Toolstia / Decimal to fraction calculator
Decimal to fraction calculator
Enter a decimal such as 0.375 to get the exact fraction 3/8. Repeating decimals work too: write the repeating part in brackets, as in 0.(3) or 0.1(6). For a long measured decimal like 3.14159 the tool also offers the closest simple fraction.
Enter a decimal number. Put repeating digits in brackets, like 0.1(6).
A decimal you type is converted exactly: 0.375 is 375/1000, which reduces to 3/8. If the number came from a measurement, like 3.14159, the closest simple fraction (355/113) may be more useful.
How it works
- Enter the decimal number.
- Read the exact fraction and the mixed number.
- Check the closest simple fraction if one is shown.
Terminating decimals
A decimal with n digits after the point is that number over 10 to the power n, then reduced. 0.375 = 375/1000 = 3/8.
Repeating decimals
Put the repeating digits in brackets. 0.(3) is 1/3, 0.1(6) is 1/6 and 0.(142857) is 1/7. The tool uses the standard method of subtracting shifted copies to cancel the repeat.
Closest simple fraction
A typed value like 3.14159 is exactly 314159/100000, but 355/113 is much simpler and very close. The tool finds the best fraction up to a denominator you choose, using continued fractions.
Whole parts
Numbers above 1 are also shown as mixed numbers, such as 2.5 = 5/2 = 2 1/2.
Questions
Is 0.333 the same as 1/3?
No. 0.333 is 333/1000. Use 0.(3) for the repeating decimal 1/3.
Does it handle negatives?
Yes, with a leading minus sign.
Is anything uploaded?
No. Your number stays in your browser and is never sent anywhere.