Math · Fractions and decimals
Fraction to decimal converter.
Turn a fraction into a decimal by long division, spotting repeating digits, or turn a decimal back into a simplified fraction.
Inputs
Converted
Enter a fraction or a decimal.
Converting between fractions and decimals
The fraction bar means divide, so 5/8 means 5 divided by 8. Long division with extra zeros gives the decimal: 5.000 ÷ 8 = 0.625.
Terminating or repeating. Some fractions end, like 3/16 = 0.1875. Others go on forever: 1/3 = 0.333…. If a remainder shows up a second time, the same steps repeat, so the digits repeat. This calculator shows a repeating part in brackets, so 0.(3) means 0.333... and 1/6 is 0.1(6).
Decimal to fraction. For a decimal that ends, put the digits over a power of ten: 0.375 is 375/1000, which simplifies to 3/8. For a repeating decimal such as 0.1(6), the tool uses (all digits − non-repeating digits) ÷ (10^k × (10^m − 1)), where k is the number of non-repeating decimal digits and m the length of the repeat, then simplifies: 0.1(6) = 16 − 1 over 90 = 15/90 = 1/6.
Frequently asked questions
How do you turn a fraction into a decimal?
Divide the top by the bottom. 5 ÷ 8 = 0.625.
What is a repeating decimal?
A decimal whose digits repeat forever, like 1/3 = 0.333…. It happens when the long division returns to a remainder it has already had.
How do you turn a decimal into a fraction?
Count the digits after the point, use that power of ten as the denominator, and simplify. 0.375 = 375/1000 = 3/8.
How do I enter a repeating decimal?
Put the repeating digits in brackets. 0.1(6) is 0.1666... and converts to 1/6. Write 0.(3) for 0.333... which is 1/3.
Why is my decimal cut off?
Very long repeating blocks are shortened on screen. The tool still detects the repeat from the remainders.
Sources
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For learning
Fractions up to a denominator of 100,000; decimals up to 15 digits. Results are rounded for display. Check with your teacher's required method when you hand in homework.