Decimal to Fraction Calculator

How to convert a decimal to a fraction

Every decimal that ends is a fraction with a power of ten underneath. Count the digits after the point, write them over 1 followed by that many zeros, then reduce:

0.375 = 375/1000 = 3/8

To reduce, divide top and bottom by their greatest common factor. 375 and 1,000 are both divisible by 125, so 375 ÷ 125 = 3 and 1,000 ÷ 125 = 8. The calculator shows this step and the factor it used. For a number above 1, keep the whole part: 2.625 is 2 + 5/8, or 21/8 as an improper fraction. To find the common factor yourself, the LCM and GCF calculator lists the prime factors of both numbers.

Repeating decimals

A decimal that repeats forever is also a fraction — it is how fractions like 1/3 and 1/7 look in decimal form. To convert one, multiply so the repeating parts line up, then subtract:

Type a repeating decimal with the repeating digits in parentheses — 0.(3), 0.1(6) — or type the digits you see and choose how many of the last digits repeat, the way you would read 0.1666 as “0.1 with the 6 repeating”. Without that choice, 0.333 is taken exactly as written: 333/1000, not 1/3.

Close simple fractions

A rounded decimal is often a simple fraction in disguise. 0.333 is exactly 333/1000, but it almost certainly came from 1/3; 0.667 from 2/3; 3.14159 from π, which 22/7 and 355/113 approximate. When the exact fraction has a large denominator, the result lists the simpler fractions that come closest, each with how far it is off. They are the convergents of the continued fraction — the best approximations for their size — so the last one listed is the most accurate fraction with a denominator up to 1,000.

Decimals to inch fractions

Tape measures and drill bits use halves, quarters, eighths and sixteenths, not decimals. To read 1.3 inches on a tape, multiply the decimal part by 16 and round: 0.3 × 16 = 4.8, which rounds to 5, so 1.3 in is about 1 5/16 in — 0.0125 in long. The table under the result does the same for 1/2 through 1/64 and shows the error, so you can choose the precision your tool marks. For adding and subtracting lengths in feet and inches, use the feet and inches calculator.

Fractions, decimals and percents

The same number has three common forms. 3/8 = 0.375 = 37.5%: to get the percent, move the decimal point two places to the right. To go the other way, from a fraction to its decimal with the repeating digits marked, use the fraction to decimal calculator; to add or multiply the fractions you get here, the fraction calculator; for percent questions, the percentage calculator.