Decimal to Fraction Converter
Convert a decimal — including repeating decimals like 0.(3) — into an exact fraction, plus a best approximation with a limited denominator.
Your inputs
Results
Exact fraction
3/8
- Mixed number
- 3/8
- Best approximation (denominator ≤ 100)
- 3/8
✓Exact calculation — rounded only for display
What this calculator does
Terminating decimals convert by place value; repeating decimals use an algebraic trick. You can also find the closest simple fraction, like 355/113 for π.
Formula and method
Terminating: digits ÷ 10^k. Repeating x = I.N(R): x = (INR − IN) ÷ (10^(k+r) − 10^k). Approximation by continued fractions.
Worked example
Calculated by this tool with its default inputs:
Inputs
- Decimal (use brackets for repeating digits, e.g. 0.1(6)): 0.375
- Also show the best approximation with denominator up to: 100
Results
- Exact fraction: 3/8
- Mixed number: 3/8
- Best approximation (denominator ≤ 100): 3/8
How to read the results
The exact fraction is mathematically equal to the decimal; the approximation is the closest fraction with a small denominator.
Assumptions and limitations
- Put repeating digits in brackets.
Questions
Is 0.999… equal to 1?
Yes. Entering 0.(9) gives exactly 1.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 6 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy