Decimal to fraction calculator
Enter a decimal such as 0.75 or a repeating decimal with the repeating digits in brackets, like 0.1(6). You get the fraction in lowest terms, the mixed number and the decimal back with its repeating block. A limit on the denominator finds the closest simple fraction to a long decimal.
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Frequently asked questions
How do I convert a decimal to a fraction by hand?
Write the digits over a power of ten with as many zeros as there are decimal places, then divide top and bottom by their greatest common divisor. 0.75 = 75/100, and dividing both by 25 gives 3/4.
How do I enter a repeating decimal?
Put the repeating digits in brackets after the point and any non-repeating digits. 0.(3) is 0.333…, 0.1(6) is 0.1666… and 1.(142857) is 1.142857142857…. The fraction is exact: 0.(9) is exactly 1.
How is a repeating decimal turned into a fraction?
With non-repeating digits A (a of them) and repeating digits B (b of them), the value is (the whole digit string AB minus the digits A) divided by 10^a × (10^b − 1). For 0.1(6) that is (16 − 1) / (10 × 9) = 15/90 = 1/6.
What does the denominator limit do?
A decimal copied from a calculator, such as 3.14159265, is a finite decimal, so its exact fraction has a huge denominator. With a limit, the tool finds the closest fraction whose denominator is at most that number: 22/7 for 10, 311/99 for 100 and 355/113 for 1000.
Why is the fraction not what I expected for 0.333?
0.333 is exactly 333/1000, not 1/3. To get 1/3, type 0.(3) with the repeating digit in brackets, or choose a denominator limit such as 100.