Decimal to Fraction Converter

Approximate a finite decimal as a reduced fraction, with a maximum denominator you choose.

How to use Decimal to Fraction Converter

1. Enter Decimal, Maximum Denominator in the stated order. 2. Follow nonzero denominator and whole-number requirements where they apply. Keep corresponding quantities on the same unit scale. 3. Select Convert or press Enter to see fraction. 4. Copy result copies the output; Reset clears the inputs and answer.

Why use this tool?

Find a usable fractional approximation when a decimal cannot be represented exactly within a chosen denominator limit.

How the calculation works

Choose the closest fraction with denominator from 1 to Maximum Denominator, then reduce it. Equal-error ties prefer the smaller denominator; a half-integer numerator tie rounds away from zero. Integer fraction outputs and decimal-ratio comparisons use exact integer arithmetic; numeric input components are bounded as stated. Numeric input magnitudes, including each fraction or ratio component, must not exceed 9,007,199,254,740,991. Mathematical references: https://openstax.org/books/prealgebra-2e/pages/4-key-concepts and https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications.

Example

Decimal = 0.3333333333333333 and Maximum Denominator = 1,000 give 1/3. Decimal = 0.125 with a maximum of 8 gives exactly 1/8.

Practical tip

A repeating decimal typed with a finite number of digits is an approximation. A small denominator limit may return zero for a tiny decimal.