Repeating decimal to fraction converter
Type the non-repeating part in the first box and the repeating digits in the second: 0.1(6) is entered as 0.1 and 6.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter part before the repeat and repeating digits.
- 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
With m non-repeating decimal digits and a block of n repeating digits: fraction = (all digits through one block − digits before the block) ÷ (10^m × (10^n − 1)). Example: 0.1(6) = (16 − 1) ÷ 90 = 1/6.
Example
Inputs: Part before the repeat = 0.1, Repeating digits = 6. Result: Simplified fraction: 1/6; Approximate value: 0.166666666667.
0.1
1/6
Limits and caveats
- The second box takes digits only, up to 30 repeating digits.
- 0.(9) equals exactly 1, and the tool reports that.
Questions about this tool
How do I convert 0.333 recurring to a fraction?
Type 0 in the first box and 3 in the second to get 1/3.
What if the repeat starts after one or more digits?
Put the non-repeating digits in the first box: 0.8333 recurring is entered as 0.8 and 3, which gives 5/6.
Is 0.999 recurring really equal to 1?
Yes. The formula gives 9 ÷ 9 = 1, and the difference between them is exactly zero.