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Fraction Converter

Convert between fractions and decimals, simplify, and find best rational approximations.

  • fraction
  • decimal
  • simplify
  • numerator
  • denominator

About Fraction Converter

Fractions and decimals are two ways of writing the same numbers, but each is better suited to different jobs. Decimals are easier to compare and add with a calculator; fractions are easier to interpret (3/4 is more legible than 0.75), and they're exact for values that decimals can only approximate — 1/3 is just 1/3, but as a decimal it's 0.333… repeating forever.

This tool does both directions. Decimal-to-fraction uses the continued-fraction algorithm to find the simplest fraction that approximates your decimal within the allowed denominator — that's how 0.333333 becomes 1/3 rather than 333333/1000000. Fraction-to-decimal reduces your input by the greatest common divisor, so 75/125 simplifies to 3/5 and converts to 0.6.

How to use

For decimal → fraction, type a decimal into the top section. The result shows both the improper fraction (e.g. 3/8) and the mixed-number form (e.g. 1 ½) when applicable, along with the precise error of the approximation. Adjust "Max denominator" to control how complex the result is allowed to get: 10 keeps things rough (great for finding simple recipes like 1/4 or 3/8), 10000 produces an extremely close fit.

For fraction → decimal, type a numerator and denominator into the bottom section. The result shows the decimal value to high precision and the fraction in its simplest form (divided through by the greatest common divisor of the inputs). Each result has a copy button beside it.

Frequently asked questions

  • How does the decimal-to-fraction conversion work?

    It uses the continued-fraction algorithm to find the simplest fraction whose denominator is at most the "Max denominator" setting and that approximates your decimal as closely as possible. For repeating decimals like 0.333…, the algorithm correctly identifies 1/3; for irrational values like π, it finds the best rational approximation under the limit.

  • What does "Max denominator" do?

    It caps how complex the resulting fraction is allowed to get. 10 forces the result into recipe-friendly fractions like 1/4 or 3/8; 100 finds approximations close enough for engineering; 10,000 produces extremely close fits that may look like 4327/12849. Pick the smallest cap that gives an acceptable error.

  • Why is 0.1 returning 1/10 but 0.2 doesn't give 1/5 sometimes?

    Because 0.2 stored in floating-point binary is not exactly 1/5 — it's a number infinitesimally different from 0.2. With a high "Max denominator", the algorithm chases that tiny floating-point error and gives a fraction with absurdly large numerator and denominator. Set "Max denominator" to a sensible cap (say 1000) and 0.2 reduces to 1/5 cleanly.

  • What is a mixed number?

    A mixed number combines a whole number with a proper fraction, like 1 ½ or 2 ¾. The decimal-to-fraction panel shows both forms — the improper fraction (3/2) and the equivalent mixed number (1 ½) — so you can pick whichever reads better in context. Recipes and measurements usually prefer mixed numbers; algebra prefers improper fractions.

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