How to convert a decimal to a fraction
- Type the decimal in the first box, such as 0.375 or 2.125.
- For a repeating decimal, put the repeating part in brackets: 0.(3) for 0.333…, 0.(142857) for 1/7, or 0.1(6) for 0.1666…
- Read the simplified fraction and the mixed number, with the steps used.
The method
For a terminating decimal, write the digits over the matching power of ten and simplify: 0.375 = 375/1000. The greatest common factor of 375 and 1000 is 125, so the fraction is 3/8. 2.125 = 2125/1000 = 17/8 = 2 1/8.
For a repeating decimal, subtract to cancel the repeating part. For 0.1666…: let x = 0.1666…; then 10x = 1.666… and 100x = 16.666…, so 90x = 15 and x = 15/90 = 1/6. The rule of thumb: the repeating digits go over as many 9s as they have digits, followed by a 0 for each non-repeating digit after the point.
| Decimal | Fraction |
|---|---|
| 0.5 | 1/2 |
| 0.25 | 1/4 |
| 0.75 | 3/4 |
| 0.2 | 1/5 |
| 0.125 | 1/8 |
| 0.333… | 1/3 |
| 0.666… | 2/3 |
| 0.1666… | 1/6 |
| 0.0625 | 1/16 |
| 0.142857… | 1/7 |
FAQ
What is 0.75 as a fraction?
3/4.
How do I convert 0.333 to a fraction?
If it means 0.333… repeating, it is 1/3 (type 0.(3)). Exactly 0.333 is 333/1000.
Can every decimal be written as a fraction?
Every terminating or repeating decimal can. Decimals that never repeat, such as π, are irrational and cannot.