Decimal to Fraction Calculator

A fraction expresses a part of a whole using two integers separated by a line: a numerator (how many parts) over a denominator (how many parts make up one whole). 3/4 means three parts out of four equal pieces.

Every terminating decimal can be written as a fraction. Place the decimal over a power of 10 that matches the number of decimal digits, then reduce. 0.4 = 4/10 = 2/5. 0.875 = 875/1000 = 7/8. The calculator above does this reduction automatically using the Greatest Common Divisor.

The Greatest Common Divisor of two numbers is the largest integer that divides both without a remainder. GCD(8, 12) = 4, so 8/12 simplifies to 2/3. The Euclidean algorithm finds the GCD by repeatedly taking the remainder of the larger divided by the smaller until the remainder is zero.

Without simplification, 0.5 would display as 5/10 or 50/100 or 5000/10000 depending on how many digits you entered. The GCD step collapses all of those to the single canonical form: 1/2.

A proper fraction has a numerator smaller than its denominator: 3/8, 5/16, 11/64. An improper fraction has a numerator at least as large as its denominator: 11/8, 17/16. A mixed number combines a whole number and a proper fraction: 2 5/8.

The improper fraction 11/8 and the mixed number 1 3/8 represent the exact same value. Improper fractions are easier to multiply and divide. Mixed numbers are easier to read off a tape measure.

Convert 0.625 to a fraction:

1. Write the decimal as a fraction over 1000 (three decimal digits): 625/1000.
2. Find the GCD of 625 and 1000. GCD = 125.
3. Divide both: 625 ÷ 125 = 5, 1000 ÷ 125 = 8. Result: 5/8.

For inch-specific fractional output (1/8, 1/16, 1/32, 1/64), use the fractional inch converter instead. Going the other direction, from an inch fraction back to decimal, works the same way on the fractional inch to decimal converter.

Convert 0.8125 to a fraction the same way: write it over 10000 (four decimal digits), giving 8125/10000. The GCD of 8125 and 10000 is 625, so dividing both by 625 gives 13/16. That matches the 13/16" mark on an inch ruler, which is exactly 0.8125" and 20.6375 mm (0.8125 × 25.4).

Notice that the number of decimal digits only sets the starting denominator; the final answer depends entirely on the GCD step. 0.8125 could have started as 8125/10000, 81250/100000, or any equivalent fraction, and the GCD always collapses it down to the same simplest form, 13/16.

General decimal-to-fraction conversion, like the kind covered on this page, accepts any denominator: thirds, fifths, sevenths, anything. Inch measurements are a special case, because tape measures, drill bits, and machinist's rules only mark fractions with denominators that are powers of two: halves, quarters, eighths, sixteenths, thirty-seconds, and sixty-fourths. A decimal like 0.6 converts to 3/5 in general math, but the nearest inch-ruler mark is 19/32" (0.59375"), not 3/5", because 3/5 is not a fraction a tape measure can show.

If you are converting a measurement rather than doing pure arithmetic, use the fractional inch converter or the equivalent fractions chart, both of which round to the nearest standard inch fraction instead of the mathematically exact reduction. For whole-number-plus-fraction results like 2 5/8, the mixed number converter handles the whole-number part separately.