New: print a decimal number line in tenths with hundredths tick marks.
Decimals worksheets to print (PDF)
These decimals worksheets are a sample of the 19 printable PDFs in this section, from tenths and hundredths to adding decimals. Click a picture for the PDF, or open one of the sets below.
Decimals are fractions in disguise
0.3 is another way to write 3/10, and 0.47 is 47/100. The decimal point marks where whole numbers end and parts begin, and each place to the right is ten times smaller: tenths, then hundredths, then thousandths. Grade 4 children connect decimals to fractions with denominators of 10 and 100 (Common Core 4.NF.C.6) and grade 5 children add, subtract and round decimals (5.NBT).
The big misconception
Many children think 0.38 is bigger than 0.4 because 38 is bigger than 4. Shading a hundred grid shows the truth: 0.4 is 40 hundredths, more than 38 hundredths. Our comparing worksheet includes plenty of these on purpose.
What is in the decimals worksheets
There are 19 decimals worksheets in four sets for grades 4 and 5, each with an answer key:
- Tenths and hundredths (Grade 4, 7 worksheets)
- Decimal place value (Grades 4 and 5, 3 worksheets)
- Comparing and rounding decimals (Grades 4 and 5, 4 worksheets)
- Adding and subtracting decimals (Grade 5, 5 worksheets)
Tenths and hundredths worksheets: from fractions to decimals
The first step in decimals is to see that a decimal is a fraction written in a new way. A tenth is one of ten equal parts, so 1/10 is 0.1. A hundredth is one of a hundred equal parts, so 1/100 is 0.01. Tenths and hundredths worksheets use a ten-by-ten grid, where one column is 0.1 and one small square is 0.01:
| Fraction | Decimal | Read as |
|---|---|---|
| 1/10 | 0.1 | one tenth |
| 2/10 | 0.2 | two tenths |
| 3/10 | 0.3 | three tenths |
| 4/10 | 0.4 | four tenths |
| 5/10 | 0.5 | five tenths |
| 6/10 | 0.6 | six tenths |
| 7/10 | 0.7 | seven tenths |
| 8/10 | 0.8 | eight tenths |
| 9/10 | 0.9 | nine tenths |
| 47/100 | 0.47 | forty-seven hundredths |
| 5/100 | 0.05 | five hundredths |
Grade 4 children connect decimals with fractions with denominators of 10 and 100 (4.NF.C.6), and they learn to write 3/10 as 30/100 (4.NF.C.5).
Decimal worksheets grade 4: place value to thousandths
Each place to the right of the decimal point is ten times smaller than the place before it. These decimal worksheets for grade 4 and 5 use a place value chart, which shows the value of each digit in 47.358:
| Place | Value | Example in 47.358 |
|---|---|---|
| Tens | 10 | 4 tens = 40 |
| Ones | 1 | 7 ones = 7 |
| Decimal point | separates whole numbers from parts | . |
| Tenths | 0.1 or 1/10 | 3 tenths = 0.3 |
| Hundredths | 0.01 or 1/100 | 5 hundredths = 0.05 |
| Thousandths | 0.001 or 1/1,000 | 8 thousandths = 0.008 |
Expanded form shows the same idea: 47.358 = 40 + 7 + 0.3 + 0.05 + 0.008. Wikipedia’s decimal article describes the system in more detail.
Comparing decimals worksheets: make the places match
The common mistake is to think that the decimal with more digits is larger. The fix is to give both numbers the same number of decimal places by adding zeros, which does not change their value. Then compare them as if they were whole numbers. Comparing decimals worksheets include pairs where the longer decimal is smaller on purpose:
| Compare | Make the same number of places | Sign |
|---|---|---|
| 0.4 and 0.38 | 0.40 and 0.38 | > |
| 0.5 and 0.5 | 0.50 and 0.50 | = |
| 3.07 and 3.7 | 3.07 and 3.70 | < |
| 0.9 and 0.09 | 0.90 and 0.09 | > |
| 12.5 and 12.45 | 12.50 and 12.45 | > |
| 0.25 and 0.25 | 0.25 and 0.25 | = |
In the first pair, 0.40 is 40 hundredths and 0.38 is 38 hundredths, so 0.4 > 0.38. Children can shade a hundred grid to see it.
Rounding decimals
To round a decimal, look at the digit to the right of the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, keep the digit. The table shows five examples:
| Number | Round to | Look at | Answer |
|---|---|---|---|
| 3.746 | the nearest tenth | 4 | 3.7 |
| 3.746 | the nearest hundredth | 6 | 3.75 |
| 0.349 | the nearest tenth | 4 | 0.3 |
| 12.05 | the nearest tenth | 5 | 12.1 |
| 7.995 | the nearest hundredth | 5 | 8.00 |
The number 12.05 rounded to the nearest tenth is 12.1, because the digit to the right is exactly 5. Rounding decimals is part of grade 5 (5.NBT.A.4).
Adding decimals worksheets: line up the decimal points
Adding decimals worksheets give problems like 3.4 + 2.75. The rule is to write the numbers with the decimal points in a line, so tens line up with tens and tenths with tenths. Add zeros to fill the empty places, then add as with whole numbers, and bring the decimal point straight down:
3.40 + 2.75 ------ 6.15
Subtraction works the same way: 8.2 − 3.45 becomes 8.20 − 3.45 = 4.75. Money is a good place to practice, because dollars and cents are decimals: $3.40 + $2.75 = $6.15. Grade 5 children add and subtract decimals to hundredths (5.NBT.B.7).
Common fractions as decimals
Some fractions are worth knowing as decimals. The table shows ten of them, and which ones end and which ones repeat:
| Fraction | Decimal | Percent | Does it end? |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Yes |
| 1/4 | 0.25 | 25% | Yes |
| 3/4 | 0.75 | 75% | Yes |
| 1/5 | 0.2 | 20% | Yes |
| 1/8 | 0.125 | 12.5% | Yes |
| 3/8 | 0.375 | 37.5% | Yes |
| 1/3 | 0.3… | 33.3% | No, it repeats |
| 2/3 | 0.6… | 66.7% | No, it repeats |
| 1/10 | 0.1 | 10% | Yes |
| 1/20 | 0.05 | 5% | Yes |
A fraction ends as a decimal when its denominator has only the prime factors 2 and 5, which is why 1/8 = 0.125 ends and 1/3 = 0.333… repeats forever.
Frequently asked questions
2 quick answers
How do you read 0.47?
Say “forty-seven hundredths”, which also tells you the fraction: 47/100.
Is 0.5 the same as 0.50?
Yes. 5 tenths is the same as 50 hundredths. Adding a zero at the end of a decimal does not change its value.