About Decimal to Fraction
Fractions, decimals and percentages describe the same thing in three different languages: a share of a whole. School marks and discounts use percentages, measurements and money use decimals, and recipes, spanners and shares of ownership stay in fractions.
This page converts decimals to fractions and shows the working, so the method is clear the next time you have to do it on paper. Mixed numbers such as 1 1/2 are accepted, and repeating decimals are matched to the closest simple fraction rather than left as a long string of digits.
How it works
A fraction, a decimal and a percentage are three ways of writing the same quantity. Turning decimals into fractions takes three steps:
- Write the decimal over a power of ten — 0.375 becomes 375/1000.
- Divide both numbers by their greatest common divisor.
- Repeating decimals are matched to the closest simple fraction, so 0.3333 becomes 1/3.
Going the other way is Fraction to Decimal.
Examples
Worked examples:
- 0.375 → 375/1000 → divide by 125 → 3/8
- 0.2 → 2/10 → 1/5
- 0.3333 → closest simple fraction → 1/3
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 1/10 | 0.1 | 10% |
| 1/16 | 0.0625 | 6.25% |
Decimal to Fraction: frequently asked questions
- How do you convert a decimal to a fraction?
- Count the decimal places, write the digits over 10, 100, 1000 and so on, then divide top and bottom by their greatest common divisor. 0.125 = 125/1000 = 1/8.
- How do you convert a repeating decimal to a fraction?
- For a single repeating digit, put it over 9: 0.333… = 3/9 = 1/3. Two repeating digits go over 99: 0.4545… = 45/99 = 5/11.
- What is 0.6 as a fraction?
- 0.6 = 6/10 = 3/5.