Decimal to Fraction Calculator

A terminating decimal is already a fraction in disguise: the digits after the point are tenths, hundredths, thousandths and so on. The calculator writes the decimal over the matching power of ten (10ⁿ for n decimal places), finds the greatest common divisor (GCD) of the two numbers with Euclid's algorithm, and divides both by it to give the fraction in simplest form — plus the mixed number for values above 1.

Because 10ⁿ only has the prime factors 2 and 5, a terminating decimal always reduces to a fraction whose denominator is built from 2s and 5s (2, 4, 5, 8, 10, 16, 20, 25 …). Inch fractions — halves, quarters, eighths, sixteenths — are exactly this family, which is why they convert cleanly.

The conversion works on the digits you type rather than on a rounded floating-point number, so very small and very large values are exact.

For shop measurements the calculator also rounds to the nearest 1/16, 1/32 and 1/64 inch: multiply by the denominator, round to a whole number, simplify, and compare with the exact value. The error is shown in inches and millimetres so you can judge whether the fraction is close enough — 0.3 in is 5/16 to the nearest sixteenth (+0.3175 mm) but 19/64 to the nearest sixty-fourth (−0.0794 mm).

The calculator treats what you type as a terminating decimal: 0.333 becomes 333/1000, not 1/3. For a repeating decimal use algebra: let x = 0.333…; then 10x = 3.333…; subtract to get 9x = 3, so x = 1/3. For two repeating digits multiply by 100 (x = 0.272727… → 99x = 27 → x = 3/11).