About the Fraction to Decimal Converter
This converter works in both directions. Type a fraction such as 7/12 and it gives the exact decimal, with any repeating digits shown in brackets: 0.58(3). Type a decimal such as 0.375 and it gives the fraction in lowest terms, 3/8. It even turns repeating decimals back into fractions, so 0.(3) becomes 1/3.
It is ideal for students learning how fractions and decimals connect, and for anyone who needs an exact fraction rather than a rounded decimal. You also get the percent, the mixed number and short steps for each conversion.
How to use it
- Type a fraction (
7/12), a mixed number (1 1/2), a decimal (0.375) or a repeating decimal into Fraction or decimal. - For repeating decimals, put the repeating digits in brackets:
0.(3)for 0.333… or0.1(6)for 0.1666…. - Read the converted value at the top.
- Check the rows for the simplified fraction, mixed number, percent and decimal type.
The formula
Fraction to decimal: divide the numerator by the denominator using long division. If a remainder comes back that you have seen before, the digits from that point repeat forever.
Decimal to fraction: write the digits over a power of ten, then simplify: 0.375 = 375/1000 = 3/8.
Repeating decimal to fraction:
fraction = (N − n) ÷ ((10r − 1) × 10k)
- N — the digits after the point up to the end of the first repeat, read as a whole number
- n — the digits that do not repeat, read as a whole number (0 if there are none)
- r — how many digits repeat
- k — how many digits come before the repeat starts
For 0.1(6): N = 16, n = 1, r = 1, k = 1, so the fraction is (16 − 1) ÷ 90 = 15/90 = 1/6.
Which fractions give terminating decimals?
Simplify the fraction first, then look at the denominator. If its only prime factors are 2 and 5, the decimal ends. Otherwise it repeats forever.
For example, 3/8 has denominator 8 = 2 × 2 × 2, so it ends: 0.375. And 7/20 has 20 = 2 × 2 × 5, so it ends: 0.35. But 1/3, 5/6 and 7/12 all have a factor of 3 in the denominator, so they repeat: 0.(3), 0.8(3) and 0.58(3).
The reason is that our number system is base ten, and 10 = 2 × 5. Only fractions whose denominators divide a power of ten can be written with a finite number of decimal places. Use the prime factorization calculator to check a denominator quickly.
Is 0.999… really equal to 1?
Yes. Type 0.(9) into the converter and it returns exactly 1. Using the formula, the repeating digit is 9, so the fraction is 9/9 = 1.
Another way to see it: 1/3 = 0.333…, and three times that is 0.999…. But three times 1/3 is 1. There is no number between 0.999… and 1, so they are the same number written two ways.
Very long repeating cycles are worth a note. Some fractions repeat only after many digits; 1/7 repeats every 6 digits, and 1/97 every 96. The converter works out up to 60 decimal places, so for very long cycles you will see the first 60 digits.
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the top number by the bottom number. For example, 3/4 = 3 ÷ 4 = 0.75.
How do you convert a decimal to a fraction?
Write the decimal over 10, 100, 1000 and so on, depending on the number of decimal places, then simplify. 0.45 = 45/100 = 9/20.
How do I type a repeating decimal?
Put the repeating part in brackets. 0.333… is 0.(3), 0.1666… is 0.1(6), and 0.142857142857… is 0.(142857).
What is 1/3 as a decimal?
1/3 = 0.333…, which the converter writes as 0.(3). Rounded, it is 0.33 or 0.333, but no finite decimal is exactly 1/3.
How do I turn a fraction into a percent?
Convert it to a decimal and multiply by 100. The converter shows the percent automatically, so 7/12 is about 58.33%.
Last updated October 24, 2026. Results are estimates for education and planning — see our disclaimer.