Decimal to Fraction
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Use 0.125 for a terminating decimal, 0.(3) for repeating 3, or 0.1(6) for repeating 6 after a fixed 1. A combining bar also works: 0.16 can be entered as 0.16̅. With ... or …, every digit after the point repeats: 0.12... means 0.121212…; use 0.1(2) when only 2 repeats.
Your result
Terminating: integer digits / 10ᵐ. Repeating: (digits through one repeat − digits before repeat) / (10ᵐ × (10ⁿ − 1)), where m is the number of fixed decimal digits and n is the repeat length. Reduce by the greatest common divisor.
Primary source: California Department of Education mathematics standards (terminating and repeating rational decimals).
Worked example
For x = 0.1(6), 100x − 10x = 16 − 1, so 90x = 15 and x = 15/90 = 1/6.
Use the Fraction Calculator to combine fractions.
How to use this tool
Enter your values, choose the options, and select Calculate to see the result and formula.
Frequently asked questions
How do I mark repeating digits?
Use parentheses, such as 0.1(6), or place a combining overline or macron on every repeating digit. The repeating block must be at the end.
What does an ellipsis mean here?
All fractional digits entered before ... or … form the repeating block. For a fixed prefix, use parentheses to remove ambiguity.
Is 0.999… equal to 1?
Yes. Enter 0.(9) or 0.9...; the exact fraction simplifies to 1/1.