How do you convert a decimal to a fraction?
Write the decimal over a power of ten (or use continued fractions) and simplify.
Decimal to Fraction Calculator
Turn a decimal into a simplified fraction using a continued-fraction approximation capped at denominator 10,000.
Enter a decimal
Type the decimal value you want to express as a fraction.
About this calculator
How to use Decimal to Fraction Calculator, plus the formulas and logic behind the results.
Tool description
This calculator finds a rational fraction that closely matches your decimal, limited to denominators of 10,000 or less, then reduces it to lowest terms.
How to use
- Enter the decimal number.
- Select Calculate to approximate it as a fraction.
- Review the simplified fraction and its decimal check.
- Adjust the input if you need a different precision.
Formulas & reference
Continued-fraction convergents approximate the decimalDenominator limit = 10,000Final fraction is reduced by gcd
Examples
- 0.75 → 3/4
- 0.125 → 1/8
- 0.3333 ≈ 1/3
- 2.5 → 5/2
Calculation logic
A continued-fraction search builds convergents until the denominator would exceed 10,000 or the error is negligible. The best valid convergent is simplified.
Irrational or long repeating values are approximated within the denominator limit; exact terminating decimals usually convert exactly.
Decimal to Fraction Calculator FAQ
Common questions about this calculator and how to use the results.
Why is there a denominator limit?
Limiting the denominator keeps results practical and avoids huge fractions for tiny errors.
Will 0.5 always become 1/2?
Yes. Terminating decimals that fit within the limit convert to exact simplified fractions.
What about repeating decimals?
Repeating values are approximated by the closest fraction within the denominator cap.
Can I convert numbers greater than 1?
Yes. Improper fractions are returned when the absolute value is greater than 1.
Does the tool show a check value?
Yes. It also displays the decimal of the resulting fraction so you can verify the fit.