Decimal to Fraction Converter
Type a decimal such as 0.75 or 0.3333 and get the simplified fraction, mixed number, percent and the working. Write repeating digits in brackets, for example 0.1(6) for 0.1666..., and use the precision setting to find the nearest simple fraction. You can also convert a fraction back to a decimal.
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How to use Decimal to Fraction Converter
- Type a decimal in the box, using brackets for repeating digits such as 0.(3).
- Read the simplified fraction, the mixed number and the percent.
- Choose a largest denominator to see the nearest simple fraction, for example 0.3333 gives 1/3.
- Use the Fraction to decimal section to go the other way.
The method
A terminating decimal with n digits after the point is the digits divided by 10 to the power n. Dividing both numbers by their greatest common divisor gives the simplest fraction.
For a repeating decimal, subtract the number with the non-repeating digits from the number with one full repeat, and divide by 10 to the non-repeating length times (10 to the repeat length minus 1).
Nearest fraction
Many measurements are rounded decimals. The nearest-fraction result uses continued fractions to find the best fraction whose denominator does not exceed your limit. A small limit gives simple fractions such as 1/3, and a larger limit follows the decimal more closely.
Percent and mixed numbers
- A percent is the value multiplied by 100.
- A mixed number splits an improper fraction into a whole part and a proper fraction.
- Negative values keep their sign in front of the whole result.
Limits
Input is limited to 80 characters. Scientific notation such as 1e-5 is not accepted; write the number out in full. Repeating decimals in results are found up to 60 digits, after which they are cut with an ellipsis. Percent values are shown to about 12 digits. Everything runs in your browser and nothing is uploaded.
Why use this decimal to fraction converter tool
- Shows the steps. See the digits placed over a power of ten, then divided by the greatest common divisor to reach lowest terms.
- Repeating decimals. Enter 0.1(6) or 0.(142857) and get the exact fraction using the standard subtraction method.
- Nearest fraction. Set a maximum denominator and the tool finds the closest fraction using continued fractions.
- Large and negative numbers. Uses whole-number maths with no rounding, so long decimals and negative values stay exact.
Frequently asked questions
How do I convert a decimal to a fraction?
Write the digits after the decimal point over a power of ten with the same number of zeros, then divide the top and bottom by their greatest common divisor. For 0.75, that is 75/100, which simplifies to 3/4. The same steps work for any terminating decimal, including longer ones such as 0.125, which is 125/1000 or 1/8.
How do I convert a repeating decimal to a fraction?
Enter the repeating digits in brackets, such as 0.(3) or 0.1(6). The tool subtracts the number without the repeat from the number with one repeat, divides by the matching 9s and zeros, and simplifies. 0.(3) becomes 1/3.
Why does 0.3333 not give exactly 1/3?
Exactly, 0.3333 is 3333/10000. The nearest-fraction setting finds the simple fraction closest to it within your chosen denominator limit, which is 1/3. Use the bracket form 0.(3) when you mean a repeating third. Raise the limit to follow the typed decimal more closely.
How do I turn a fraction into a decimal?
Divide the top number by the bottom number. Use the Fraction to decimal section: enter the top, the bottom and an optional whole number. Repeating results are shown in bracket form, such as 1/6 equals 0.1(6). Mixed numbers work too: whole 2 with 3/8 gives 2.375.
Can it handle negative numbers and mixed numbers?
Yes. A minus sign is kept in front of the fraction and the mixed number. Improper results such as 2.5 are also shown as a mixed number, 2 1/2. Zero and whole numbers are handled too, so 0.5 gives 1/2 and 4 gives 4/1. The percent equivalent is shown beside the decimal.
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