Decimal to Fraction Converter

How to convert a decimal to a fraction

A decimal is simply a fraction whose denominator is a power of ten. The digits after the point tell you which power: one digit means tenths, two digits mean hundredths, three digits mean thousandths and so on. So 0.375 has three decimal places and is written 375/1000. That fraction is correct but not tidy, so the second step is simplifying: find the greatest common divisor of the numerator and denominator (here 125) and divide both by it, giving 3/8. This converter does exactly that with exact big-integer arithmetic, so long decimals never suffer from floating-point rounding errors.

Whole numbers in front of the point become a mixed number. The decimal 3.25 is 325/100, which simplifies to 13/4, or 3 1/4 as a mixed number. Negative decimals work the same way, and the sign is carried onto the fraction. The result card also shows the matching percent value, which is handy when you are switching between the three notations in homework or recipes.

Exact fractions versus practical approximations

Many decimals you meet in practice are rounded versions of repeating values: 0.3333 stands for 1/3, 0.1667 for 1/6 and 3.14159 for roughly 22/7 or 355/113. Converting the typed digits exactly would give an awkward fraction like 3333/10000. Use the denominator limit to ask for the closest fraction whose denominator does not exceed a chosen size. A limit of 16 suits ruler and woodworking measurements, 64 suits machining and drill bits, and 100 or 1000 suits general use. When an approximation is used, the tool says so, so you always know whether the answer is exact.

Tips: to check an answer, divide the numerator by the denominator on any calculator and compare. If you need the reverse direction, use the fraction to decimal converter, and for percentages see the percent to fraction converter. Everything runs locally in your browser; nothing you type is sent anywhere.