Decimal to Fraction Calculator
Type a decimal and get the exact fraction. For a repeating decimal, put the repeating digits in brackets: 0.(3) for 0.333…, 0.1(6) for 0.1666…, 2.(142857) for 2.142857142857…
Answer
Step by step
- There are 3 digits after the decimal point, so write it over 1,000: 625/1000.
- Simplify: divide the top and bottom by their greatest common factor, 125: 625/1000 = 5/8.
Answer: 5/8
Still stuck? Ask the tutor about these steps
How it works
0.abc = abc / 1000, then simplifyx = 0.(ab) → 100x − x = ab → x = ab/99Read the decimal aloud using place value: 0.625 is “six hundred twenty-five thousandths”, which is 625/1000. The number of decimal places tells you how many zeros go on the bottom.
Simplify by dividing the top and bottom by their greatest common factor: 625/1000 ÷ 125 = 5/8.
Repeating decimals never end, so place value alone can’t catch them. Instead call the number x, multiply by a power of ten so the repeating part lines up, and subtract — the endless tail cancels out.
Your calculator display may show 0.3333333333, which looks like it ends; it doesn’t. If you know it repeats, enter it with brackets for an exact answer.
0.625 = 625/1,000 = 5/8 (÷ 125)
Read it as “625 thousandths” — the place name of the last digit is the denominator.
Worked example
Convert 0.625 to a fraction.
- 3 decimal places → over 1000: 625/1000
- GCF(625, 1000) = 125
- 625 ÷ 125 = 5, 1000 ÷ 125 = 8 → 5/8
Common fractions, decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3̅ | 33.3̅% |
| 2/3 | 0.6̅ | 66.6̅% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.16̅ | 16.6̅% |
| 5/6 | 0.83̅ | 83.3̅% |
| 1/7 | 0.1̅4̅2̅8̅5̅7̅ | 14.2̅8̅5̅7̅1̅4̅% |
| 2/7 | 0.2̅8̅5̅7̅1̅4̅ | 28.5̅7̅1̅4̅2̅8̅% |
| 3/7 | 0.4̅2̅8̅5̅7̅1̅ | 42.8̅5̅7̅1̅4̅2̅% |
| 4/7 | 0.5̅7̅1̅4̅2̅8̅ | 57.1̅4̅2̅8̅5̅7̅% |
| 5/7 | 0.7̅1̅4̅2̅8̅5̅ | 71.4̅2̅8̅5̅7̅1̅% |
| 6/7 | 0.8̅5̅7̅1̅4̅2̅ | 85.7̅1̅4̅2̅8̅5̅% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/9 | 0.1̅ | 11.1̅% |
| 2/9 | 0.2̅ | 22.2̅% |
| 4/9 | 0.4̅ | 44.4̅% |
| 5/9 | 0.5̅ | 55.5̅% |
| 7/9 | 0.7̅ | 77.7̅% |
| 8/9 | 0.8̅ | 88.8̅% |
| 1/10 | 0.1 | 10% |
| 3/10 | 0.3 | 30% |
| 7/10 | 0.7 | 70% |
| 9/10 | 0.9 | 90% |
| 1/11 | 0.0̅9̅ | 9.0̅9̅% |
| 2/11 | 0.1̅8̅ | 18.1̅8̅% |
| 3/11 | 0.2̅7̅ | 27.2̅7̅% |
| 4/11 | 0.3̅6̅ | 36.3̅6̅% |
| 5/11 | 0.4̅5̅ | 45.4̅5̅% |
| 6/11 | 0.5̅4̅ | 54.5̅4̅% |
| 7/11 | 0.6̅3̅ | 63.6̅3̅% |
| 8/11 | 0.7̅2̅ | 72.7̅2̅% |
| 9/11 | 0.8̅1̅ | 81.8̅1̅% |
| 10/11 | 0.9̅0̅ | 90.9̅0̅% |
| 1/12 | 0.083̅ | 8.3̅% |
| 5/12 | 0.416̅ | 41.6̅% |
| 7/12 | 0.583̅ | 58.3̅% |
| 11/12 | 0.916̅ | 91.6̅% |
A bar over digits means they repeat forever: 0.3̅ = 0.333…
Frequently asked questions
How do you convert a decimal to a fraction?
Write the digits after the point over 10, 100, 1000… (one zero per decimal place), then simplify. 0.45 = 45/100 = 9/20.
How do I convert a repeating decimal like 0.333…?
Let x = 0.333…; then 10x = 3.333…; subtract to get 9x = 3, so x = 3/9 = 1/3. Enter it here as 0.(3).
What is 0.75 as a fraction?
0.75 = 75/100 = 3/4.
What about decimals greater than 1?
They work the same way. 2.25 = 225/100 = 9/4, which is 2 1/4 as a mixed number.