Fraction to decimal converter
Enter a numerator and denominator to get the full decimal value. Repeating digits are shown in brackets, so 1/6 appears as 0.1(6).
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How to use it
- Enter numerator and denominator.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Long division of the numerator by the denominator while tracking remainders: when a remainder repeats, the digits between the two occurrences form the repeating block.
Example
Inputs: Numerator = 1, Denominator = 6. Result: Decimal: 0.1(6); Approximate value: 0.166666666667; Repeating block length: 1.
Limits and caveats
- If the repeating block is longer than 2000 digits, only the first 2000 decimal places are shown.
- The approximate value uses normal floating point; the first line is exact.
Questions about this tool
When does a fraction give a terminating decimal?
When the simplified denominator has no prime factors other than 2 and 5, as in 3/8 or 7/20. Any other factor, such as 3 or 7, gives a repeating decimal.
What do the brackets in the result mean?
The digits inside the brackets repeat forever, so 0.(142857) means 0.142857142857 and so on.
Can the numerator be larger than the denominator?
Yes. 22/7 gives 3.(142857), where the part before the point is the whole number.