Decimal to Fraction Calculator
Convert a decimal to a simplified fraction and a mixed number.
About this tool
Finite decimals are converted exactly and simplified by the greatest common divisor. Repeating or long decimals are matched with the closest fraction whose denominator is no bigger than the limit you choose, using continued fractions.
Recipes, measurements and maths homework often need fractions while calculators give decimals. Type a decimal to get it as a simplified fraction, as a mixed number such as 2 3/8, and as a percentage. For repeating decimals like 0.333…, or when you want the nearest fraction with a small denominator, such as sixteenths of an inch, choose a limit and the calculator finds the closest match.
How to use the Decimal to Fraction Calculator
- Type the decimal, for example 0.625 or 2.375.
- Choose the largest denominator you want; 16 suits inch measurements.
- Read the simplified fraction and mixed number.
- Check the accuracy line to see whether the fraction is exact or the closest match.
Converting 0.625 and 2.375
0.625 has three decimal places, so it is 625/1000. Both numbers divide by 125, giving 5/8. 2.375 is 2375/1000, which simplifies to 19/8, or the mixed number 2 3/8. For 0.3333 with a limit of 1 000, the closest fraction is 1/3; for 3.14159 with a limit of 1 000 it is 355/113.
How decimals become fractions
A finite decimal is a fraction with a power of ten underneath: the number of decimal places tells you how many zeros. 0.75 is 75/100 and 0.125 is 125/1000. Divide the top and bottom by their greatest common divisor to simplify: 75/100 becomes 3/4. Repeating decimals such as 0.1666… are fractions too (1/6), but a calculator only shows a rounded version, so the tool looks for the simplest fraction that matches. It uses continued fractions, the method that also finds famous approximations such as 22/7 and 355/113 for π. Limiting the denominator is useful for practical work: tape measures use sixteenths, and cooking uses halves, thirds and quarters.
Frequently asked questions
How do I convert a decimal to a fraction by hand?
Write the digits over 1 followed by as many zeros as there are decimal places, then simplify. 0.45 is 45/100 = 9/20.
What is 0.333 as a fraction?
0.333 exactly is 333/1000. If you mean the repeating decimal 0.333…, it is 1/3, which the calculator finds with a limit of 1 000.
What is a mixed number?
A whole number and a proper fraction together, such as 2 3/8, which equals 19/8.
Can it convert negative decimals?
Yes. −0.75 becomes −3/4.