Rounding Decimals

Related Topics: More Lessons for Arithmetic Math Worksheets

Rounding Decimals

How to round decimals? The rules for rounding decimals are the same as the rules for whole numbers. Step 1: Decide on the place the number is to be rounded to. Step 2: Look at the first digit to the right of that place. Step 3: If the digit is equal to or more than 5, round up Step 4: If the digit is less than 5, round down. Step 5: We may drop the zeros.

Round 74.862 to the nearest tenths

The digit at the tenth place is 8. The digit to the right of 8 is 6. Since 6 > 5 we round up.

decimal rounding problem solving

74.862 rounded to the nearest tenths is 74.9

Round 74.862 to the nearest hundredths

The digit at the hundredth place is 6. The digit to the right of 6 is 2. Since 2 < 5 we round down.

decimal rounding problem solving

74.862 rounded to the nearest hundredths is 74.86

Round 74.862 to the nearest whole number

The digit at the ones place is 4. The digit to the right of 4 is 8. Since 8 > 5 we round up.

decimal rounding problem solving

74.862 rounded to the nearest whole number is 75

This two-part video shows more examples of how to round decimals.

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Rounding Numbers Worksheet Rounding Challenges

Welcome to our Rounding Numbers Worksheet collection of Rounding Challenges. Here you will find a wide range of free printable math Worksheets, which will help your child learn to apply their rounding knowledge to solve a variety of rounding challenges.

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Rounding Numbers Worksheets

Rounding challengs.

Here you will find a range of selection of printable rounding challenges to give your child practice and consolidation with their rounding work.

These sheets are carefully graded so that the easier sheets come first.

Each challenge consists of 4 clues and 8 possible answers, of which only one is correct.

Children have to look at the clues and use them to work out the correct answer.

These activities can be used individually with children working through the challenges on their own, but they are also great for partner work, and children discussing and sharing their ideas, and developing their mathematical language.

Each sheets comes with a separate printable answer sheet.

Using these sheets will help your child to:

  • apply their rounding knowledge to solve problems;
  • solve mathematical problems;
  • develop children's vocabulary and understanding of the properties of numbers.

All the free Rounding challenges in this section support the Elementary Math Benchmarks.

Rounding Challenges to the nearest 10

  • Rounding Challenges 1
  • Rounding Challenges 1 Answers
  • PDF version
  • Rounding Challenges 2
  • Rounding Challenges 2 Answers

Rounding Challenges to the nearest 10 & 100

  • Rounding Challenges 3
  • Rounding Challenges 3 Answers
  • Rounding Challenges 4
  • Rounding Challenges 4 Answers

Rounding Challenges to the nearest 10, 100 & 1000

  • Rounding Challenges 5
  • Rounding Challenges 5 Answers
  • Rounding Challenges 6
  • Rounding Challenges 6 Answers

Looking for something harder?

The rounding decimals challenges in this section involve rounding decimal numbers to the nearest whole, tenth or 2dp.

They are at a more challenging level than those on this page, and involve decimals.

  • Rounding Decimals Worksheet Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Rounding Off Worksheet Generator

Here is our generator for generating your own rounding off numbers worksheets.

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  • rounding off to the nearest 10, 100, 1000 or 10000
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How to Round whole numbers

  • learn to round numbers to the nearest 10, 100 or 1000.

Each of the webpages below comes with rounding help as well as practice worksheets.

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  • Rounding Decimals to the nearest whole

Online Rounding Practice Zone

In our Rounding Practice zone, you can practice rounding a range of numbers. You can round numbers to the nearest 10, 100 or even 1000. Want to round numbers to the nearest decimal place, you can do that too!

Select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

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Helping with Math

Rounding Decimals

Introduction.

Numbers are very commonly used in our day to day life. In general, we need not state the exact number as an answer to the question which requires us to tell about how many. In other words, in order to ease our calculations, we often approximate the numbers to some extent. It helps us give approximate answers where exact values are not required. For instance, we may say that there are around 600 students in a school. That does not necessarily mean that there are exactly 600 students in a school. The exact number of students in the school may be somewhere around 600 which, for convenience, we have rounded off to 600. Rounding off is also termed as a shortcut method. Another example can be if you plan an event at home you can just estimate the number of guests that are supposed to attend the event. It can be a rough estimate of the number of people say 200. This does not mean that exactly 200 people will attend the event. This means we can round off numbers to the nearest place value, say 10, 100, 1000 etc. 

But can we round off decimal numbers as well in the same manner as we do for whole numbers ? Let us find out.  

Before we learn about rounding off decimal numbers , it is important to recall what we mean by decimals ?

What are Decimals?

Let us recall what we mean by a decimal . A decimal is another way of expressing a fraction. For example the fraction 110 in decimal form is written as 0.1. This dot between the two digits is called the decimal point. So, the decimal number 1.8 will be read as one point eight. Now, just like the place values of whole numbers such as ones, tens and hundreds, the decimal numbers also have their own place value system. This is extremely important to understand as unless we are not aware of the place of a digit in a decimal, we cannot round it off.   Therefore, let us recall the place value system of decimals.

Place Value System of Decimals

We know that each place in the place value table has a value ten times the value of the next place on its right. In other words, the value of a place is one-tenth of the value of the next place on its left. We observe that if one digit moves one place left to right its value becomes one-tenth ($\frac{1}{10}$ ) of its previous value and when it moves two places left to right its value comes one-hundredth ( $\frac{1}{100}$ ) of its previous term and so on. Therefore, if we wish to move beyond ones place which is the case of decimals, we will have to extend the place value table by introducing the places of tenths ( $\frac{1}{10}$ ), hundredths ($\frac{1}{100}$ ), thousandths ( $\frac{1}{1000}$ ) and so on.

Therefore, the place value table in case of a decimal number will be of the form –

For example, the decimal number 257.32 in the place value system will be written as –

A decimal or a decimal number may contain a whole number part and a decimal part. The following table shows the whole number part and the decimal part of some decimals – 

From the above discussion, we can see that the first three places on the right of the decimal point are tenths, hundredths and thousandths. Let us learn about rounding off decimals at these place values. 

Round Off to the Nearest Tenth

Rounding off to the nearest tenth is also known as rounding off to one decimal place. So, how do we round off a number to the nearest tenth? Let us understand this by an example.

Suppose a tree is 6.84 m tall. Let us round off its height to the nearest tenth. To round off this number to the nearest tenth, let us draw a number line and show the decimals as below 

decimal rounding problem solving

In the above number line, we can see that 6.84 is closer to 6.80 than to 6.90. Hence, 6.84 will be rounded off the nearest decimal place 6.8.

However, every time we wish to round off a number we cannot draw a number to the line to check which decimal number is the given number closer to. Therefore, it is important to follow some rules for rounding off a number to the nearest tenth.

The following are the rules that must be followed for rounding off a number to the nearest tenth – 

  • Identify the place you want to the round to. ( In case we have the tenth place )
  • Examine the digit to the right of the rounding place digit.
  • If that digit is equal to 5 or greater than 5. Add 1 to the rounding place digit. If the digit is less than 5, let the rounding place digit remain as such. 
  • In both the cases, drop all the digits to the right of the rounding place digit.

From the above rules, we can clearly see that similar to rounding of whole numbers, there are two ways of rounding decimals to the nearest tenth  –

Rounding Up

Rounding down.

Let us understand both the cases for rounding off to the nearest tenth.

If the number at the tenth’s place is followed by 5, 6, 7, 8, or 9, the number is rounded up. 

Example  – We want to round off 54.89 to the nearest 10.

  • Look for the digit at the ten’s place. It is 8.

decimal rounding problem solving

  • Now look for the digit to the right of the digit at the tenth’s place. The number is 9

decimal rounding problem solving

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 9 becomes 10 which by adding to 8 at the tenth’s place, becomes 90.

Hence, the number 54.89 after being rounded off to the nearest tenth is 54.90 or 54.9.

If the number at the tenth’s place is followed by 0, 1, 2, 3 or 4, the number is rounded down. Let us understand it by an example.

Suppose we want to round off the number 24.61 to the nearest tenth. We will follow the following steps – 

  • Look for the digit at the tenth’s place. It is 6 .

decimal rounding problem solving

  • Now look for the digit to the right of the digit at the tenth’s place. The number is 1 .

decimal rounding problem solving

  • Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which by adding to 6 at the tenth’s place, becomes 60.
  • Hence, the number 24.61 after being rounded off to the nearest tenth is 24.60 or 24.6

Now, that we have understood how to round off a decimal to the tenth’s place, let us now learn how to round off a decimal to the hundredth place.

Round Off to the Nearest Hundredth

Rounding off to the nearest hundredth is also known as rounding off to two decimal places. This is the most common form of rounding off that we use in solving everyday problems, especially when related to money. So, how do we round off a number to the nearest hundredth? Let us understand this by an example.

The following are the rules that must be followed for rounding off a number to the nearest hundredth – 

  • Identify the place you want to the round to. ( In case we have the hundredths place )

From the above rules, we can clearly see that similar to rounding of whole numbers, there are two ways of rounding decimals to the nearest hundredth –

Let us understand both the cases for rounding off to the nearest hundredth.

If the number at the hundredth place is followed by 5, 6, 7, 8, or 9, the number is rounded up. 

Example  – We want to round off 54.689 to the nearest 10.

  • Look for the digit at the hundredth’s place. It is 8.

decimal rounding problem solving

  • Now look for the digit to the right of the digit at the thousandth’s place. The number is 9

decimal rounding problem solving

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 9 becomes 10 which by adding to 8 at the hundredth’s place, becomes 90.

Hence, the number 54.689 after being rounded off to the nearest hundredth is 54.690 or 54.69.

If the number at the hundredth’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. Let us understand it by an example.

Suppose we want to round off the number 24.361 to the nearest tenth. We will follow the following steps – 

  • Look for the digit at the hundredth’s place. It is 6 .

decimal rounding problem solving

  • Now look for the digit to the right of the digit at the hundredth’s place. The number is 1 .

decimal rounding problem solving

  • Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which by adding to 6 at the hundredth place, becomes 60.
  • Hence, the number 24.361 after being rounded off to the nearest hundredth is 24.360 or 24.36

Now, that we have understood how to round off a decimal to the hundredth place, let us now learn how to round off a decimal to the thousandth’s place.

Round Off to the Nearest Thousandth 

Rounding off to the nearest thousandth is also known as rounding off to three decimal places. So, how do we round off a number to the nearest thousandth? Let us understand this by an example.

The following are the rules that must be followed for rounding off a number to the nearest thousandth – 

  • Identify the place you want to the round to. ( In case we have the thousandth place )

From the above rules, we can clearly see that similar to rounding of whole numbers, there are two ways of rounding decimals to the nearest thousandth –

Let us understand both the cases for rounding off to the nearest thousandth.

If the number at the thousandth place is followed by 5, 6, 7, 8, or 9, the number is rounded up. 

Example  – We want to round off 54.1689 to the nearest 10.

  • Look for the digit at the thousandth place. It is 8.

decimal rounding problem solving

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 9 becomes 10 which by adding to 8 at the thousandth’s place, becomes 90.

Hence, the number 54.1689 after being rounded off to the nearest hundredth is 54.169 or 54.169.

If the number at the thousandth’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. Let us understand it by an example.

Suppose we want to round off the number 24.5163 to the nearest tenth. We will follow the following steps – 

  • Look for the digit at the thousandth’s place. It is 6 .

decimal rounding problem solving

  • Now look for the digit to the right of the digit at the thousandth’s place. The number is 3 .

decimal rounding problem solving

  • Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which by adding to 6 at the thousandth’s place, becomes 60.
  • Hence, the number 24.5163 after being rounded off to the nearest thousandths is 24.516 or 24.516

Note: Here we moved down the number to the nearest thousandths, which is why it is called rounding down.

Solved Examples

Example 1 Round off 17.3829 to the nearest hundredth

Solution We have been given the number 17.3829.  we need to round off this number to the nearest hundredth.

From the steps above we can see that the digit to the right of the digit at the hundredth’s place is 2 which is less than 5. Hence we will round it down to 0 which on adding to 8 at the hundredths place become 80.

Hence, 17.3829 on rounding off the nearest hundredth is 17.380

Example 2 Round off 19.83 to the nearest tenth

Solution We have been given the number 19.83. We need to round off this number to the nearest tenth.

From the steps above we can see that the digit to the right of the digit at the tenths place is 3 which is less than 5. Hence we will round it down to 0 which on adding to 3 at the tenth place become 30.

Hence, 19.83 on rounding off the nearest hundredth is 19.80 or 19.8.

Example 3 Round off 23.8254 to the nearest thousandth 

Solution We have been given the number 23.8254. We need to round off this number to the nearest thousandth.

From the steps above we can see that the digit to the right of the digit at the thousandth place is 4 which is less than 5. Hence we will round it down to 0 which on adding to 5 at the thousandth place become 50.

Hence, 23.8254 on rounding off the nearest thousandth is 23.825

Key Facts and Summary

  • A decimal is another way of expressing a fraction.
  • Rounding off to the nearest tenth is also known as rounding off to one decimal place.
  • If the number at the tenth place is followed by 5, 6, 7, 8, or 9, the number is rounded up. 
  • If the number at the hundredth’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. 
  • Rounding off to the nearest tenth is also known as rounding off to two decimal places.
  • Rounding off to the nearest thousandth is also known as rounding off to three decimal places.

Recommended Worksheets

Rounding Decimals (Adventure Themed) Worksheets Rounding Whole Numbers and Decimals (Basketball Themed) Worksheets Rounding Off Decimals Up To Thousandths 5th Grade Math Worksheets

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All Round Decimals Resources

Round Tenths Using a Number Line Game

Round Tenths Using a Number Line Game

Enter the madness of math-multiverse by exploring how to round tenths using a number line.

Round Tenths to the Nearest Whole Game

Round Tenths to the Nearest Whole Game

Enjoy the marvel of mathematics by exploring how to round tenths to the nearest whole.

Round Up or Round Down Worksheet

Round Up or Round Down Worksheet

Reinforce math concepts by practicing to round up or round down.

Round off Decimal Numbers Worksheet

Round off Decimal Numbers Worksheet

Reinforce math concepts by practicing to round off decimal numbers.

Round Hundredths to the Nearest Whole Game

Round Hundredths to the Nearest Whole Game

Sharpen your number skills by rounding hundredths to the nearest whole.

Round Thousandths to the Nearest Whole Game

Round Thousandths to the Nearest Whole Game

Dive deep into the world of math by rounding thousandths to the nearest whole.

Round Decimals to the Nearest Whole Worksheet

Round Decimals to the Nearest Whole Worksheet

Use this printable worksheet to round decimals to the nearest whole to strengthen your math skills.

Missing Digits in Rounding Decimals to the Nearest Whole - Worksheet

Missing Digits in Rounding Decimals to the Nearest Whole Worksheet

A worksheet designed to practice rounding decimals to the nearest whole number by filling in the missing digits.

Round Hundredths Using a Number Line Game

Round Hundredths Using a Number Line Game

Shine bright in the math world by learning how to round hundredths using a number line.

Round Hundredths to the Nearest Tenth Game

Round Hundredths to the Nearest Tenth Game

Use your number skills to round hundredths to the nearest tenth.

Possible Decimal Numbers that Round to the Nearest Whole - Worksheet

Possible Decimal Numbers that Round to the Nearest Whole Worksheet

A worksheet on identifying decimal numbers that can be rounded to the nearest whole number.

Round Decimals to the Nearest Whole and Check the Statements - Worksheet

Round Decimals to the Nearest Whole and Check the Statements Worksheet

Practice rounding decimals to the nearest whole and validating statements with this worksheet.

Round Thousandths to the Nearest Tenth Game

Round Thousandths to the Nearest Tenth Game

Learn to solve math problems by rounding thousandths to the nearest tenth.

Round Thousandths Using a Number Line Game

Round Thousandths Using a Number Line Game

Take a deep dive into the world of math by rounding thousandths using a number line.

Round Decimals to the Nearest Whole and Select the Correct Number - Worksheet

Round Decimals to the Nearest Whole and Select the Correct Number Worksheet

A worksheet on rounding decimals to the nearest whole and selecting the correct number.

Round Decimals to the Nearest Whole Using Number Line - Worksheet

Round Decimals to the Nearest Whole Using Number Line Worksheet

Enhance your skills in rounding decimals to the nearest whole with this engaging worksheet using number lines.

Round to the Nearest Hundredth Game

Round to the Nearest Hundredth Game

Add more arrows to your child’s math quiver by rounding to the nearest hundredth.

Guess the Number (Rounded to Whole) Game

Guess the Number (Rounded to Whole) Game

Kids must guess the number (rounded to whole) to play.

Round Up the Decimals to the Nearest Whole - Worksheet

Round Up the Decimals to the Nearest Whole Worksheet

This worksheet provides exercises for students to practice rounding decimal numbers to the nearest whole number.

Rounding Decimals to the Nearest Whole - Worksheet

Rounding Decimals to the Nearest Whole Worksheet

Master the skill of rounding decimals to the nearest whole with this engaging worksheet.

Guess the Number (Rounded to Hundredth) Game

Guess the Number (Rounded to Hundredth) Game

Shine bright in the math world by guessing the number (rounded to hundredth).

Guess the Number (Rounded to Thousandth) Game

Guess the Number (Rounded to Thousandth) Game

Practice the superpower of decimals by guessing the correct number rounded to the thousandths.

Round Decimals to the Nearest Tenth Worksheet

Round Decimals to the Nearest Tenth Worksheet

Focus on core math skills with this fun worksheet by solving to round decimals to the nearest tenth.

Thousandths That Rounds to a Whole Number When Rounded to Nearest Tenths - Worksheet

Thousandths That Rounds to a Whole Number When Rounded to Nearest Tenths Worksheet

Identify and highlight decimals that round up to whole numbers when approximated to the nearest tenth in this worksheet!

Hundredths That Rounds to a Whole Number When Rounded to Nearest Tenths - Worksheet

Hundredths That Rounds to a Whole Number When Rounded to Nearest Tenths Worksheet

Identify decimals that round up to a whole number when rounded to the nearest tenth in this worksheet!

Missing Digits in Rounding Decimals to the Nearest Tenth - Worksheet

Missing Digits in Rounding Decimals to the Nearest Tenth Worksheet

This worksheet provides exercises on determining missing digits when rounding decimals to the nearest tenth.

Possible Decimal Numbers that Round to the Nearest Tenth - Worksheet

Possible Decimal Numbers that Round to the Nearest Tenth Worksheet

Boost your skills with this worksheet on identifying decimals that round to the nearest tenth.

Round Decimals to the Nearest Tenth and Check the Statements - Worksheet

Round Decimals to the Nearest Tenth and Check the Statements Worksheet

A worksheet designed to enhance skills in rounding decimals to the nearest tenth and verifying mathematical statements.

Round Decimals to the Nearest Tenth and Select the Correct Number - Worksheet

Round Decimals to the Nearest Tenth and Select the Correct Number Worksheet

Sharpen your decimal rounding skills with this worksheet on rounding to the nearest tenth!

Round Decimals to the Nearest Tenth Using Number Line - Worksheet

Round Decimals to the Nearest Tenth Using Number Line Worksheet

Engaging worksheet to practice rounding decimals to the nearest tenth using number lines.

Round Up the Decimals to the Nearest Tenth - Worksheet

Round Up the Decimals to the Nearest Tenth Worksheet

This worksheet offers exercises to practice and enhance skills in rounding decimals to their nearest tenth place.

Rounding Decimals to the Nearest Tenth - Worksheet

Rounding Decimals to the Nearest Tenth Worksheet

A worksheet designed to enhance students' skills in rounding off decimals to the nearest tenth place.

Round Decimals to the Nearest Hundredth Worksheet

Round Decimals to the Nearest Hundredth Worksheet

Help your child revise number sense by rounding decimals to the nearest hundredth.

Missing Digits in Rounding Decimals to the Nearest Hundredth - Worksheet

Missing Digits in Rounding Decimals to the Nearest Hundredth Worksheet

This worksheet tests your skills in identifying missing digits when rounding decimals to the nearest hundredth.

Possible Decimal Numbers that Round to the Nearest Hundredth - Worksheet

Possible Decimal Numbers that Round to the Nearest Hundredth Worksheet

This worksheet provides exercises on identifying decimal numbers that can be rounded to the nearest hundredth.

Puzzles on Rounding Decimals to the Nearest Whole,Tenth and Hundredth - Worksheet

Puzzles on Rounding Decimals to the Nearest Whole,Tenth and Hundredth Worksheet

Engaging worksheet with puzzles to practice rounding decimals to the nearest whole, tenth, and hundredth.

Round Decimals to the Nearest Hundredth and Check the Statements - Worksheet

Round Decimals to the Nearest Hundredth and Check the Statements Worksheet

Enhance your decimal rounding skills with this worksheet on rounding to the nearest hundredth!

Round Decimals to the Nearest Hundredth and Select the Correct Number - Worksheet

Round Decimals to the Nearest Hundredth and Select the Correct Number Worksheet

Practice rounding decimals to the nearest hundredth with this engaging worksheet.

Round Decimals to the Nearest Hundredth Using Number Line - Worksheet

Round Decimals to the Nearest Hundredth Using Number Line Worksheet

Boost decimal rounding skills with this worksheet on rounding to the nearest hundredth using a number line.

Round Up the Decimals to the Nearest Hundredth - Worksheet

Round Up the Decimals to the Nearest Hundredth Worksheet

This worksheet provides exercises for practicing rounding decimal numbers up to the nearest hundredth place.

Rounding Decimals to the Nearest Hundredth - Worksheet

Rounding Decimals to the Nearest Hundredth Worksheet

A worksheet focused on enhancing skills in rounding decimals to the nearest hundredth for improved numerical accuracy.

Rounding Decimals to the Nearest Whole, Tenth and Hundredth - Worksheet

Rounding Decimals to the Nearest Whole, Tenth and Hundredth Worksheet

Enhance your skills in rounding decimals with this worksheet, focusing on whole, tenth, and hundredth places.

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Unit 5: Using Decimals in Real Life

Topic B: Decimal Word Problems

Spend a few minutes reviewing the key words that will help you identify addition, subtraction, multiplication and division word problems.

Some key words that point to addition include:

  • total amount
  • increased by

Some key words that point to subtraction include:

  • amount left
  • subtracted from
  • decreased by

Some key words which point to multiplication include:

Some key words which point to division include:

  • What is the cost per…?
  • What is the distance per…?
  • average (speed, cost, weight, time)

Read over some of the problems that you have done in each unit to remind yourself of the patterns to expect for different operations.

Steps for Solving Word Problems

Carefully review the f i ve steps to use when solving problems:

Step 1: Question

  • Read the problem carefully.
  • What is the question being asked?
  • Does the problem have two parts?
  • Draw a picture to help you see the problem described.

Step 2: Information

  • What information is necessary to solve the problem?
  • Often you are given extra numbers and information that are not needed.
  • Keep the question (destination) in mind.
  • Circle the information you need.
  • Write that information on the picture you drew.

Step 3: Operation

  • Decide what arithmetic operation to use.
  • Do you need to add, subtract, multiply, or divide?
  • Key words often point to the operation needed.
  • Drawing a diagram or sketch is always helpful.
  • Write an equation (a number sentence).

Step 4: Estimate

  • Round the numbers so you can work with them quickly.
  • Use the operation you chose in Step 3 and come to a quick answer.
  • Does this estimated answer make sense?
  • Does it answer the question of the problem?
  • Think carefully before you do Step 5.

Step 5: Solve

  • Check your arithmetic.
  • Compare your answer in Step 4 to your estimate from Step 3.
  • Think again about the question. Does your solution make sense?
  • When you write your answer, include the units. For example: 3 dozen eggs, 7.5 kilometres, 68 people
  • Estimation:
  • Actual Solution:
  • How much do you pay if you buy “rent-to-own”?
  • How much do you save if you pay cash?

Answers to Exercise 1

  • Estimation: 300kg + 60 kg + 70 kg ≈ 430 kg Actual Solution: 293.937 kg + 62.142 kg + 68.39 kg = 424.469 kg Answer: The ATV weighed 424.469 kg when loaded.
  • Estimation: 12 km × 30 km ≈ 360 km per day Actual Solution: 12.73 km × 30 km = 381.9 km Answer: The bus drives 381.9 km a day.
  • Estimation: $60 × 12 + $75 ≈ $795 Actual Solution: $56.19 × 12 + $75.00 = $749.28 Answer: Mary paid $749.28 for the TV set.
  • Estimation: 20 000 hours × $10.00 ≈ $200 000 Actual Solution: 19 600 hours × $9.575 = $187 670 Answer: The Dryer Company paid out $187 670 for the payroll that week.
  • Estimation: 900 km ÷ 90 L ≈ 10 km/L Actual solution: 896 km ÷ 94.5 L = 9.48 km/L Answer: Joe‘s truck uses 9.48 kilometres per litre.
  • Estimation: $30 + $14 + $5 ≈ $49 Actual Solution: $29.95 + $13.50 + $5.21 = $48.66 Answer: Andy spent $48.66
  • Estimation: $50 – $49≈$1 Actual Solution: $50 − $48.66 = $1.34 Answer: Andy got $1.34 change from his $50.
  • Estimations: 50 × 0.50 ≈ 25 games won, 50 × 0.50 = 25 games lost Actual Solutions: 48×0.625 =30 games won 48 × 0.375 =18 games lost
  • Estimation: $30 000 ÷ 10 ≈ $3 000 Actual Solution: $28 606.60 ÷ 12 = $2 383.88 Answer: Diane‘s monthly salary will be $2 383.88 .
  • Estimation: $250 ÷ 10 ≈ $25 Actual Solution: $235.75 ÷ 12 = $19.65 Answer: Treena paid $19.65 monthly.
  • $27.50 × 6 = $165 $165 + 50 = $215 Answer: If you pay on time you will pay $215.
  • $215 − $199.99 = $15.01 Answer: If you pay cash, you will save $15.01.

Topic B: Self-Test

Mark /6               Aim 5 / 6

Answers to Topic B Self-Test

  • Estimation: 3 cm − 1 cm ≈ 2 cm Actual Solution: 2.6 cm − 1.25 cm = 1.35 cm He has to drill 1.35 cm farther.
  • Estimation: 7 kg × $3 ≈ $21 Actual Solution: 6.75 kg × $2.95 = $19.91 Sebastian  got $19.91 for his berries.
  • Estimation: $60 ÷ 12 ≈ 5 Actual Solution: $57.38 ÷ 12.75 = 4.5 Karla worked for 4.5 hours.

Design Your Own House Project Part 4: Fencing and Decorating

Use the graph paper house sketch that you made in Unit 2, Topic B: Subtracting Decimals in the Design Your Own House Project Part 1 do this activity.

Give your house a yard.

  • What is the perimeter of the yard?
  • Calculate the total area of your yard, not including the area of the house. (area = length × width) There are two ways to do this. You can calculate the whole area and then subtract the area of the house, or you could calculate the area of each section of the yard (front, back, and two sides) and add them together.
  • Use a flyer from a hardware store or go online to look at types of fencing (for example, chain-link, cedar, metal, wood panel, picket, etc.). Choose a style of fencing for your yard. Write your choice here.
  • Calculate the price per metre of your fence.
  • When making curtains, it is a good idea to use fabric that is 2.5 times the width of the window. Remember that each of your windows is 1m wide. What length of fabric will you need to buy to make curtains for all four windows?

a rectangular piece of artwork

  • What size glass should you buy?
  • How much trim will you need to buy for your picture frame?

Marking Rubric for House Project Part 4

  • The house has a yard and measurements have been clearly marked on the sketch.

Calculations:

  • The perimeter of the yard has been calculated correctly.
  • The area of the yard has been calculated correctly.
  • The total price of each fencing material has been calculated correctly.
  • The price per metre of the fence has been calculated correctly.
  • The width of fabric necessary to cover all four windows has been calculated correctly.
  • The size of glass necessary to cover the artwork has been calculated correctly.
  • The amount of trim necessary for the picture frame has been calculated correctly.

The result of an addition question, the answer to an addition question.

The amount altogether.

The result of a subtraction question, the answer. Subtraction gives the difference between two numbers.

Balance has many meanings. In money matters, the balance is the amount left. It might be the amount left in a bank account (bank balance) or it might be the amount you still must pay on a bill (balance owing).

The result of a multiplying question, the answer.

The price for a set amount. E.g., price per litre, price per gram.

Adult Literacy Fundamental Mathematics: Book 4 - 2nd Edition Copyright © 2023 by Katherine Arendt; Mercedes de la Nuez; and Liz Girard is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Reasoned Rounding

  • Student Solutions
  • Teachers' Resources

Reasoned Rounding printable sheet

This is a rounding game for two players. 

11 circles, each split in half, with labels from 0 to 100 counting up in 10s

You will need a  recording sheet  shared between the two players. One sheet is enough for three games. The first player rolls a 0-9 dice twice and chooses which two-digit number they would like to make from the numbers rolled. They then round this number to the nearest 10, find the matching circle on the recording sheet and write their two digit number in one of the spaces in that circle. The second player rolls the dice twice to take their turn in a similar way. A circle is complete when it has two numbers in it and this scores a point for the person who wrote the second number in. (Even if the first number was written in by the other player.) The game is over when all the circles are full and then the points are counted up to find the winner.

Decimals Worksheets

Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.

Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions.

Most Popular Decimals Worksheets this Week

Adding and Subtracting Decimals With Up to Three Places Before and After the Decimal

Grids and Charts Useful for Learning Decimals

decimal rounding problem solving

General use decimal printables are used in a variety of contexts and assist students in completing math questions related to decimals.

The thousandths grid is a useful tool in representing decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.

  • Thousandths and Hundredths Grids Thousandths Grid Hundredths Grids ( 4 on a page) Hundredths Grids ( 9 on a page) Hundredths Grids ( 20 on a page)
  • Decimal Place Value Charts Decimal Place Value Chart ( Ones to Hundredths ) Decimal Place Value Chart ( Ones to Thousandths ) Decimal Place Value Chart ( Hundreds to Hundredths ) Decimal Place Value Chart ( Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Millions to Millionths )

Decimals in Expanded Form

decimal rounding problem solving

For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart, and allow them to use it when converting standard form numbers to expanded form. There are actually five ways (two more than with integers) to write expanded form for decimals, and which one you use depends on your application or preference. Here is a quick summary of the various ways using the decimal number 1.23. 1. Expanded Form using decimals: 1 + 0.2 + 0.03 2. Expanded Form using fractions: 1 + 2 ⁄ 10 + 3 ⁄ 100 3. Expanded Factors Form using decimals: (1 × 1) + (2 × 0.1) + (3 × 0.01) 4. Expanded Factors Form using fractions: (1 × 1) + (2 × 1 ⁄ 10 ) + (3 × 1 ⁄ 100 ) 5. Expanded Exponential Form: (1 × 10 0 ) + (2 × 10 -1 ) + (3 × 10 -2 )

  • Converting Decimals from Standard Form to Expanded Form Using Decimals Converting Decimals from Standard to Expanded Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Form Using Fractions Converting Decimals from Standard to Expanded Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Factors Form Using Decimals Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Factors Form Using Fractions Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 9 Decimal Places)
  • Converting Decimals from Standard Form to Expanded Exponential Form Converting Decimals from Standard to Expanded Exponential Form ( 3 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 4 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 5 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 6 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 7 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 8 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 9 Decimal Places)
  • Retro Converting Decimals from Standard Form to Expanded Form Retro Standard to Expanded Form (3 digits before decimal; 2 after) Retro Standard to Expanded Form (4 digits before decimal; 3 after) Retro Standard to Expanded Form (6 digits before decimal; 4 after) Retro Standard to Expanded Form (12 digits before decimal; 3 after)
  • Retro European Format Converting Decimals from Standard Form to Expanded Form Standard to Expanded Form (3 digits before decimal; 2 after) Standard to Expanded Form (4 digits before decimal; 3 after) Standard to Expanded Form (6 digits before decimal; 4 after)

Of course, being able to convert numbers already in expanded form to standard form is also important. All five versions of decimal expanded form are included in these worksheets.

  • Converting Decimals to Standard Form from Expanded Form Using Decimals Converting Decimals from Expanded Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Form Using Fractions Converting Decimals from Expanded Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Factors Form Using Decimals Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Factors Form Using Fractions Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 9 Decimal Places)
  • Converting Decimals to Standard Form from Expanded Exponential Form Converting Decimals from Expanded Exponential Form to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 9 Decimal Places)
  • Retro Converting Decimals to Standard Form from Expanded Form Retro Expanded to Standard Form (3 digits before decimal; 2 after) Retro Expanded to Standard Form (4 digits before decimal; 3 after) Retro Expanded to Standard Form (6 digits before decimal; 4 after) Retro Expanded to Standard Form (12 digits before decimal; 3 after)
  • Retro European Format Converting Decimals to Standard Form from Expanded Form Retro European Format Expanded to Standard Form (3 digits before decimal; 2 after) Retro European Format Expanded to Standard Form (4 digits before decimal; 3 after) Retro European Format Expanded to Standard Form (6 digits before decimal; 4 after)

Rounding Decimals Worksheets

decimal rounding problem solving

Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4.567 to the nearest tenth. First, truncate the number after the tenths place 4.5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4.6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6.959 to the nearest tenth. Truncate: 6.9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7.0. Watch that students do not write 6.10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...

We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6.5 --> 7; 3.555 --> 3.56; 0.60500 --> 0.61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5.5 would be rounded up to 6, but 8.5 would be rounded down to 8. The main reason for this is not to skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most pre-college students round up on a 5, that is what we have done in the worksheets that follow.

  • Rounding Decimals to Whole Numbers Round Tenths to a Whole Number Round Hundredths to a Whole Number Round Thousandths to a Whole Number Round Ten Thousandths to a Whole Number Round Various Decimals to a Whole Number
  • Rounding Decimals to Tenths Round Hundredths to Tenths Round Thousandths to Tenths Round Ten Thousandths to Tenths Round Various Decimals to Tenths
  • Rounding Decimals to Hundredths Round Thousandths to Hundredths Round Ten Thousandths to Hundredths Round Various Decimals to Hundredths
  • Rounding Decimals to Thousandths Round Ten Thousandths to Thousandths
  • Rounding Decimals to Various Decimal Places Round Hundredths to Various Decimal Places Round Thousandths to Various Decimal Places Round Ten Thousandths to Various Decimal Places Round Various Decimals to Various Decimal Places
  • European Format Rounding Decimals to Whole Numbers European Format Round Tenths to a Whole Number European Format Round Hundredths to a Whole Number European Format Round Thousandths to a Whole Number European Format Round Ten Thousandths to Whole Number
  • European Format Rounding Decimals to Tenths European Format Round Hundredths to Tenths European Format Round Thousandths to Tenths European Format Round Ten Thousandths to Tenths
  • European Format Rounding Decimals to Hundredths European Format Round Thousandths to Hundredths European Format Round Ten Thousandths to Hundredths
  • European Format Rounding Decimals to Thousandths European Format Round Ten Thousandths to Thousandths

Comparing and Ordering/Sorting Decimals Worksheets.

decimal rounding problem solving

The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.

Students who have mastered comparing whole numbers should find comparing decimals to be fairly easy. The easiest strategy is to compare the numbers before the decimal (the whole number part) first and only compare the decimal parts if the whole number parts are equal. These sorts of questions allow teachers/parents to get a good idea of whether students have grasped the concept of decimals or not. For example, if a student thinks that 4.93 is greater than 8.7, then they might need a little more instruction in place value. Close numbers means that some care was taken to make the numbers look similar. For example, they could be close in value, e.g. 3.3. and 3.4 or one of the digits might be changed as in 5.86 and 6.86.

  • Comparing Decimals up to Tenths Comparing Decimals up to Tenths ( Both Numbers Random ) Comparing Decimals up to Tenths ( One Digit Differs ) Comparing Decimals up to Tenths ( Both Numbers Close in Value ) Comparing Decimals up to Tenths ( Various Tricks )
  • Comparing Decimals up to Hundredths Comparing Decimals up to Hundredths ( Both Numbers Random ) Comparing Decimals up to Hundredths ( One Digit Differs ) Comparing Decimals up to Hundredths ( Two Digits Swapped ) Comparing Decimals up to Hundredths ( Both Numbers Close in Value ) Comparing Decimals up to Hundredths ( One Number has an Extra Digit ) Comparing Decimals up to Hundredths ( Various Tricks )
  • Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths ( One Digit Differs ) Comparing Decimals up to Thousandths ( Two Digits Swapped ) Comparing Decimals up to Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Thousandths ( Various Tricks )
  • Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths ( One Digit Differs ) Comparing Decimals up to Ten Thousandths ( Two Digits Swapped ) Comparing Decimals up to Ten Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Ten Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Ten Thousandths ( Various Tricks )
  • Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths ( One Digit Differs ) Comparing Decimals up to Hundred Thousandths ( Two Digits Swapped ) Comparing Decimals up to Hundred Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Hundred Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Hundred Thousandths ( Various Tricks )
  • European Format Comparing Decimals European Format Comparing Decimals up to Tenths European Format Comparing Decimals up to Tenths (tight) European Format Comparing Decimals up to Hundredths European Format Comparing Decimals up to Hundredths (tight) European Format Comparing Decimals up to Thousandths European Format Comparing Decimals up to Thousandths (tight)

Ordering decimals is very much like comparing decimals except there are more than two numbers. Generally, students determine the least (or greatest) decimal to start, cross it off the list then repeat the process to find the next lowest/greatest until they get to the last number. Checking the list at the end is always a good idea.

  • Ordering/Sorting Decimals Ordering/Sorting Decimal Hundredths Ordering/Sorting Decimal Thousandths
  • European Format Ordering/Sorting Decimals European Format Ordering/Sorting Decimal Tenths (8 per set) European Format Ordering/Sorting Decimal Hundredths (8 per set) European Format Ordering/Sorting Decimal Thousandths (8 per set) European Format Ordering/Sorting Decimal Ten Thousandths (8 per set) European Format Ordering/Sorting Decimals with Various Decimal Places(8 per set)

Converting Decimals to Fractions and Other Number Formats

decimal rounding problem solving

There are many good reasons for converting decimals to other number formats. Dealing with a fraction in arithmetic is often easier than the equivalent decimal. Consider 0.333... which is equivalent to 1/3. Multiplying 300 by 0.333... is difficult, but multiplying 300 by 1/3 is super easy! Students should be familiar with some of the more common fraction/decimal conversions, so they can switch back and forth as needed.

  • Converting Between Decimals and Fractions Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
  • Converting Between Decimals, Fraction, Percents and Ratios Converting Fractions to Decimals, Percents and Part-to-Part Ratios Converting Fractions to Decimals, Percents and Part-to-Whole Ratios Converting Decimals to Fractions, Percents and Part-to-Part Ratios Converting Decimals to Fractions, Percents and Part-to-Whole Ratios Converting Percents to Fractions, Decimals and Part-to-Part Ratios Converting Percents to Fractions, Decimals and Part-to-Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios with 7ths and 11ths

Adding and Subtracting Decimals

decimal rounding problem solving

Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3.25 + 4.98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3.25 + 4.98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8.23)

  • Adding Tenths Adding Decimal Tenths with 0 Before the Decimal (range 0.1 to 0.9) Adding Decimal Tenths with 1 Digit Before the Decimal (range 1.1 to 9.9) Adding Decimal Tenths with 2 Digits Before the Decimal (range 10.1 to 99.9)
  • Adding Hundredths Adding Decimal Hundredths with 0 Before the Decimal (range 0.01 to 0.99) Adding Decimal Hundredths with 1 Digit Before the Decimal (range 1.01 to 9.99) Adding Decimal Hundredths with 2 Digits Before the Decimal (range 10.01 to 99.99)
  • Adding Thousandths Adding Decimal Thousandths with 0 Before the Decimal (range 0.001 to 0.999) Adding Decimal Thousandths with 1 Digit Before the Decimal (range 1.001 to 9.999) Adding Decimal Thousandths with 2 Digits Before the Decimal (range 10.001 to 99.999)
  • Adding Ten Thousandths Adding Decimal Ten Thousandths with 0 Before the Decimal (range 0.0001 to 0.9999) Adding Decimal Ten Thousandths with 1 Digit Before the Decimal (range 1.0001 to 9.9999) Adding Decimal Ten Thousandths with 2 Digits Before the Decimal (range 10.0001 to 99.9999)
  • Adding Various Decimal Places Adding Various Decimal Places with 0 Before the Decimal Adding Various Decimal Places with 1 Digit Before the Decimal Adding Various Decimal Places with 2 Digits Before the Decimal Adding Various Decimal Places with Various Numbers of Digits Before the Decimal
  • European Format Adding Decimals European Format Adding decimal tenths with 0 before the decimal (range 0,1 to 0,9) European Format Adding decimal tenths with 1 digit before the decimal (range 1,1 to 9,9) European Format Adding decimal hundredths with 0 before the decimal (range 0,01 to 0,99) European Format Adding decimal hundredths with 1 digit before the decimal (range 1,01 to 9,99) European Format Adding decimal thousandths with 0 before the decimal (range 0,001 to 0,999) European Format Adding decimal thousandths with 1 digit before the decimal (range 1,001 to 9,999) European Format Adding decimal ten thousandths with 0 before the decimal (range 0,0001 to 0,9999) European Format Adding decimal ten thousandths with 1 digit before the decimal (range 1,0001 to 9,9999) European Format Adding mixed decimals with Various Decimal Places European Format Adding mixed decimals with Various Decimal Places (1 to 9 before decimal)

Base ten blocks can be used for decimal subtraction. Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.

  • Subtracting Tenths Subtracting Decimal Tenths with No Integer Part Subtracting Decimal Tenths with an Integer Part in the Minuend Subtracting Decimal Tenths with an Integer Part in the Minuend and Subtrahend
  • Subtracting Hundredths Subtracting Decimal Hundredths with No Integer Part Subtracting Decimal Hundredths with an Integer Part in the Minuend and Subtrahend Subtracting Decimal Hundredths with a Larger Integer Part in the Minuend
  • Subtracting Thousandths Subtracting Decimal Thousandths with No Integer Part Subtracting Decimal Thousandths with an Integer Part in the Minuend and Subtrahend
  • Subtracting Ten Thousandths Subtracting Decimal Ten Thousandths with No Integer Part Subtracting Decimal Ten Thousandths with an Integer Part in the Minuend and Subtrahend
  • Subtracting Various Decimal Places Subtracting Various Decimals to Hundredths Subtracting Various Decimals to Thousandths Subtracting Various Decimals to Ten Thousandths
  • European Format Subtracting Decimals European Format Decimal subtraction (range 0,1 to 0,9) European Format Decimal subtraction (range 1,1 to 9,9) European Format Decimal subtraction (range 0,01 to 0,99) European Format Decimal subtraction (range 1,01 to 9,99) European Format Decimal subtraction (range 0,001 to 0,999) European Format Decimal subtraction (range 1,001 to 9,999) European Format Decimal subtraction (range 0,0001 to 0,9999) European Format Decimal subtraction (range 1,0001 to 9,9999) European Format Decimal subtraction with Various Decimal Places European Format Decimal subtraction with Various Decimal Places (1 to 9 before decimal)

Adding and subtracting decimals is fairly straightforward when all the decimals are lined up. With the questions arranged horizontally, students are challenged to understand place value as it relates to decimals. A wonderful strategy for placing the decimal is to use estimation. For example if the question is 49.2 + 20.1, the answer without the decimal is 693. Estimate by rounding 49.2 to 50 and 20.1 to 20. 50 + 20 = 70. The decimal in 693 must be placed between the 9 and the 3 as in 69.3 to make the number close to the estimate of 70.

The above strategy will go a long way in students understanding operations with decimals, but it is also important that they have a strong foundation in place value and a proficiency with efficient strategies to be completely successful with these questions. As with any math skill, it is not wise to present this to students until they have the necessary prerequisite skills and knowledge.

  • Horizontally Arranged Adding Decimals Adding Decimals to Tenths Horizontally Adding Decimals to Hundredths Horizontally Adding Decimals to Thousandths Horizontally Adding Decimals to Ten Thousandths Horizontally Adding Decimals Horizontally With Up to Two Places Before and After the Decimal Adding Decimals Horizontally With Up to Three Places Before and After the Decimal Adding Decimals Horizontally With Up to Four Places Before and After the Decimal
  • Horizontally Arranged Subtracting Decimals Subtracting Decimals to Tenths Horizontally Subtracting Decimals to Hundredths Horizontally Subtracting Decimals to Thousandths Horizontally Subtracting Decimals to Ten Thousandths Horizontally Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal
  • Horizontally Arranged Mixed Adding and Subtracting Decimals Adding and Subtracting Decimals to Tenths Horizontally Adding and Subtracting Decimals to Hundredths Horizontally Adding and Subtracting Decimals to Thousandths Horizontally Adding and Subtracting Decimals to Ten Thousandths Horizontally Adding and Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal

Multiplying and Dividing Decimals

decimal rounding problem solving

Multiplying decimals by whole numbers is very much like multiplying whole numbers except there is a decimal to deal with. Although students might initially have trouble with it, through the power of rounding and estimating, they can generally get it quite quickly. Many teachers will tell students to ignore the decimal and multiply the numbers just like they would whole numbers. This is a good strategy to use. Figuring out where the decimal goes at the end can be accomplished by counting how many decimal places were in the original question and giving the answer that many decimal places. To better understand this method, students can round the two factors and multiply in their head to get an estimate then place the decimal based on their estimate. For example, multiplying 9.84 × 91, students could first round the numbers to 10 and 91 (keep 91 since multiplying by 10 is easy) then get an estimate of 910. Actually multiplying (ignoring the decimal) gets you 89544. To get that number close to 910, the decimal needs to go between the 5 and the 4, thus 895.44. Note that there are two decimal places in the factors and two decimal places in the answer, but estimating made it more understandable rather than just a method.

  • Multiplying Decimals by 1-Digit Whole Numbers Multiply 2-digit tenths by 1-digit whole numbers Multiply 2-digit hundredths by 1-digit whole numbers Multiply 2-digit thousandths by 1-digit whole numbers Multiply 3-digit tenths by 1-digit whole numbers Multiply 3-digit hundredths by 1-digit whole numbers Multiply 3-digit thousandths by 1-digit whole numbers Multiply various decimals by 1-digit whole numbers
  • Multiplying Decimals by 2-Digit Whole Numbers Multiplying 2-digit tenths by 2-digit whole numbers Multiplying 2-digit hundredths by 2-digit whole numbers Multiplying 3-digit tenths by 2-digit whole numbers Multiplying 3-digit hundredths by 2-digit whole numbers Multiplying 3-digit thousandths by 2-digit whole numbers Multiplying various decimals by 2-digit whole numbers
  • Multiplying Decimals by Tenths Multiplying 2-digit whole by 2-digit tenths Multiplying 2-digit tenths by 2-digit tenths Multiplying 2-digit hundredths by 2-digit tenths Multiplying 3-digit whole by 2-digit tenths Multiplying 3-digit tenths by 2-digit tenths Multiplying 3-digit hundredths by 2-digit tenths Multiplying 3-digit thousandths by 2-digit tenths Multiplying various decimals by 2-digit tenths
  • Multiplying Decimals by Hundredths Multiplying 2-digit whole by 2-digit hundredths Multiplying 2-digit tenths by 2-digit hundredths Multiplying 2-digit hundredths by 2-digit hundredths Multiplying 3-digit whole by 2-digit hundredths Multiplying 3-digit tenths by 2-digit hundredths Multiplying 3-digit hundredths by 2-digit hundredths Multiplying 3-digit thousandths by 2-digit hundredths Multiplying various decimals by 2-digit hundredths
  • Multiplying Decimals by Various Decimal Places Multiplying 2-digit by 2-digit numbers with various decimal places Multiplying 3-digit by 2-digit numbers with various decimal places
  • Decimal Long Multiplication in Various Ranges Decimal Multiplication (range 0.1 to 0.9) Decimal Multiplication (range 1.1 to 9.9) Decimal Multiplication (range 10.1 to 99.9) Decimal Multiplication (range 0.01 to 0.99) Decimal Multiplication (range 1.01 to 9.99) Decimal Multiplication (range 10.01 to 99.99) Random # Digits Random # Places
  • European Format Multiplying Decimals by 2-Digit Whole Numbers European Format 2-digit whole × 2-digit hundredths European Format 2-digit tenths × 2-digit whole European Format 2-digit hundredths × 2-digit whole European Format 3-digit tenths × 2-digit whole European Format 3-digit hundredths × 2-digit whole European Format 3-digit thousandths × 2-digit whole
  • European Format Multiplying Decimals by 2-Digit Tenths European Format 2-digit whole × 2-digit tenths European Format 2-digit tenths × 2-digit tenths European Format 2-digit hundredths × 2-digit tenths European Format 3-digit whole × 2-digit tenths European Format 3-digit tenths × 2-digit tenths European Format 3-digit hundredths × 2-digit tenths European Format 3-digit thousandths × 2-digit tenths
  • European Format Multiplying Decimals by 2-Digit Hundredths European Format 2-digit tenths × 2-digit hundredths European Format 2-digit hundredths × 2-digit hundredths European Format 3-digit whole × 2-digit hundredths European Format 3-digit tenths × 2-digit hundredths European Format 3-digit hundredths × 2-digit hundredths European Format 3-digit thousandths × 2-digit hundredths
  • European Format Multiplying Decimals by Various Decimal Places European Format 2-digit × 2-digit with various decimal places European Format 3-digit × 2-digit with various decimal places
  • Dividing Decimals by Whole Numbers Divide Tenths by a Whole Number Divide Hundredths by a Whole Number Divide Thousandths by a Whole Number Divide Ten Thousandths by a Whole Number Divide Various Decimals by a Whole Number

In case you aren't familiar with dividing with a decimal divisor, the general method for completing questions is by getting rid of the decimal in the divisor. This is done by multiplying the divisor and the dividend by the same amount, usually a power of ten such as 10, 100 or 1000. For example, if the division question is 5.32/5.6, you would multiply the divisor and dividend by 10 to get the equivalent division problem, 53.2/56. Completing this division will result in the exact same quotient as the original (try it on your calculator if you don't believe us). The main reason for completing decimal division in this way is to get the decimal in the correct location when using the U.S. long division algorithm.

A much simpler strategy, in our opinion, is to initially ignore the decimals all together and use estimation to place the decimal in the quotient. In the same example as above, you would complete 532/56 = 95. If you "flexibly" round the original, you will get about 5/5 which is about 1, so the decimal in 95 must be placed to make 95 close to 1. In this case, you would place it just before the 9 to get 0.95. Combining this strategy with the one above can also help a great deal with more difficult questions. For example, 4.584184 ÷ 0.461 can first be converted the to equivalent: 4584.184 ÷ 461 (you can estimate the quotient to be around 10). Complete the division question without decimals: 4584184 ÷ 461 = 9944 then place the decimal, so that 9944 is about 10. This results in 9.944.

Dividing decimal numbers doesn't have to be too difficult, especially with the worksheets below where the decimals work out nicely. To make these worksheets, we randomly generated a divisor and a quotient first, then multiplied them together to get the dividend. Of course, you will see the quotients only on the answer page, but generating questions in this way makes every decimal division problem work out nicely.

  • Decimal Long Division with Quotients That Work Out Nicely Dividing Decimals by Various Decimals with Various Sizes of Quotients Dividing Decimals by 1-Digit Tenths (e.g. 0.72 ÷ 0.8 = 0.9) Dividing Decimals by 1-Digit Tenths with Larger Quotients (e.g. 3.2 ÷ 0.5 = 6.4) Dividing Decimals by 2-Digit Tenths (e.g. 10.75 ÷ 2.5 = 4.3) Dividing Decimals by 2-Digit Tenths with Larger Quotients (e.g. 387.75 ÷ 4.7 = 82.5) Dividing Decimals by 3-Digit Tenths (e.g. 1349.46 ÷ 23.8 = 56.7) Dividing Decimals by 2-Digit Hundredths (e.g. 0.4368 ÷ 0.56 = 0.78) Dividing Decimals by 2-Digit Hundredths with Larger Quotients (e.g. 1.7277 ÷ 0.39 = 4.43) Dividing Decimals by 3-Digit Hundredths (e.g. 31.4863 ÷ 4.61 = 6.83) Dividing Decimals by 4-Digit Hundredths (e.g. 7628.1285 ÷ 99.91 = 76.35) Dividing Decimals by 3-Digit Thousandths (e.g. 0.076504 ÷ 0.292 = 0.262) Dividing Decimals by 3-Digit Thousandths with Larger Quotients (e.g. 2.875669 ÷ 0.551 = 5.219)

These worksheets would probably be used for estimating and calculator work.

  • Horizontally Arranged Decimal Division Random # Digits Random # Places
  • European Format Dividing Decimals with Quotients That Work Out Nicely European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number

In the next set of questions, the quotient does not always work out well and may have repeating decimals. The answer key shows a rounded quotient in these cases.

  • European Format Dividing Decimals by Whole Numbers European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number
  • European Format Dividing Decimals by Decimals European Format Decimal Tenth (0,1 to 9,9) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Hundredth (0,01 to 9,99) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Thousandth (0,001 to 9,999) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Ten Thousandth (0,0001 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Various Decimal Places (1,1 to 9,9999)

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Round Decimals – Reasoning and Problem Solving

Round Decimals - Reasoning and Problem Solving

Round Decimals - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of rounding decimals.

decimal rounding problem solving

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What's included in the pack? Round Decimals Reasoning and Problem Solving worksheet Answer sheet

National Curriculum Objectives:

  • (6F10)  Solve problems which require answers to be rounded to specified degrees of accuracy

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decimal rounding problem solving

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COMMENTS

  1. Round decimals word problems (practice)

    Round decimals word problems. Emma says the length of her favorite movie is 120 minutes, but she has rounded the time to the nearest ten. Which could be the number of minutes of Emma's favorite movie before she rounded it? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history ...

  2. Rounding Decimals Worksheet Challenges

    Here you will find our Rounding Decimals Worksheet Challenges to help your child apply their skills to round decimals to the nearest 1, tenth or 2 decimal places by the Math Salamanders. ... apply their rounding knowledge to solve problems; solve mathematical problems; develop children's vocabulary and understanding of the properties of numbers.

  3. Rounding Decimals (examples, solutions, videos)

    The rules for rounding decimals are the same as the rules for whole numbers. Step 1: Decide on the place the number is to be rounded to. Step 2: Look at the first digit to the right of that place. Step 3: If the digit is equal to or more than 5, round up. Step 4: If the digit is less than 5, round down. Step 5: We may drop the zeros.

  4. Rounding Numbers Worksheet

    Online Rounding Practice Zone. In our Rounding Practice zone, you can practice rounding a range of numbers. You can round numbers to the nearest 10, 100 or even 1000. Want to round numbers to the nearest decimal place, you can do that too! Select the numbers you want to practice with, and print out your results when you have finished.

  5. Solving Decimal Word Problems

    Step 1: Step 2: The least decimal is 9.75. Now we must determine how 9.75 compares with the winning score. Answer: The last swimmer must get a score less than 9.75 s in order to win. Example 4: To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm.

  6. Solving More Decimal Word Problems

    Round your answer to the nearest tenth. Analysis: We will divide 956.4 by 15.9, then round the quotient to the nearest tenth. Step 1: Step 2: Answer: Rounded to the nearest tenth, the average speed of the car is 60.2 miles per hour. Summary: In this lesson we learned how to solve word problems involving decimals.

  7. Math Practice Problems

    Decimal Rounding - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded ...

  8. Rounding Decimals

    The number is 1. Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which by adding to 6 at the hundredth place, becomes 60. Hence, the number 24.361 after being rounded off to the nearest hundredth is 24.360 or 24.36.

  9. Decimals word problems

    Decimals word problems. Welcome to our page for problems with decimal numbers! Here you will find interactive practice and printable worksheets to practice solving word problems involving decimal numbers, such as problems with money, problems with real-life data, and other problems and challenges which include decimal numbers.

  10. Estimating and rounding decimals

    Estimating and rounding decimals. Year level: 7. Strand: Number. Lesson length: 60 mins. In this lesson, students draw on prior knowledge of rounding whole numbers to develop their understanding and fluency when rounding decimals and are encouraged to reason and problem-solve through a variety of contextual activities.

  11. PDF Year 5 Rounding Decimals Reasoning and Problem Solving

    National Curriculum Objectives: Mathematics Year 5: (5F7) Round decimals with two decimal places to the nearest whole number and to one decimal place. Differentiation: Questions 1, 4 and 7 (Problem Solving) Developing Complete the maze by travelling through decimal numbers (up to 1 decimal place) which round to a given whole number.

  12. Rounding Decimals

    Rounding Decimals Activities. Teach your child all about round decimals with amazing educational resources for children. These online round decimals learning resources break down the topic into smaller parts for better conceptual understanding and grasp. Get started now to make round decimals practice a smooth, easy and fun process for your child!

  13. Topic B: Decimal Word Problems

    Estimate the answer to the problem. Round the numbers so you can work with them quickly. Use the operation you chose in Step 3 and come to a quick answer. Does this estimated answer make sense? Does it answer the question of the problem? Think carefully before you do Step 5. Step 5: Solve. Solve the problem using the actual numbers. Check your ...

  14. Reasoned Rounding

    Reasoned Rounding printable sheet. This is a rounding game for two players. You will need a recording sheet shared between the two players. One sheet is enough for three games. The first player rolls a 0-9 dice twice and chooses which two-digit number they would like to make from the numbers rolled. They then round this number to the nearest 10 ...

  15. Rounding Practice Questions

    The Corbettmaths Practice Questions on Rounding. Previous: Similar Shapes Area/Volume Practice Questions

  16. Decimals Worksheets

    On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value.

  17. Art of Problem Solving

    This article focuses on the non-integer real-numbers. Decimal can also refer to base ten number system. A decimal is a number that is not an integer and is expressed in neither fraction or percent form. The whole number portion is separated from the fractional portion by a decimal point (.) which looks identical to a period.

  18. Round Decimals

    Round Decimals - Reasoning and Problem Solving. This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of rounding decimals.

  19. Rounding Numbers Calculator

    If your number to round is negative you can round the digits as you would for rounding a positive number. For positive numbers: Numbers less than the halfway point between 2 and 3, which is 2.5, round down, toward 0. Numbers greater than or equal to the halfway point between 2 and 3 round up, away from 0. 2.4 rounds down to 2; 2.48 rounds down to 2

  20. Decimals Reasoning and Problem Solving

    Decimals Reasoning and Problem Solving. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity. File previews. pdf, 394.64 KB. These problems will give your Year 6 pupils the opportunity to reason and solve problems with decimals. This is a sample resource. For a full year's worth of reasoning and problem solving for Year 6 ...