Decimals to fractions, including recurring ones
Convert a decimal — terminating or recurring — into its simplest fraction, or go the other way from a fraction to its decimal form, with the tool identifying whether the decimal terminates or repeats forever and marking the repeating block.
How to use
- Choose decimal-to-fraction or fraction-to-decimal
- Enter the decimal (recurring digits in parentheses, like 0.1(6)) or the numerator and denominator
- Read the simplified result, with the algebraic working shown below
Common questions
Can I enter a recurring decimal, like 0.1666...?
Yes — use the repeating-digit notation 0.1(6), with the repeating part in parentheses. The tool uses the classic algebraic trick (multiplying by powers of ten and subtracting) to turn it into an exact fraction rather than approximating it.
How does converting a fraction to a decimal show whether it repeats?
It performs long division and tracks every remainder seen; the moment a remainder repeats, the digits between the two sightings are marked as the recurring block with an overline, and the result also says whether the decimal terminates or repeats forever.
Is there a digit limit?
Up to 15 digits (decimal places, or the repeating block length) — beyond that the conversion is no longer guaranteed to be exact, so longer input is declined rather than silently rounded.