A decimal fraction is a fraction whose denominator is 10, 100, 1000 or any other power of ten. 7/10 and 45/100 are decimal fractions. 3/8 is not, but it can be rewritten as 375/1000, and that is what lets you write it as 0.375. The guide to terminating decimal fractions explains which denominators give a terminating decimal. Here 0.75 is written with a decimal point; many other countries write 0,75 with a comma. The decimal to fraction calculator accepts both.
| Fraction | Is it a decimal fraction? | Decimal notation |
|---|---|---|
| 3/10 | Yes, the denominator is already 10 | 0.3 |
| 75/100 | Yes | 0.75 |
| 3/4 | No, but it equals 75/100 | 0.75 |
| 5/8 | No, but it equals 625/1000 | 0.625 |
| 1/3 | No, and no equivalent fraction is one either | 0.3̅, which never ends |
The table separates three situations: fractions that already are decimal fractions, fractions that can be converted into one, and fractions that have no equivalent decimal fraction. The rest of the guide goes through all three.
What tenths, hundredths and thousandths are worth
Each digit after the decimal point has a name and a denominator. The first place is tenths (1/10), the second hundredths (1/100) and the third thousandths (1/1000). Each place is worth ten times less than the one to its left, just as with whole numbers: ten thousandths make one hundredth, and ten hundredths make one tenth.
That is why the number of decimal places sets the denominator. One digit calls for a denominator of 10, two call for 100, and three call for 1000. In 0.375 there are 3 tenths, 7 hundredths and 5 thousandths, and the sum 3/10 + 7/100 + 5/1000 equals 300 + 70 + 5 = 375 thousandths.
How to turn a decimal into a fraction
Count the decimal places, write the number without the point over a 1 followed by that many zeros, and simplify with the GCF (greatest common factor, also called GCD or HCF), the largest number that divides both numerator and denominator.
Worked example: 0.375
Write 0.375 as a decimal fraction and as a fraction in lowest terms.
- Count the decimal places. There are three, so the denominator is 1000.
- Remove the decimal point. The numerator is 375, and the decimal fraction is 375/1000.
- Find the GCF. GCF(375, 1000) = 125.
- Divide top and bottom by 125. 375 ÷ 125 = 3 and 1000 ÷ 125 = 8.
Result: 3/8.
Check: 3 ÷ 8 = 0.375, the number you started with.
Zeros at the end do not change the value. So 0.50 is 50/100 = 1/2, just like 0.5. A zero right after the decimal point does count as a digit. In 2.05 there are two decimal places, so the fraction is 205/100 = 41/20, not 25/10. If the number has a whole-number part, like 2.375, write everything without the point: 2375/1000 = 19/8.
How to turn a fraction into a decimal fraction
If the denominator is not a power of ten, build up to an equivalent fraction. Multiply numerator and denominator by the same number until you reach 10, 100 or 1000. For 3/4 you need to turn the 4 into 100, and 4 × 25 = 100.
3/4 = (3 × 25)/(4 × 25) = 75/100 = 0.75
Multiplying by 25/25 is multiplying by 1, so the value does not change; only the size of the parts does: fourths become hundredths. With 7/20 you multiply by 5 and get 35/100. With 5/8 you multiply by 125 and get 625/1000.
Building up to an equivalent fraction and simplifying are the same operation in opposite directions, and the page on equivalent fractions compares them.
Percents are hundredths
A percent is a decimal fraction with denominator 100, so 25% means 25 out of every 100, that is, 25/100 = 1/4. If the percent has a decimal in it, multiply top and bottom by 10 before simplifying. So 12.5% = 12.5/100 = 125/1000 = 1/8. The fraction to percent and percent to fraction tools do the calculation in both directions.
A mistake when reading decimals: 0.5 and 0.05
When there is no equivalent decimal fraction
1/3 cannot be built up to 10, 100 or 1000, because none of those powers of ten is a multiple of 3. Its decimal 0.333… never ends, and any cutoff is an approximation: 0.333 falls 1/3000 short of 1/3. The guide to terminating and repeating decimals explains how they are written and how to convert them to fractions.
Practice the conversion
Four conversions
- Write 0.8 as a fraction in lowest terms.
- How many hundredths are in 0.37?
- Convert 7/20 into a decimal fraction.
- Convert 0.06 into a fraction in lowest terms.
Show the answers
- 8/10 = 4/5
- 37 hundredths, because 0.37 = 37/100
- 35/100, multiplying top and bottom by 5
- 6/100 = 3/50
Where to go next
To convert a specific decimal, the decimal to fraction calculator returns the fraction in lowest terms. For the reverse direction there is the fraction to decimal calculator. If you want the most common equivalents side by side, see the table of fractions, decimals and percents. The tool for simplifying fractions does the last step of every example.