Decimal ↔ Fraction Converter
Convert decimals to simplified fractions (including repeating decimals like 0.333…) and fractions to decimals with the repeating part marked.
How to use
- 1Choose the direction.
- 2Enter a decimal like 0.375, or a fraction like 5/8. For repeating decimals, enter enough digits (0.3333) or use parentheses: 0.(3).
How it's calculated
Decimal → fraction: the best rational approximation by continued fractions, simplified. Fraction → decimal: long division, detecting the repeating cycle.
Frequently asked questions
How do I write a repeating decimal?
Put the repeating part in parentheses: 0.(3) for 0.333…, or 0.1(6) for 0.1666….
Why does 0.1 + 0.2 look odd in some calculators?
Binary floating point can't represent 0.1 exactly. This converter finds the exact fraction 3/10.
What about mixed numbers?
Improper fractions are also shown as mixed numbers, e.g. 7/4 = 1 3/4.