Decimals Worksheets Sub-Topics

Thanks for visiting the U.S. number format version of the decimals and percents 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 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. At the end of the page, you will find decimal numbers used in order of operations questions.

Most Popular Decimals Worksheets this Week

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 operations with 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.

Expanded form with decimals worksheets including converting from standard to expanded form and from expanded form to standard form.

For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart first, and let them use it to help them write numbers in expanded form. There are many ways to write numbers in expanded form. 1.23 could be written as 1 + 0.2 + 0.03 OR 1 + 2/10 + 3/100 OR 1 × 10^{0} + 2 × 10^{-1} + 3 × 10^{-2} OR any of the previous two written with parentheses/brackets OR 1 + 2 × 1/10 + 3 × 1/100 with or without parentheses, etc. Despite what the answer key shows, please teach any or all of the ways depending on your students' learning needs.

Rounding decimals worksheets with options for rounding a variety of decimal numbers to a variety of places.

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 to not 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 before college students round up on a 5, that is what we have done in the worksheets that follow.

Comparing and ordering decimals worksheets to help students recognize ordinality in decimal numbers.

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.

Converting decimals worksheets mainly for converting between decimals and fractions but also to percents and ratios.

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 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
OLD Converting Between Fractions, Decimals, Percents and Ratios

Adding and subtracting decimals worksheets with various difficulties including adding and subtracting by themselves and also mixed on the page.

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 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 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 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 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 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

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 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 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 Decimal Thousandths with No Integer Part
Subtracting Decimal Thousandths with an Integer Part in the Minuend and Subtrahend
Subtracting Decimal Ten Thousandths with No Integer Part
Subtracting Decimal Ten Thousandths with an Integer Part in the Minuend and Subtrahend
Subtracting Various Decimals to Hundredths
Subtracting Various Decimals to Thousandths
Subtracting Various Decimals to Ten Thousandths

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.

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

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

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 worksheets with a variety of difficulty levels.

Multiplying 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 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 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 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

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.

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)

Order of operations with decimals worksheets inlcuding worksheets that also include fractions.

2-Step Positive Decimals Order of Operations
3-Step Positive Decimals Order of Operations
4-Step Positive Decimals Order of Operations
5-Step Positive Decimals Order of Operations
6-Step Positive Decimals Order of Operations
2-Step Positive & Negative Decimals Order of Operations
3-Step Positive & Negative Decimals Order of Operations
4-Step Positive & Negative Decimals Order of Operations
5-Step Positive & Negative Decimals Order of Operations
6-Step Positive & Negative Decimals Order of Operations

2-Step Positive Decimals Order of Operations (Comma Decimal)
3-Step Positive Decimals Order of Operations (Comma Decimal)
4-Step Positive Decimals Order of Operations (Comma Decimal)
5-Step Positive Decimals Order of Operations (Comma Decimal)
6-Step Positive Decimals Order of Operations (Comma Decimal)
2-Step Positive & Negative Decimals Order of Operations (Comma Decimal)
3-Step Positive & Negative Decimals Order of Operations (Comma Decimal)
4-Step Positive & Negative Decimals Order of Operations (Comma Decimal)
5-Step Positive & Negative Decimals Order of Operations (Comma Decimal)
6-Step Positive & Negative Decimals Order of Operations (Comma Decimal)