How to Convert a Decimal to a Fraction
A decimal and a fraction can describe the same number, and converting between them is a common task in cooking, carpentry, and math homework. This guide shows you how to write any decimal as a fraction, in simplest form, whether it is a simple value like 0.75 or a repeating decimal like 0.333. Once you know the place value rule, you can convert decimals by hand without a tool.
Skip the manual math. Enter your numbers and get the answer instantly.
Try the Fraction CalculatorThe Place Value Rule for Converting a Decimal to a Fraction
Every decimal has a place value that sets its denominator. The decimal 0.75 ends in the hundredths place, so write it as 75 over 100. The decimal 0.5 ends in the tenths place, so write it as 5 over 10. Count the digits after the decimal point to know whether the denominator is 10, 100, 1000, or more.
Simplifying the Fraction
Once you have the fraction, simplify it by dividing the numerator and denominator by their greatest common divisor. For 0.75, write 75/100 and divide both by 25 to get 3/4. For 0.5, write 5/10 and divide both by 5 to get 1/2. Always reduce to lowest terms so the answer is clean.
Converting Decimals Greater Than One
Decimals larger than one convert the same way, then become an improper fraction or a mixed number. The decimal 1.25 is 125/100, which simplifies to 5/4, or 1 1/4 as a mixed number. The decimal 1.5 is 15/10, which simplifies to 3/2, or 1 1/2. The process never changes.
Repeating Decimals
Repeating decimals such as 0.333 either repeat forever or are rounded, so they convert to a fraction only approximately. The decimal 0.333 is close to 1/3, and 0.666 is close to 2/3. For an exact answer you would use the fraction directly, which is why a fraction calculator returns a clean result rather than a rounded decimal.
Worked Example
Convert 0.75 to a fraction. The decimal ends in the hundredths place, so write it as 75/100. Divide the top and bottom by their greatest common divisor of 25 to get 3/4. So 0.75 as a fraction is 3/4.
Last updated: · by CalculatorPro Tools