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
Decimal Place Value Charts
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 × 100) + (2 × 10-1) + (3 × 10-2)
Converting Decimals from Standard Form to Expanded Form Using Decimals
Converting Decimals from Standard Form to Expanded Form Using Fractions
Converting Decimals from Standard Form to Expanded Factors Form Using Decimals
Converting Decimals from Standard Form to Expanded Factors Form Using Fractions
Converting Decimals from Standard Form to Expanded Exponential Form
Retro Converting Decimals from Standard Form to Expanded Form
Retro European Format Converting Decimals from Standard Form to Expanded Form
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 to Standard Form from Expanded Form Using Fractions
Converting Decimals to Standard Form from Expanded Factors Form Using Decimals
Converting Decimals to Standard Form from Expanded Factors Form Using Fractions
Converting Decimals to Standard Form from Expanded Exponential Form
Retro Converting Decimals to Standard Form from Expanded Form
Retro European Format Converting Decimals to Standard Form from Expanded Form
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
Rounding Decimals to Tenths
Rounding Decimals to Hundredths
Rounding Decimals to Thousandths
Rounding Decimals to Various Decimal Places
European Format Rounding Decimals to Whole Numbers
European Format Rounding Decimals to Tenths
European Format Rounding Decimals to Hundredths
European Format Rounding Decimals 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 Hundredths
Comparing Decimals up to Thousandths
Comparing Decimals up to Ten Thousandths
Comparing Decimals up to Hundred Thousandths
European Format Comparing Decimals
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
European Format Ordering/Sorting Decimals
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 Between Decimals, Fraction, Percents and Ratios
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 Hundredths
Adding Thousandths
Adding Ten Thousandths
Adding Various Decimal Places
European Format Adding Decimals
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 Hundredths
Subtracting Thousandths
Subtracting Ten Thousandths
Subtracting Various Decimal Places
European Format Subtracting Decimals
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
Horizontally Arranged Subtracting Decimals
Horizontally Arranged Mixed Adding and Subtracting Decimals
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
Multiplying Decimals by 2-Digit Whole Numbers
Multiplying Decimals by Tenths
Multiplying Decimals by Hundredths
Multiplying Decimals by Various Decimal Places
Decimal Long Multiplication in Various Ranges
European Format Multiplying Decimals by 2-Digit Whole Numbers
European Format Multiplying Decimals by 2-Digit Tenths
European Format Multiplying Decimals by 2-Digit Hundredths
European Format Multiplying Decimals by Various Decimal Places
Dividing Decimals by Whole Numbers
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
These worksheets would probably be used for estimating and calculator work.
Horizontally Arranged Decimal Division
European Format Dividing Decimals with Quotients That Work Out Nicely
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 Dividing Decimals by Decimals
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)
