questions for Class 9 Maths Chapter 1 Real Numbers

• Last modified on: 1 year ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

Himanshu has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a is a rational number?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

(iii) If x and y are two odd positive integers, then which of the following is true?

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2  is odd (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

(a) always true (b) always false (c) sometimes true (d) None of these

(v) If n is any odd integer, then n 2  – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

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Private: Learning Math: Number and Operations

Professional Development > Private: Learning Math: Number and Operations > 11. Classroom Case Studies, 3-5

Mathematics

K-2 , 3-5 , 6-8

Classroom Case Studies, 3-5

Watch this program in the 10th session for grade 3-5 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 3-5 teachers (former course participants) who have adapted their new knowledge to their classrooms.

As in other sessions, you will be prompted to view short video segments throughout the session; you may also choose to watch the full-length video for this session. See  Note 1 below.

LEARNING OBJECTIVES In this session, you will do the following: • Explore the development of number and operations concepts at your grade level • Examine students understanding of number and operations concepts • Explore how you would teach problems involving different number and operations concepts

Note 1 This session uses classroom case studies to examine how students in grades 3-5 think about and work with number and operations. If possible, work on this session with another teacher or a group of teachers. Using your own classroom and the classrooms of fellow teachers as case studies will allow you to make additional observations.

Previously Introduced

even numbers

Even numbers are integers divisible by 2. Any number that ends with the digit 0, 2, 4, 6, or 8 is an even number.

A factor of a number is a counting number that divides evenly into that number. For example, 3 is a factor of 15, since 3 divides evenly into 15 (five times). Four is not a factor of 15, but it is a factor of 16.

prime number

A counting number is a prime number if it has exactly two factors: 1 and the number itself. For example, 17 is prime, 16 is not prime, and 1 itself is not prime, since it has only one factor. New in This Session

cubic number

A cubic number is obtained as a result of multiplying a number by itself three times. For example, 1 (i.e., 1 3 or 1 • 1 • 1), 8 (i.e., 2 3 or 2 • 2 • 2), 27 (i.e., 3 3 or 3 • 3 • 3), 64 (i.e., 4 3 or 4 • 4 • 4), and so on, are cubic numbers. Cubic numbers of dots can be arranged to make a cube.

square number

A square number is obtained by multiplying a number by itself (e.g., 1, 4, 9, 25, …).

triangular number

A triangular number is a number obtained as the sum of consecutive integers. For example, 1 (i.e., 0 + 1), 3 (i.e., 1 + 2), 6 (i.e., 1 + 2 + 3), 10 (i.e., 1 + 2 + 3 + 4), and so on are triangular numbers.

Series Directory

• 1 Part A: A Simpler Number System (70 minutes)
• 2 Part B: Comparing Number Systems (15 minutes)
• 3 Part C: Building the Number Line (35 minutes)
• 1 Part A: Number Sets (35 minutes)
• 2 Part B: The Size of Infinity (35 minutes)
• 3 Part C: Examining Zero (50 minutes)
• 1 Part A: Base Two Numbers (45 minutes)
• 2 Part B: Exponents and Logarithms (35 minutes)
• 3 Part C: Place-Value Representation in Base Ten and Base Four (40 minutes)
• 1 Part A: Meanings and Relationships of the Operations (40 minutes)
• 2 Part B: Area Models for Multiplication and Division (45 minutes)
• 3 Part C: Colored-Chip Models (35 minutes)
• 1 Part A: Alpha Math (35 minutes)
• 2 Part B: Divisibility Test (50 minutes)
• 3 Part C: Factors (35 minutes)
• 1 Part A: Models for Multiples and Factors (75 minutes)
• 2 Part B: Looking for Prime Numbers (45 minutes)
• 1 Part A: Fractions to Decimals (65 minutes)
• 2 Part B: Decimals to Fractions (30 minutes)
• 3 Part C: Ordering Fractions (25 minutes)
• 1 Part A: Interpreting Fractions, Units, and Unitizing (45 minutes)
• 2 Part B: Fractions With Cuisenaire Rods (45 minutes)
• 3 Part C: Absolute and Relative Reasoning (30 minutes)
• 4 Session 8: Homework
• 1 Part A: Models for the Multiplication and Division of Fractions (45 minutes)
• 2 Part B: Decimals and Percents (45 minutes)
• 3 Part C: Fibonacci Numbers (30 minutes)
• 1 Part A: Observing a Case Study (25 minutes)
• 2 Part B: Reasoning About Number and Operations (40 minutes)
• 3 Part C: Problems That Illustrate Reasoning About Number and Operations (55 minutes)
• 2 Part B: Reasoning About Number and Operations (40 minutes) – Exploring Standards
• 3 Part B (continued): Reasoning About Number and Operations – Examining Students’ Reasoning
• 4 Part C: Problems That Illustrate Reasoning About Number and Operations (55 minutes)
• 5 Homework – Grades 6-8
• Closed Captioning
• ISBN: 1-57680-678-2

11.1 Part A: Observing a Case Study (25 minutes)

11.2 part b: reasoning about number and operations (40 minutes), 11.3 part c: problems that illustrate reasoning about number and operations (55 minutes), 11.4 homework, session 1 what is a number system.

Understand the nature of the real number system, the elements and operations that make up the system, and some of the rules that govern the operations. Examine a finite number system that follows some (but not all) of the same rules, and then compare this system to the real number system. Use a number line to classify the numbers we use, and examine how the numbers and operations relate to one another.

Session 2 Number Sets, Infinity, and Zero

Continue examining the number line and the relationships among sets of numbers that make up the real number system. Explore which operations and properties hold true for each of the sets. Consider the magnitude of these infinite sets and discover that infinity comes in more than one size. Examine place value and the significance of zero in a place value system.

Session 3 Place Value

Look at place value systems based on numbers other than 10. Examine the base two numbers and learn uses for base two numbers in computers. Explore exponents and relate them to logarithms. Examine the use of scientific notation to represent numbers with very large or very small magnitude. Interpret whole numbers, common fractions, and decimals in base four.

Session 4 Meanings and Models for Operations

Examine the operations of addition, subtraction, multiplication, and division and their relationships to whole numbers. Work with area models for multiplication and division. Explore the use of two-color chips to model operations with positive and negative numbers.

Session 5 Divisibility Tests and Factors

Explore number theory topics. Analyze Alpha math problems and discuss how they help with the conceptual understanding of operations. Examine various divisibility tests to see how and why they work. Begin examining factors and multiples.

Session 6 Number Theory

Examine visual methods for finding least common multiples and greatest common factors, including Venn diagram models and area models. Explore prime numbers. Learn to locate prime numbers on a number grid and to determine whether very large numbers are prime.

Session 7 Fractions and Decimals

Extend your understanding of fractions and decimals. Examine terminating and non-terminating decimals. Explore ways to predict the number of decimal places in a terminating decimal and the period of a non-terminating decimal. Examine which fractions terminate and which repeat as decimals, and why all rational numbers must fall into one of these categories. Explore methods to convert decimals to fractions and vice versa. Use benchmarks and intuitive methods to order fractions.

Session 8 Rational Numbers and Proportional Reasoning

Begin examining rational numbers. Explore a model for computations with fractions. Analyze proportional reasoning and the difference between absolute and relative thinking. Explore ways to represent proportional relationships and the resulting operations with ratios. Examine how ratios can represent either part-part or part-whole comparisons, depending on how you define the unit, and explore how this affects their behavior in computations.

Session 9 Fractions, Percents, and Ratios

Continue exploring rational numbers, working with an area model for multiplication and division with fractions, and examining operations with decimals. Explore percents and the relationships among representations using fractions, decimals, and percents. Examine benchmarks for understanding percents, especially percents less than 10 and greater than 100. Consider ways to use an elastic model, an area model, and other models to discuss percents. Explore some ratios that occur in nature.

Session 10 Classroom Case Studies, K-2

Watch this program in the 10th session for K-2 teachers. Explore how the concepts developed in this course can be applied through case studies of K-2 teachers (former course participants) who have adapted their new knowledge to their classrooms.

Session 11 Classroom Case Studies, 3-5

Session 12 classroom case studies, 6-8.

Watch this program in the 10th session for grade 6-8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6-8 teachers (former course participants) who have adapted their new knowledge to their classrooms.

Join us for conversations that inspire, recognize, and encourage innovation and best practices in the education profession.

Available on Apple Podcasts, Spotify, Google Podcasts, and more.

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What the data says about gun deaths in the U.S.

More Americans died of gun-related injuries in 2021 than in any other year on record, according to the latest available statistics from the Centers for Disease Control and Prevention (CDC). That included record numbers of both gun murders and gun suicides. Despite the increase in such fatalities, the rate of gun deaths – a statistic that accounts for the nation’s growing population – remained below the levels of earlier decades.

Here’s a closer look at gun deaths in the United States, based on a Pew Research Center analysis of data from the CDC, the FBI and other sources. You can also read key public opinion findings about U.S. gun violence and gun policy .

This Pew Research Center analysis examines the changing number and rate of gun deaths in the United States. It is based primarily on data from the Centers for Disease Control and Prevention (CDC) and the Federal Bureau of Investigation (FBI). The CDC’s statistics are based on information contained in official death certificates, while the FBI’s figures are based on information voluntarily submitted by thousands of police departments around the country.

For the number and rate of gun deaths over time, we relied on mortality statistics in the CDC’s WONDER database covering four distinct time periods:  1968 to 1978 ,  1979 to 1998 ,  1999 to 2020 , and 2021 . While these statistics are mostly comparable for the full 1968-2021 period, gun murders and suicides between 1968 and 1978 are classified by the CDC as involving firearms  and  explosives; those between 1979 and 2021 are classified as involving firearms only. Similarly, gun deaths involving law enforcement between 1968 and 1978 exclude those caused by “operations of war”; those between 1979 and 2021 include that category, which refers to gun deaths among military personnel or civilians  due to war or civil insurrection in the U.S . All CDC gun death estimates in this analysis are adjusted to account for age differences over time and across states.

The FBI’s statistics about the types of firearms used in gun murders in 2020 come from the bureau’s  Crime Data Explorer website . Specifically, they are drawn from the expanded homicide tables of the agency’s  2020 Crime in the United States report . The FBI’s statistics include murders and non-negligent manslaughters involving firearms.

How many people die from gun-related injuries in the U.S. each year?

In 2021, the most recent year for which complete data is available, 48,830 people died from gun-related injuries in the U.S., according to the CDC. That figure includes gun murders and gun suicides, along with three less common types of gun-related deaths tracked by the CDC: those that were accidental, those that involved law enforcement and those whose circumstances could not be determined. The total excludes deaths in which gunshot injuries played a contributing, but not principal, role. (CDC fatality statistics are based on information contained in official death certificates, which identify a single cause of death.)

What share of U.S. gun deaths are murders and what share are suicides?

Though they tend to get less public attention than gun-related murders, suicides have long accounted for the majority of U.S. gun deaths . In 2021, 54% of all gun-related deaths in the U.S. were suicides (26,328), while 43% were murders (20,958), according to the CDC. The remaining gun deaths that year were accidental (549), involved law enforcement (537) or had undetermined circumstances (458).

What share of all murders and suicides in the U.S. involve a gun?

About eight-in-ten U.S. murders in 2021 – 20,958 out of 26,031, or 81% – involved a firearm. That marked the highest percentage since at least 1968, the earliest year for which the CDC has online records. More than half of all suicides in 2021 – 26,328 out of 48,183, or 55% – also involved a gun, the highest percentage since 2001.

How has the number of U.S. gun deaths changed over time?

The record 48,830 total gun deaths in 2021 reflect a 23% increase since 2019, before the onset of the coronavirus pandemic .

Gun murders, in particular, have climbed sharply during the pandemic, increasing 45% between 2019 and 2021, while the number of gun suicides rose 10% during that span.

The overall increase in U.S. gun deaths since the beginning of the pandemic includes an especially stark rise in such fatalities among children and teens under the age of 18. Gun deaths among children and teens rose 50% in just two years , from 1,732 in 2019 to 2,590 in 2021.

How has the rate of U.S. gun deaths changed over time?

While 2021 saw the highest total number of gun deaths in the U.S., this statistic does not take into account the nation’s growing population. On a per capita basis, there were 14.6 gun deaths per 100,000 people in 2021 – the highest rate since the early 1990s, but still well below the peak of 16.3 gun deaths per 100,000 people in 1974.

The gun murder rate in the U.S. remains below its peak level despite rising sharply during the pandemic. There were 6.7 gun murders per 100,000 people in 2021, below the 7.2 recorded in 1974.

The gun suicide rate, on the other hand, is now on par with its historical peak. There were 7.5 gun suicides per 100,000 people in 2021, statistically similar to the 7.7 measured in 1977. (One caveat when considering the 1970s figures: In the CDC’s database, gun murders and gun suicides between 1968 and 1978 are classified as those caused by firearms and explosives. In subsequent years, they are classified as deaths involving firearms only.)

Which states have the highest and lowest gun death rates in the U.S.?

The rate of gun fatalities varies widely from state to state. In 2021, the states with the highest total rates of gun-related deaths – counting murders, suicides and all other categories tracked by the CDC – included Mississippi (33.9 per 100,000 people), Louisiana (29.1), New Mexico (27.8), Alabama (26.4) and Wyoming (26.1). The states with the lowest total rates included Massachusetts (3.4), Hawaii (4.8), New Jersey (5.2), New York (5.4) and Rhode Island (5.6).

The results are somewhat different when looking at gun murder and gun suicide rates separately. The places with the highest gun murder rates in 2021 included the District of Columbia (22.3 per 100,000 people), Mississippi (21.2), Louisiana (18.4), Alabama (13.9) and New Mexico (11.7). Those with the lowest gun murder rates included Massachusetts (1.5), Idaho (1.5), Hawaii (1.6), Utah (2.1) and Iowa (2.2). Rate estimates are not available for Maine, New Hampshire, Vermont or Wyoming.

The states with the highest gun suicide rates in 2021 included Wyoming (22.8 per 100,000 people), Montana (21.1), Alaska (19.9), New Mexico (13.9) and Oklahoma (13.7). The states with the lowest gun suicide rates were Massachusetts (1.7), New Jersey (1.9), New York (2.0), Hawaii (2.8) and Connecticut (2.9). Rate estimates are not available for the District of Columbia.

How does the gun death rate in the U.S. compare with other countries?

The gun death rate in the U.S. is much higher than in most other nations, particularly developed nations. But it is still far below the rates in several Latin American countries, according to a 2018 study of 195 countries and territories by researchers at the Institute for Health Metrics and Evaluation at the University of Washington.

The U.S. gun death rate was 10.6 per 100,000 people in 2016, the most recent year in the study, which used a somewhat different methodology from the CDC. That was far higher than in countries such as Canada (2.1 per 100,000) and Australia (1.0), as well as European nations such as France (2.7), Germany (0.9) and Spain (0.6). But the rate in the U.S. was much lower than in El Salvador (39.2 per 100,000 people), Venezuela (38.7), Guatemala (32.3), Colombia (25.9) and Honduras (22.5), the study found. Overall, the U.S. ranked 20th in its gun fatality rate that year .

How many people are killed in mass shootings in the U.S. every year?

This is a difficult question to answer because there is no single, agreed-upon definition of the term “mass shooting.” Definitions can vary depending on factors including the number of victims and the circumstances of the shooting.

The FBI collects data on “active shooter incidents,” which it defines as “one or more individuals actively engaged in killing or attempting to kill people in a populated area.” Using the FBI’s definition, 103 people – excluding the shooters – died in such incidents in 2021 .

The Gun Violence Archive, an online database of gun violence incidents in the U.S., defines mass shootings as incidents in which four or more people are shot, even if no one was killed (again excluding the shooters). Using this definition, 706 people died in these incidents in 2021 .

Regardless of the definition being used, fatalities in mass shooting incidents in the U.S. account for a small fraction of all gun murders that occur nationwide each year.

How has the number of mass shootings in the U.S. changed over time?

The same definitional issue that makes it challenging to calculate mass shooting fatalities comes into play when trying to determine the frequency of U.S. mass shootings over time. The unpredictability of these incidents also complicates matters: As Rand Corp. noted in a research brief , “Chance variability in the annual number of mass shooting incidents makes it challenging to discern a clear trend, and trend estimates will be sensitive to outliers and to the time frame chosen for analysis.”

The FBI found an increase in active shooter incidents between 2000 and 2021. There were three such incidents in 2000. By 2021, that figure had increased to 61.

Which types of firearms are most commonly used in gun murders in the U.S.?

In 2020, the most recent year for which the FBI has published data, handguns were involved in 59% of the 13,620 U.S. gun murders and non-negligent manslaughters for which data is available. Rifles – the category that includes guns sometimes referred to as “assault weapons” – were involved in 3% of firearm murders. Shotguns were involved in 1%. The remainder of gun homicides and non-negligent manslaughters (36%) involved other kinds of firearms or those classified as “type not stated.”

It’s important to note that the FBI’s statistics do not capture the details on all gun murders in the U.S. each year. The FBI’s data is based on information voluntarily submitted by police departments around the country, and not all agencies participate or provide complete information each year.

Note: This is an update of a post originally published on Aug. 16, 2019.

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What is cloud computing?

With cloud computing, organizations essentially buy a range of services offered by cloud service providers (CSPs). The CSP’s servers host all the client’s applications. Organizations can enhance their computing power more quickly and cheaply via the cloud than by purchasing, installing, and maintaining their own servers.

The cloud-computing model is helping organizations to scale new digital solutions with greater speed and agility—and to create value more quickly. Developers use cloud services to build and run custom applications and to maintain infrastructure and networks for companies of virtually all sizes—especially large global ones. CSPs offer services, such as analytics, to handle and manipulate vast amounts of data. Time to market accelerates, speeding innovation to deliver better products and services across the world.

What are examples of cloud computing’s uses?

Get to know and directly engage with senior mckinsey experts on cloud computing.

Brant Carson is a senior partner in McKinsey’s Vancouver office; Chandra Gnanasambandam and Anand Swaminathan are senior partners in the Bay Area office; William Forrest is a senior partner in the Chicago office; Leandro Santos is a senior partner in the Atlanta office; Kate Smaje is a senior partner in the London office.

Cloud computing came on the scene well before the global pandemic hit, in 2020, but the ensuing digital dash  helped demonstrate its power and utility. Here are some examples of how businesses and other organizations employ the cloud:

• A fast-casual restaurant chain’s online orders multiplied exponentially during the 2020 pandemic lockdowns, climbing to 400,000 a day, from 50,000. One pleasant surprise? The company’s online-ordering system could handle the volume—because it had already migrated to the cloud . Thanks to this success, the organization’s leadership decided to accelerate its five-year migration plan to less than one year.
• A biotech company harnessed cloud computing to deliver the first clinical batch of a COVID-19 vaccine candidate for Phase I trials in just 42 days—thanks in part to breakthrough innovations using scalable cloud data storage and computing  to facilitate processes ensuring the drug’s safety and efficacy.
• Banks use the cloud for several aspects of customer-service management. They automate transaction calls using voice recognition algorithms and cognitive agents (AI-based online self-service assistants directing customers to helpful information or to a human representative when necessary). In fraud and debt analytics, cloud solutions enhance the predictive power of traditional early-warning systems. To reduce churn, they encourage customer loyalty through holistic retention programs managed entirely in the cloud.
• Automakers are also along for the cloud ride . One company uses a common cloud platform that serves 124 plants, 500 warehouses, and 1,500 suppliers to consolidate real-time data from machines and systems and to track logistics and offer insights on shop floor processes. Use of the cloud could shave 30 percent off factory costs by 2025—and spark innovation at the same time.

That’s not to mention experiences we all take for granted: using apps on a smartphone, streaming shows and movies, participating in videoconferences. All of these things can happen in the cloud.

Learn more about our Cloud by McKinsey , Digital McKinsey , and Technology, Media, & Telecommunications  practices.

How has cloud computing evolved?

Going back a few years, legacy infrastructure dominated IT-hosting budgets. Enterprises planned to move a mere 45 percent of their IT-hosting expenditures to the cloud by 2021. Enter COVID-19, and 65 percent of the decision makers surveyed by McKinsey increased their cloud budgets . An additional 55 percent ended up moving more workloads than initially planned. Having witnessed the cloud’s benefits firsthand, 40 percent of companies expect to pick up the pace of implementation.

The cloud revolution has actually been going on for years—more than 20, if you think the takeoff point was the founding of Salesforce, widely seen as the first software as a service (SaaS) company. Today, the next generation of cloud, including capabilities such as serverless computing, makes it easier for software developers to tweak software functions independently, accelerating the pace of release, and to do so more efficiently. Businesses can therefore serve customers and launch products in a more agile fashion. And the cloud continues to evolve.

Introducing McKinsey Explainers : Direct answers to complex questions

Cost savings are commonly seen as the primary reason for moving to the cloud but managing those costs requires a different and more dynamic approach focused on OpEx rather than CapEx. Financial-operations (or FinOps) capabilities  can indeed enable the continuous management and optimization of cloud costs . But CSPs have developed their offerings so that the cloud’s greatest value opportunity is primarily through business innovation and optimization. In 2020, the top-three CSPs reached $100 billion  in combined revenues—a minor share of the global $2.4 trillion market for enterprise IT services—leaving huge value to be captured. To go beyond merely realizing cost savings, companies must activate three symbiotic rings of cloud value creation : strategy and management, business domain adoption, and foundational capabilities.

What’s the main reason to move to the cloud?

The pandemic demonstrated that the digital transformation can no longer be delayed—and can happen much more quickly than previously imagined. Nothing is more critical to a corporate digital transformation than becoming a cloud-first business. The benefits are faster time to market, simplified innovation and scalability, and reduced risk when effectively managed. The cloud lets companies provide customers with novel digital experiences—in days, not months—and delivers analytics absent on legacy platforms. But to transition to a cloud-first operating model, organizations must make a collective effort that starts at the top. Here are three actions CEOs can take to increase the value their companies get from cloud computing :

• Establish a sustainable funding model.
• Develop a new business technology operating model.
• Set up policies to attract and retain the right engineering talent.

How much value will the cloud create?

Fortune 500 companies adopting the cloud could realize more than $1 trillion in value  by 2030, and not from IT cost reductions alone, according to McKinsey’s analysis of 700 use cases.

For example, the cloud speeds up design, build, and ramp-up, shortening time to market when companies have strong DevOps (the combination of development and operations) processes in place; groups of software developers customize and deploy software for operations that support the business. The cloud’s global infrastructure lets companies scale products almost instantly to reach new customers, geographies, and channels. Finally, digital-first companies use the cloud to adopt emerging technologies and innovate aggressively, using digital capabilities as a competitive differentiator to launch and build businesses .

If companies pursue the cloud’s vast potential in the right ways, they will realize huge value. Companies across diverse industries have implemented the public cloud and seen promising results. The successful ones defined a value-oriented strategy across IT and the business, acquired hands-on experience operating in the cloud, adopted a technology-first approach, and developed a cloud-literate workforce.

Learn more about our Cloud by McKinsey and Digital McKinsey practices.

What is the cloud cost/procurement model?

Some cloud services, such as server space, are leased. Leasing requires much less capital up front than buying, offers greater flexibility to switch and expand the use of services, cuts the basic cost of buying hardware and software upfront, and reduces the difficulties of upkeep and ownership. Organizations pay only for the infrastructure and computing services that meet their evolving needs. But an outsourcing model  is more apt than other analogies: the computing business issues of cloud customers are addressed by third-party providers that deliver innovative computing services on demand to a wide variety of customers, adapt those services to fit specific needs, and work to constantly improve the offering.

What are cloud risks?

The cloud offers huge cost savings and potential for innovation. However, when companies migrate to the cloud, the simple lift-and-shift approach doesn’t reduce costs, so companies must remediate their existing applications to take advantage of cloud services.

For instance, a major financial-services organization  wanted to move more than 50 percent of its applications to the public cloud within five years. Its goals were to improve resiliency, time to market, and productivity. But not all its business units needed to transition at the same pace. The IT leadership therefore defined varying adoption archetypes to meet each unit’s technical, risk, and operating-model needs.

Legacy cybersecurity architectures and operating models can also pose problems when companies shift to the cloud. The resulting problems, however, involve misconfigurations rather than inherent cloud security vulnerabilities. One powerful solution? Securing cloud workloads for speed and agility : automated security architectures and processes enable workloads to be processed at a much faster tempo.

What kind of cloud talent is needed?

The talent demands of the cloud differ from those of legacy IT. While cloud computing can improve the productivity of your technology, it requires specialized and sometimes hard-to-find talent—including full-stack developers, data engineers, cloud-security engineers, identity- and access-management specialists, and cloud engineers. The cloud talent model  should thus be revisited as you move forward.

Six practical actions can help your organization build the cloud talent you need :

• Find engineering talent with broad experience and skills.
• Balance talent maturity levels and the composition of teams.
• Build an extensive and mandatory upskilling program focused on need.
• Build an engineering culture that optimizes the developer experience.
• Consider using partners to accelerate development and assign your best cloud leaders as owners.
• Retain top talent by focusing on what motivates them.

How do different industries use the cloud?

Different industries are expected to see dramatically different benefits from the cloud. High-tech, retail, and healthcare organizations occupy the top end of the value capture continuum. Electronics and semiconductors, consumer-packaged-goods, and media companies make up the middle. Materials, chemicals, and infrastructure organizations cluster at the lower end.

Nevertheless, myriad use cases provide opportunities to unlock value across industries , as the following examples show:

• a retailer enhancing omnichannel  fulfillment, using AI to optimize inventory across channels and to provide a seamless customer experience
• a healthcare organization implementing remote heath monitoring to conduct virtual trials and improve adherence
• a high-tech company using chatbots to provide premier-level support combining phone, email, and chat
• an oil and gas company employing automated forecasting to automate supply-and-demand modeling and reduce the need for manual analysis
• a financial-services organization implementing customer call optimization using real-time voice recognition algorithms to direct customers in distress to experienced representatives for retention offers
• a financial-services provider moving applications in customer-facing business domains to the public cloud to penetrate promising markets more quickly and at minimal cost
• a health insurance carrier accelerating the capture of billions of dollars in new revenues by moving systems to the cloud to interact with providers through easier onboarding

The cloud is evolving  to meet the industry-specific needs of companies. From 2021 to 2024, public-cloud spending on vertical applications (such as warehouse management in retailing and enterprise risk management in banking) is expected to grow by more than 40 percent annually. Spending on horizontal workloads (such as customer relationship management) is expected to grow by 25 percent. Healthcare and manufacturing organizations, for instance, plan to spend around twice as much on vertical applications as on horizontal ones.

Learn more about our Cloud by McKinsey , Digital McKinsey , Financial Services , Healthcare Systems & Services , Retail , and Technology, Media, & Telecommunications  practices.

What are the biggest cloud myths?

Views on cloud computing can be clouded by misconceptions. Here are seven common myths about the cloud —all of which can be debunked:

• The cloud’s value lies primarily in reducing costs.
• Cloud computing costs more than in-house computing.
• On-premises data centers are more secure than the cloud.
• Applications run more slowly in the cloud.
• The cloud eliminates the need for infrastructure.
• The best way to move to the cloud is to focus on applications or data centers.
• You must lift and shift applications as-is or totally refactor them.

How large must my organization be to benefit from the cloud?

Here’s one more huge misconception: the cloud is just for big multinational companies. In fact, cloud can help make small local companies become multinational. A company’s benefits from implementing the cloud are not constrained by its size. In fact, the cloud shifts barrier to entry skill rather than scale, making it possible for a company of any size to compete if it has people with the right skills. With cloud, highly skilled small companies can take on established competitors. To realize the cloud’s immense potential value fully, organizations must take a thoughtful approach, with IT and the businesses working together.

For more in-depth exploration of these topics, see McKinsey’s Cloud Insights collection. Learn more about Cloud by McKinsey —and check out cloud-related job opportunities if you’re interested in working at McKinsey.

Articles referenced include:

• “ Six practical actions for building the cloud talent you need ,” January 19, 2022, Brant Carson , Dorian Gärtner , Keerthi Iyengar, Anand Swaminathan , and Wayne Vest
• “ Cloud-migration opportunity: Business value grows, but missteps abound ,” October 12, 2021, Tara Balakrishnan, Chandra Gnanasambandam , Leandro Santos , and Bhargs Srivathsan
• “ Cloud’s trillion-dollar prize is up for grabs ,” February 26, 2021, Will Forrest , Mark Gu, James Kaplan , Michael Liebow, Raghav Sharma, Kate Smaje , and Steve Van Kuiken
• “ Unlocking value: Four lessons in cloud sourcing and consumption ,” November 2, 2020, Abhi Bhatnagar , Will Forrest , Naufal Khan , and Abdallah Salami
• “ Three actions CEOs can take to get value from cloud computing ,” July 21, 2020, Chhavi Arora , Tanguy Catlin , Will Forrest , James Kaplan , and Lars Vinter

Want to know more about cloud computing?

Related articles.

Cloud’s trillion-dollar prize is up for grabs

The cloud transformation engine

Cloud cost-optimization simulator

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Long COVID or Post-COVID Conditions

Some people who have been infected with the virus that causes COVID-19 can experience long-term effects from their infection, known as Long COVID or Post-COVID Conditions (PCC). Long COVID is broadly defined as signs, symptoms, and conditions that continue or develop after acute COVID-19 infection. This definition  of Long COVID was developed by the Department of Health and Human Services (HHS) in collaboration with CDC and other partners.

People call Long COVID by many names, including Post-COVID Conditions, long-haul COVID, post-acute COVID-19, long-term effects of COVID, and chronic COVID. The term post-acute sequelae of SARS CoV-2 infection (PASC) is also used to refer to a subset of Long COVID.

What You Need to Know

• Long COVID is a real illness and can result in chronic conditions that require comprehensive care. There are resources available .
• Long COVID can include a wide range of ongoing health problems; these conditions can last weeks, months, or years.
• Long COVID occurs more often in people who had severe COVID-19 illness, but anyone who has been infected with the virus that causes COVID-19 can experience it.
• People who are not vaccinated against COVID-19 and become infected may have a higher risk of developing Long COVID compared to people who have been vaccinated.
• People can be reinfected with SARS-CoV-2, the virus that causes COVID-19, multiple times. Each time a person is infected or reinfected with SARS-CoV-2, they have a risk of developing Long COVID.
• While most people with Long COVID have evidence of infection or COVID-19 illness, in some cases, a person with Long COVID may not have tested positive for the virus or known they were infected.
• CDC and partners are working to understand more about who experiences Long COVID and why, including whether groups disproportionately impacted by COVID-19 are at higher risk.

In July 2021, Long COVID was added as a recognized condition that could result in a disability under the Americans with Disabilities Act (ADA). Learn more: Guidance on “Long COVID” as a Disability Under the ADA .

About Long COVID

Long COVID is a wide range of new, returning, or ongoing health problems that people experience after being infected with the virus that causes COVID-19. Most people with COVID-19 get better within a few days to a few weeks after infection, so at least 4 weeks after infection is the start of when Long COVID could first be identified. Anyone who was infected can experience Long COVID. Most people with Long COVID experienced symptoms days after first learning they had COVID-19, but some people who later experienced Long COVID did not know when they got infected.

There is no test that determines if your symptoms or condition is due to COVID-19. Long COVID is not one illness. Your healthcare provider considers a diagnosis of Long COVID based on your health history, including if you had a diagnosis of COVID-19 either by a positive test or by symptoms or exposure, as well as based on a health examination.

Science behind Long COVID

RECOVER: Researching COVID to Enhance Recovery

People with Long COVID may experience many symptoms.

People with Long COVID can have a wide range of symptoms that can last weeks, months, or even years after infection. Sometimes the symptoms can even go away and come back again. For some people, Long COVID can last weeks, months, or years after COVID-19 illness and can sometimes result in disability.

Long COVID may not affect everyone the same way. People with Long COVID may experience health problems from different types and combinations of symptoms that may emerge, persist, resolve, and reemerge over different lengths of time. Though most patients’ symptoms slowly improve with time, speaking with your healthcare provider about the symptoms you are experiencing after having COVID-19 could help determine if you might have Long COVID.

People who experience Long COVID most commonly report:

General symptoms ( Not a Comprehensive List)

• Tiredness or fatigue that interferes with daily life
• Symptoms that get worse after physical or mental effort (also known as “ post-exertional malaise ”)

Respiratory and heart symptoms

• Difficulty breathing or shortness of breath
• Fast-beating or pounding heart (also known as heart palpitations)

Neurological symptoms

• Difficulty thinking or concentrating (sometimes referred to as “brain fog”)
• Sleep problems
• Dizziness when you stand up (lightheadedness)
• Pins-and-needles feelings
• Change in smell or taste
• Depression or anxiety

Digestive symptoms

• Stomach pain

Other symptoms

• Joint or muscle pain
• Changes in menstrual cycles

Symptoms that are hard to explain and manage

Some people with Long COVID have symptoms that are not explained by tests or easy to manage.

People with Long COVID may develop or continue to have symptoms that are hard to explain and manage. Clinical evaluations and results of routine blood tests, chest X-rays, and electrocardiograms may be normal. The symptoms are similar to those reported by people with myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) and other poorly understood chronic illnesses that may occur after other infections. People with these unexplained symptoms may be misunderstood by their healthcare providers, which can result in a delay in diagnosis and receiving the appropriate care or treatment.

Review these tips to help prepare for a healthcare provider appointment for Long COVID.

Health conditions

Some people experience new health conditions after COVID-19 illness.

Some people, especially those who had severe COVID-19, experience multiorgan effects or autoimmune conditions with symptoms lasting weeks, months, or even years after COVID-19 illness. Multi-organ effects can involve many body systems, including the heart, lung, kidney, skin, and brain. As a result of these effects, people who have had COVID-19 may be more likely to develop new health conditions such as diabetes, heart conditions, blood clots, or neurological conditions compared with people who have not had COVID-19.

People experiencing any severe illness may develop health problems

People experiencing any severe illness, hospitalization, or treatment may develop problems such as post-intensive care syndrome (PICS).

PICS refers to the health effects that may begin when a person is in an intensive care unit (ICU), and which may persist after a person returns home. These effects can include muscle weakness, problems with thinking and judgment, and symptoms of post-traumatic stress disorder  (PTSD), a long-term reaction to a very stressful event. While PICS is not specific to infection with SARS-CoV-2, it may occur and contribute to the person’s experience of Long COVID. For people who experience PICS following a COVID-19 diagnosis, it is difficult to determine whether these health problems are caused by a severe illness, the virus itself, or a combination of both.

People More Likely to Develop Long COVID

Some people may be more at risk for developing Long COVID.

Researchers are working to understand which people or groups of people are more likely to have Long COVID, and why. Studies have shown that some groups of people may be affected more by Long COVID. These are examples and not a comprehensive list of people or groups who might be more at risk than other groups for developing Long COVID:

• People who have experienced more severe COVID-19 illness, especially those who were hospitalized or needed intensive care.
• People who had underlying health conditions prior to COVID-19.
• People who did not get a COVID-19 vaccine.

Health Inequities May Affect Populations at Risk for Long COVID

Some people are at increased risk of getting sick from COVID-19 because of where they live or work, or because they can’t get health care. Health inequities may put some people from racial or ethnic minority groups and some people with disabilities at greater risk for developing Long COVID. Scientists are researching some of those factors that may place these communities at higher risk of getting infected or developing Long COVID.

Preventing Long COVID

The best way to prevent Long COVID is to protect yourself and others from becoming infected. For people who are eligible, CDC recommends staying up to date on COVID-19 vaccination , along with improving ventilation, getting tested for COVID-19 if needed, and seeking treatment for COVID-19 if eligible. Additional preventative measures include avoiding close contact with people who have a confirmed or suspected COVID-19 illness and washing hands  or using alcohol-based hand sanitizer.

Research suggests that people who get a COVID-19 infection after vaccination are less likely to report Long COVID, compared to people who are unvaccinated.

CDC, other federal agencies, and non-federal partners are working to identify further measures to lessen a person’s risk of developing Long COVID. Learn more about protecting yourself and others from COVID-19 .

Living with Long COVID

Living with Long COVID can be hard, especially when there are no immediate answers or solutions.

People experiencing Long COVID can seek care from a healthcare provider to come up with a personal medical management plan that can help improve their symptoms and quality of life. Review these tips  to help prepare for a healthcare provider appointment for Long COVID. In addition, there are many support groups being organized that can help patients and their caregivers.

Although Long COVID appears to be less common in children and adolescents than in adults, long-term effects after COVID-19 do occur in children and adolescents .

Talk to your doctor if you think you or your child has Long COVID. Learn more: Tips for Talking to Your Healthcare Provider about Post-COVID Conditions

Data for Long COVID

Studies are in progress to better understand Long COVID and how many people experience them.

CDC is using multiple approaches to estimate how many people experience Long COVID. Each approach can provide a piece of the puzzle to give us a better picture of who is experiencing Long COVID. For example, some studies look for the presence of Long COVID based on self-reported symptoms, while others collect symptoms and conditions recorded in medical records. Some studies focus only on people who have been hospitalized, while others include people who were not hospitalized. The estimates for how many people experience Long COVID can be quite different depending on who was included in the study, as well as how and when the study collected information.  Estimates of the proportion of people who had COVID-19 that go on to experience Long COVID can vary.

CDC posts data on Long COVID and provides analyses, the most recent of which can be found on the U.S. Census Bureau’s Household Pulse Survey .

CDC and other federal agencies, as well as academic institutions and research organizations, are working to learn more about the short- and long-term health effects associated with COVID-19 , who gets them and why.

Scientists are also learning more about how new variants could potentially affect Long COVID. We are still learning to what extent certain groups are at higher risk, and if different groups of people tend to experience different types of Long COVID. CDC has several studies that will help us better understand Long COVID and how healthcare providers can treat or support patients with these long-term effects. CDC will continue to share information with healthcare providers to help them evaluate and manage these conditions.

CDC is working to:

• Better identify the most frequent symptoms and diagnoses experienced by patients with Long COVID.
• Better understand how many people are affected by Long COVID, and how often people who are infected with COVID-19 develop Long COVID
• Better understand risk factors and protective factors, including which groups might be more at risk, and if different groups experience different symptoms.
• Help understand how Long COVID limit or restrict people’s daily activity.
• Help identify groups that have been more affected by Long COVID, lack access to care and treatment for Long COVID, or experience stigma.
• Better understand the role vaccination plays in preventing Long COVID.
• Collaborate with professional medical groups to develop and offer clinical guidance and other educational materials for healthcare providers, patients, and the public.

Related Pages

• Caring for People with Post-COVID Conditions
• Preparing for Appointments for Post-COVID Conditions
• Researching COVID to Enhance Recovery
• Guidance on “Long COVID” as a Disability Under the ADA

For Healthcare Professionals

• Post-COVID Conditions: Healthcare Providers

Search for and find historical COVID-19 pages and files. Please note the content on these pages and files is no longer being updated and may be out of date.

• Visit archive.cdc.gov for a historical snapshot of the COVID-19 website, capturing the end of the Federal Public Health Emergency on June 28, 2023.
• Visit the dynamic COVID-19 collection  to search the COVID-19 website as far back as July 30, 2021.

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