Decimal to Fraction Calculator
Turn any decimal into a fraction in lowest terms — with the work shown, just like you would write it out. Repeating decimals are handled too: type 0.33... or 0.1(6) and the calculator applies the nines method. A fraction-to-decimal converter with repeating-block detection is included below.
Repeating decimals work too: type 0.33... (trailing dots) or 0.1(6) — digits in parentheses repeat.
Fraction
3/8
Improper fraction
3/8
The work
- 0.375 = 375/1,000 (3 decimal places → denominator 1,000)
- GCD(375, 1,000) = 125
- 375 ÷ 125 = 3 and 1,000 ÷ 125 = 8 → 3/8
Fraction to decimal
Exact decimal
0.41(6)
Rounded
0.416667
The digits in parentheses repeat forever: 0.41666…
How the conversion works
A terminating decimal converts in two moves. Write the decimal digits over a power of ten, then simplify with the greatest common divisor: 0.75 = 75/100, and since GCD(75, 100) = 25, dividing both gives 3/4.
Repeating decimals need the nines method. For 0.1(6) — that is, 0.1666... — subtract the non-repeating digits from all the digits: 16 − 1 = 15. The denominator gets one 9 for each repeating digit and one 0 for each non-repeating digit: 90. So 0.1666... = 15/90 = 1/6 exactly. Whether a fraction terminates or repeats is decided entirely by its denominator: only prime factors 2 and 5 give a terminating decimal (the 2ᵃ·5ᵇ rule).
Common decimal–fraction conversions
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.125 | 1/8 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.375 | 3/8 |
| 0.4 | 2/5 |
| 0.5 | 1/2 |
| 0.6 | 3/5 |
| 0.625 | 5/8 |
| 0.666... | 2/3 |
| 0.75 | 3/4 |
| 0.8 | 4/5 |
| 0.875 | 7/8 |
More math calculators
Once you have a fraction, the fraction calculator adds, subtracts, multiplies, and divides fractions for you, and the percentage calculator handles the decimal-to-percent side. The repeating decimals here come straight from division — see how in the long division calculator. Also useful for homework: the percent change calculator, slope calculator, and z-score calculator.