Fraction to Decimal Calculator
Divide the numerator by the denominator — this tool does it exactly and marks any digits that repeat forever.
Convert a fraction
How it works
decimal = numerator ÷ denominator
Long division either ends (a terminating decimal) or falls into a repeating cycle. A fraction in lowest terms terminates only when its denominator has no prime factors other than 2 and 5 — that is why 5/8 = 0.625 ends, but 1/3 = 0.333… and 1/7 = 0.142857142857… repeat.
Worked example
Convert 5/8
- Divide: 5 ÷ 8 = 0.625
- The denominator 8 = 2 × 2 × 2, so the decimal terminates
- As a percentage: 0.625 × 100 = 62.5%
5/8 = 0.625 = 62.5%
Reading repeating decimals
The repeating block is shown in brackets: 0.1(6) means 0.1666…, and 0.(142857) means 0.142857142857… In print this is often written with a bar over the repeating digits.
Common conversions
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.(3) |
| 1/4 | 0.25 |
| 1/5 | 0.2 |
| 1/6 | 0.1(6) |
| 1/8 | 0.125 |
| 1/9 | 0.(1) |
| 1/10 | 0.1 |
See the full fraction to decimal chart for denominators up to 16 and 32nds.