Fraction to Decimal Calculator
Divide the numerator by the denominator, and know what you will get.
The method
A fraction is a division. 5/8 means 5 ÷ 8, which is 0.625. That is the whole conversion — the fraction bar and the division sign mean the same thing.
Terminating or repeating
Reduce the fraction, then look at the denominator's prime factors. If they are only 2s and 5s, the decimal terminates. Anything else and it repeats forever.
| Fraction | Denominator factors | Decimal |
|---|---|---|
| 5/8 | 2 × 2 × 2 | 0.625, terminates |
| 3/20 | 2 × 2 × 5 | 0.15, terminates |
| 1/3 | 3 | 0.333…, repeats |
| 5/6 | 2 × 3 | 0.8333…, repeats |
| 1/7 | 7 | 0.142857…, repeats with period 6 |
Why 2 and 5
A terminating decimal is a fraction whose denominator is a power of ten. Ten factorises as 2 × 5, so a denominator can be scaled to a power of ten only if it contains nothing but 2s and 5s. A 3 or a 7 can never be cleared.
Long division still matters
Doing it by hand shows where the repetition comes from: once a remainder repeats, the digits must repeat too. Since the remainders dividing by n are limited to 0 through n−1, any non-terminating decimal has to start cycling within n steps — which is why 1/7 has a period of exactly 6.