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Decimal Word Problem Worksheets

Extensive decimal word problems are presented in these sets of worksheets, which require the learner to perform addition, subtraction, multiplication, and division operations. This batch of printable decimal word problem worksheets is curated for students of grade 3 through grade 7. Free worksheets are included.

Adding Decimals Word Problems

Decimal word problems presented here help the children learn decimal addition based on money, measurement and other real-life units.

• Download the set

Subtracting Decimals Word Problems

These decimal word problem worksheets reinforce the real-life subtraction skills such as tender the exact change, compare the height, the difference between the quantities and more.

Decimals: Addition and Subtraction

It's review time for grade 4 and grade 5 students. Take these printable worksheets that help you reinforce the knowledge in adding and subtracting decimals. There are five word problems in each pdf worksheet.

Multiplying Decimals Whole Numbers

Reduce the chaos and improve clarity in your decimal multiplication skill using this collection of no-prep, printable worksheets. A must-have resource for young learners looking to ace their class!

Decimal Division Whole Numbers

Revive your decimal division skills with a host of interesting lifelike word problems involving whole numbers. Keep up with consistent practice and you’ll fly high in the topic in no time!

Multiplying Decimals Word Problems

Each decimal word problem involves multiplication of a whole number with a decimal number. 5th grade students are expected to find the product and check their answer using the answer key provided in the second page.

Dividing Decimals Word Problems

These division word problems require children to divide the decimals with the whole numbers. Ask the 6th graders to perform the division to find the quotient by applying long division method. Avoid calculator.

Decimals: Multiplication and Division

These decimal worksheets emphasize decimal multiplication and division. The perfect blend of word problems makes the grade 6 and grade 7 children stronger in performing the multiplication and division operation.

Related Worksheets

» Fraction Word Problems

» Ratio Word Problems

» Division Word Problems

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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

Grids and Charts Useful for Learning Decimals

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

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

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.

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

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

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

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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How to Perform Operations of Decimals: Word Problems

Greetings, budding mathematicians! Today, we're going to jump into an adventure with decimals. Working with decimals is a fundamental math skill that you'll use in many aspects of life, from managing money to measuring distances.

Introduction to Decimal Operations

First things first, let’s talk about decimals. A decimal is a way of representing a number that’s less than one, or a number that’s a whole and a fraction together. When you work with decimals, the same rules apply as when you’re working with whole numbers, but the decimal point plays a crucial role.

There are four major operations that you can perform on decimals:

• Subtraction
• Multiplication

Now, let’s tackle some word problems involving decimal operations.

Step-By-Step Guide to Solving Word Problems with Decimal Operations

Step 1: understand the problem.

First and foremost, carefully read through the problem. Identify what you know and what you need to find out.

Step 2: Plan the Solution

Next, decide which operation (addition, subtraction, multiplication, or division) will help you solve the problem. This will depend on what the problem is asking.

Step 3: Carry Out the Operation

Perform the operation on the decimals. Remember to align the decimal points when you’re adding or subtracting, and apply the rules for multiplication and division of decimals correctly.

Step 4: Check the Answer

Finally, check if your answer makes sense in the context of the problem.

Consider this problem: Laura bought \(2.3\) kilograms of apples and \(1.5\) kilograms of grapes. How many kilograms of fruit did she buy in total?

Step 1: Understand that you know the weight of apples and grapes separately, and you need to find the total weight.

Step 2: Realize that to find the total, you need to add the weights together.

Step 3: Add the weights: \(2.3\ kg + 1.5\ kg = 3.8\ kg\).

Step 4: Check that the answer makes sense. Laura bought \(2.3\ kg\) of apples and \(1.5\ kg\) of grapes, so it makes sense that she bought \(3.8\ kg\) in total.

Keep practicing with different word problems, and you’ll get the hang of decimal operations in no time. Remember, the more you practice, the better you’ll get. Happy calculating!

by: Effortless Math Team about 10 months ago (category: Articles )

Effortless Math Team

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Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

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Calcworkshop

Decimal Word Problems Simple How-To w/ 13+ Examples!

// Last Updated: October 23, 2020 - Watch Video //

Have you ever found yourself stuck on a decimal word problem and not quite sure what to do?

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Don’t worry!

You’re in good company because we can all relate to struggling with word problems and wondering how to begin.

Steps In Solving Word Problems

The good thing is that there are steps and tools that you can use that will help to read word problems effectively and boost your confidence.

All you have to do is remember the FACTS !

How To Solve A Word Problem

• Focus on what you know and not on what you don’t know. Sometimes just looking at word problems can overwhelm us even before we’ve read a single word. The key to problem-solving, especially problem solving with decimals, is to focus on what you know.
• Actively participate . This means you need to circle or underline keywords or phrases, write down important information that the problem is presenting. Once you write down or mark up the word problem, you will quickly realize that you are always given a ton of information to work with, now you just need to …
• Choose a method and go for it! What keywords pop out at you? Does it tell you to add or subtract decimals? Multiply, divide, or compare? Maybe you need to approximate so that rounding may be the best method. Or do you need to use more than one method or operation to calculate the correct answer? What is the problem asking, and what is provided that will help you get there?
• And once you’ve chosen your method, all that’s left is to try it ! Don’t give up, even if it’s challenging. The best thing you can do is try! So, try your method of choice and locate the answer you need.
• Lastly, you need to Scrutinize your work . All this means is that you need to ask yourself, “does my answer make sense?”

Step-by-Step Example

Let’s look at an example.

Helen’s monthly salary is $5463.79.

Her monthly expenses are as follows:

• Rent $2,700
• Transportation $715.12
• Food $650.50
• Utilities $732.48
• Phone & Cable $95.96
• Insurance $156.27

After paying all of her expenses, how much money does Helen have left?

First, we FOCUS on what we know, and we become ACTIVE readers by marking up our problem and writing down keywords and phrases.

Words And Phrases To Math Symbols

Now we CHOOSE our method, which will involve two steps:

• Adding to find the sum of all of Helen’s monthly bills.
• Subtracting to see the amount leftover.

And finally, we ask ourselves, does our answer make SENSE ?

Yes, Helen has $413.46 remaining after paying all of her bills.

This video will walk you through countless examples of problem-solving using decimals, just like the one above, so that you can attack word problems (like those on IXL ) with confidence!

All you need are the FACTS!

Worksheet (PDF) — Hands on Practice

Practice solving decimal word problems with hands-on worksheets (addition, subtraction, multiplication, division) & step-by-step solutions.

Practice Problems Step-by-Step Solutions

Decimal Word Problems – Lesson & Examples (Video)

1 hr 22 min

• Introduction to Video: Problem Solving with Decimals
• 00:00:37 – Review of Keywords and Overview of Problem Solving Steps: FACTS
• 00:08:02 – Solve each one-step problem using decimals (Examples #1-4)
• 00:24:10 – Solve the one-method word problem with decimals (Examples #5-8)
• 00:46:24 – Solve the application problem using two-methods (Examples #9-10)
• 01:02:18 – Solve the decimal word problem using more than one technique (Examples #11-12)
• 01:13:36 – Solve using estimation (Examples #13-14)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Worksheet on Decimal Word Problems

Solve the questions given in the worksheet on decimal word problems at your own space. This worksheet provides a mixture of questions on decimals involving order of operations i.e., addition, subtraction, multiplication and division.

1.  Aaron scored 452.65 marks out of 600 in the final examination. How many marks did he lose?

2.  Amy had 0.87 litre of cold drink.  Flora  had 0.92 litres more cold drink. How much cold drink did Manu have?

3.  The weight of a baby elephant was 218.99 kg. After two years, his weight increased by 109.85 kg. Find the weight of elephant after two years.

4.   Kathi  had a rope of 63.45 m. She cut the rope into two pieces. If the length of one piece was 23.59 m, what was the length of the other piece?

5.  Each side of a regular polygon is 5.2 m and its perimeter is 36.4 m. Find the number of sides of the polygon.

6. Trisha took 3.25 minutes to complete the race and Rachel took 3.207 minutes to complete the race. Who won the race?

7. The annual rainfall received by Arunachal Pradesh is 278.2 cm and that by Assam is 281.8 cm. Who received less rainfall?

8. Sharon’s height is 145.62 cm. She stands on a tool of height 10.50 cm. What is the combined height now?

9. The milkman delivers 5.02 liter of milk to a house in the morning and 2.120 liter in the evening. What is the total quantity of milk delivered by the milkman?

10. Rebecca ‘s kite is flying at a height of 17.2 m and Shelly’s at a height of 21.5 m from the ground. Whose kite is flying high and by how much?

11. A car travels 367.80 km in 6 hours. How much distance will it travel in 1 hour?

12. Ron jogged 2.2 km, Mike jogged 3.7 times more distance than Ron. Find the distance covered by Mike.

13. The daily consumption of milk in a house is 3.25 litres. How much milk will be consumed in 30 days?

14. A tin contains 18.5 litre of oil. How many such tin contain 129.5 litre of oil?

15. Find the cost of 47.2 m cloth if the cost of 1 m cloth is $33.90.

16. Shruti bought a bag for $298.05. She gave the shopkeeper 2 notes of $200. How much money will she get back?

17. A tailor needs 35.25 m of cloth for the shirts and 45.80 m for trousers. How much cloth does the tailor need in all?

18. A spool of thread has a thread measuring 86.50 m. If 42.33 m thread has been cut, what length of thread is still left in the spool?

19. The cost of a chair is $2045.83. Tania wants to buy 6 chairs for her house. How much money will she pay to the shopkeeper?

20. David has a jug full of milk. He pours the complete milk in 4 glasses, each glass of capacity 0.8 l. How much milk was there in the jug?

21. Find the area of a square whose side is 3.60 m.

22. The weight of 1 bag of sugar is 12.5 kg. What is the weight of 15 such bags?

23. A vehicle covers a distance of 48.3 km in 2.3 litre of petrol. How much distance will it cover in 1 litre of petrol?

24. Ron has 3.60 l of juice. He pours it into 9 glasses equally. How much juice is there in each glass?

25. Shelly has a ribbon of length 35.14 m. She cuts it into 7 equal parts. What is the length of each equal part?

26. The cost of 5 pens is $140.50. What is the cost of 1 pen?

27. The weight of a box is 150.094 kg. What will be the weight of 27 such boxes?

28. Sonia has 14.84 l of juice. She pours it into 7 jars equally. How much juice is there in each jar?

Answers for the   worksheet on decimal word problems  are given below to check the exact answer of the above problems.

1.  147.35 marks

2.  1.79 litres

3.  328.84 kg

4.  39.86 m

5.  7 sides

6.  Rachel

7.  Arunachal Pradesh

8.  156.12

9.  7.145 liter

10.  Shelly, 4.3 m

11.  61.3 km

12.  8.14 km

13.  97.5 litres

14.  7 tin

15.  $1600.08

16.  $101.95

17.  81.05 m

18.  44.17 m

19.  $12,274.98

20.  3.2 l

21.  12.96 m 2 

22.  187.5 kg

23.  21 km

24.  0.4 l

25.  5.02 m

26.  $28.10

27.  4052.538 kg

28.  2.12 l

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Decimal Worksheets

Conversion :: Addition :: Subtraction :: Multiplication :: Division

Conversion to Decimal

Subtraction, multiplication.

Decimals Questions

The decimals questions and answers on this page may assist students in quickly learning the concept. Several questions in almost all competitive and board examinations are based on the idea of “Decimals”. These questions can be used by students to get a rapid overview of the topics and to practice them so that they better comprehend the concept. Double-check your answers by studying the whole explanations for each question. Click here to read more about decimals .

Below are some decimals questions and answers for you to study and practice.

Decimals Questions with Solutions

1. Find the value of 29.94 ÷ 1.45, if 2994 ÷ 14.5 = 172.

Given that, 2994 ÷ 14.5 = 172

29.94/1.45 can be written as 299.4/14.5

Again, 299.4 /14.5 is written in the form as follows:

= [(2994/14.5)×(1/10)

Now, substitute 2994 ÷ 14.5 = 172

= 172 × (1/10)

Hence, the value of 29.94 ÷ 1.45 is 17.2.

2. Simply the value [489.1375 × 0.0483 × 1.956]/[0.0873 × 92.581 × 99.749], and then find the value closest to it.

Now, write the given values rounded to its nearest value.

= 489/(9 × 93 × 10)

= (163/279) × (1/10)

= 0.58/10 = 0.058, which is approximately equal to 0.06.

Hence, the value closest to the expression [489.1375 × 0.0483 × 1.956]/[0.0873 × 92.581 × 99.749] is 0.06.

3. 11.98 × 11.98 + 11.98 × x + 0.02 × 0.02 should be a perfect square for “m” equal to:

Given expression: (11.98 × 11.98 + 11.98 × m + 0.02 × 0.02)

11.98 × 11.98 + 11.98 × m + 0.02 × 0.02 = (11.98) 2 + (0.02) 2 + 11.98 × m.

For the expression to be a perfect square, we should have,

11.98 × m = 2 × 11.98 × 0.02

11.98 × m = 0.4792

Hence, m = 0.4792/11.98

Thus, 11.98 × 11.98 + 11.98 × m + 0.02 × 0.02 should be a perfect square for “m” equal to 0.04.

4. Find the unknown value in the given equation: 3889 + 12.952 – ? = 3854.002

Let the unknown value be a.

Thus, 3889 + 12.952 – a = 3854.002.

Rearranging the above equation, we can write

a = (3889 + 12.952) – 3854.002

a = 3901.952 – 3854.002

Thus, the unknown value is 47.95.

5. Convert the given fractions into decimals and arrange them in ascending order: 1/4, 1/7, 3/4, 6/2, 1/2.

First convert the fractions into decimals.

1/7 = 0.143

Now, arrange the decimal values in the ascending order :

0.143, 0.25, 0.5, 0.75, 3.

6. Find the quotient if 4.036 is divided by 0.04.

Given fraction: 4.036/0.04

Now, multiply the fraction’s numerator and denominator by 100.

4.036/0.04 = 403.6/4 = 100.9.

Thus, 4.036 divided by 0.04 gives 100.9.

7. What is the equivalent of 0.002 × 0.5?

Given expression: 0.002 × 0.5

On simplifying the expression 0.002 × 0.5, we get;

0.002 × 0.5 = 0.001.

8. Write the decimal number for “Fifty Seven and Twenty Three One-Hundredths”.

Fifty-Seven and Twenty Three One-Hundredths is written in the form 57 + (23/100)

Now, simply the above value,

= 57 + 0.23

Hence, Fifty Seven and Twenty Three One-Hundredths in decimal form is 57.23.

9. Jack biked 1.2 miles. Then he ran 0.75 mile. How far did Jack go?

Given: Distance travelled by jack = 1.2 + 0.75 = 1.95.

Hence, the total distance travelled by Jack = 1.95 miles.

10. Convert the fraction 43/100 into decimal form.

To convert the fraction into a decimal, divide the fraction’s numerator by the denominator,

43/100 = 0.43

Hence, the fraction 43/100 is written in decimal form as 0.43.

Practice Questions

• Simply the value: 0.04 × 0.0162.
• Find the value of a, if 0.152 × a = 0.189392
• Find the value of 617 + 6.017 + 0.617 + 6.0017.

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Decimal Word Problems Worksheets

Decimal word problem worksheets help students gain a clear understanding of decimals and word problems based on them. The decimal number system is a standardized number system that denotes any integer or non-integer value. This math topic has great significance in many real-life applications like calculating money, weight, length, and many more. By solving the problems available in these worksheets, students will attain step by step understanding and clarity on how to solve decimal word problems.

Benefits of Decimal Word Problems Worksheets

Decimal word problem worksheets provide a comprehensive and precise understanding of decimal word problems. These worksheets offer a wide variety of questions geared towards improving a child's conceptual fluency on decimals.

These worksheets are well-curated to help students gradually solve the rising difficulty level of questions. The primary purpose of these worksheets is to promote a problem-solving mindset in students.

Download Decimal Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

☛ Check Grade wise Decimal Worksheets

• 4th Grade Decimals worksheets
• Decimals worksheets for Grade 5

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Course: 5th grade   >   Unit 1

• Rounding decimals on the number line
• Round decimals using a number line
• Worked example: Rounding decimals to nearest tenth
• Round decimals
• Understand decimal rounding
• Rounding decimals word problems

Round decimals word problems

• Decimal place value: FAQ
• (Choice A)   111.25 ‍   A 111.25 ‍  
• (Choice B)   124.9 ‍   B 124.9 ‍  
• (Choice C)   115.95 ‍   C 115.95 ‍  

Decimal Word Problems (1-Step Word Problem)

In these lessons, we will learn to use block models (or tape diagrams, bar models) to visualize and solve decimal work problems.

Related Pages More Word Problems Decimal Worksheets More Singapore Math

Here are some examples of decimal word problems. We will illustrate how block diagrams can be used to help you to visualize the decimal word problems in terms of the information given and the data that needs to be found. Block diagrams or bar modeling are used in Singapore Math and tape diagrams are used in Common Core Math.

Example: The length of a ribbon is 1.28 m. The length of a rope is 2.74 m longer than the ribbon. What is the length of the rope?

1.28 + 2.74 = 4.02

The length of the rope is 4.02 m.

Example: The mass of a jar of sugar is 1.9 kg. What is the total mass of 4 such jars of sugar?

1.9 × 4 = 7.6

The total mass of 4 such jars of sugar is 7.6 kg.

Example: A pail holds 5.2 l of water. A bottle holds 3.9 l less water than the pail. What is the volume of water in the bottle?

5.2 – 3.9 = 1.3

The volume of water in the bottle is 1.3 l.

Example: Susan has 4 times as much money as her sister. If Susan has $10, how much money does her sister have?

$10 ÷ 4 = $2.50

Susan’s sister has $2.50.

Decimal Word Problems: Addition, Subtraction, Multiplication, Division

• Maneesha purchased a box of pencils for $1.28 and gave the cashier $10.00. How much change should she get back?
• If you buy an ebook for $29.62 and download 5 songs for $1.29 each, what is the total amount you have spent?
• Emilio’s batting average in his first year playing baseball was 0.089. In his second year, he improved to an average of 0.29. His third year, he improved even more to an average of 0.329. What is Emilio’s average over the three years? What is the difference between the first and third year averages?
• Shanelle purchased 4 pencils for $0.28 each. If she had a $5 bill, how much money did she have left after purchasing the pencils?
• A train took 1.2 hours to go 73.8 miles from Cary to Fayetteville. Find the rate of the train.
• I have a pile of DVD’s. Each DVD has a height of 0.3 cm. If the pile is 75 cm tall, how many DVD’s are there in the pile?

Word Problems With Decimals

Solve word problems involving addition, subtraction, multiplication and division of decimal numbers.

• Matt deposits a check for $234.95 into his checking account. He now has a total of $1,479.87 in the account. How much was the account before the deposit?
• Stan compares his checkbook record with his monthly bank statement that says he has $876.47. Stan sees that checks for $32.85, $97.10 and $158.78 have not been cashed yet. How much money does Stan really have available?
• An ad for a computer system lists the price as $899.95. There is an instant rebate of $55.55 and a mail-in rebate of $66.66. What is the final price of the system after both rebates?
• At work, Amy receives $22.25 per hour for up to 40 hours per week. Any time beyond that is paid at a rate of $37.80 per hour. If she receives $1,173.50 in her paycheck, how much time did she work that week?
• The total receipts for a basketball game is $1,400 for 788 tickets sold. Adults pay $2.50 and students pay $1.25. How many tickets of each kind were sold?

Decimals Word Problem Using Block Model

Solving a 2-part decimals word problem using block modeling.

Example: David took a walk around a park twice. He took 12.4 minutes to walk the first round. In the second round, he took 3.2 fewer minutes than he did the first round. How long did David take to complete his walk altogether?

How to solve decimal word problems using tape diagrams?

The following video shows an example of a decimal word problem.

Example: Manny tracked the amount of food he ate from Monday to Friday. He ate 16.3 pounds of food. On Monday, he ate 3.2 pounds and on Tuesday, he ate 2.9 pounds. He ate an equal amount on the other three days. How much did he eat on those days?

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Decimals and Fractions Practice Questions

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Decimals Reasoning and Problem Solving

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 April 2022

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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 please see:

https://www.tes.com/teaching-resource/reasoning-and-problem-solving-for-year-6-12201133

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Watch CBS News

Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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Stormy Daniels Takes the Stand

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On today’s episode

Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

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Here are six takeaways from Ms. Daniels’s earlier testimony.

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