About the Decimal to Fraction Converter
This tool expresses a decimal as a fraction and reduces it to lowest terms, so 0.75 becomes 3/4 and 0.125 becomes 1/8. It works from the number of decimal places, then divides top and bottom by their greatest common divisor. Convert several at once, one per line.
It is useful for schoolwork and for converting a measurement to a fraction. Exact terminating decimals give clean fractions; a rounded decimal such as 0.333 gives 333/1000 rather than 1/3, since that is literally what the decimal is. To go the other way, use Fraction to Decimal.
The starting fraction comes straight from place value, since three decimal places means a denominator of 1000, and the reduction uses the Euclidean algorithm: divide the larger number by the smaller, keep the remainder, repeat until the remainder is zero, and the last non-zero divisor is the greatest common divisor. For 750 and 1000 that gives 250 in two steps, so 750/1000 collapses to 3/4.
Because the tool works from the digits you type, it can only produce what those digits literally say, which is right for an exact measurement and wrong for a truncated repeating decimal, so 0.16666 gives its own unwieldy fraction rather than 1/6. Where the fraction has to be exact, start from the fraction. Everyday uses are turning a decimal inch into a workshop fraction, putting a probability back into ratio form, and reading a ratio off a chart. Input is handled to twelve decimal places, which is already past the point where a double stays trustworthy.
How to use
- Paste decimals, one per line.
- Copy the reduced fractions.
- Swap to convert fractions to decimals.
Common questions
- Why does 0.333 not become 1/3?
- Because 0.333 is exactly 333/1000. Enter a repeating decimal with more digits, or use the fraction directly, for 1/3.
- Are fractions reduced?
- Yes, to lowest terms using the greatest common divisor.
- How many decimal places are handled?
- Up to twelve, which covers ordinary use.