Decimal to Fraction Calculator
Enter a decimal number and, optionally, the largest denominator you want.
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Decimal to Fraction Calculator by TheCalcTools
How the Decimal to Fraction Calculator works
A terminating decimal is a fraction over a power of 10 (0.875 = 875/1000), which simplifies to lowest terms (7/8). The calculator uses continued fractions, which also find the closest fraction when the denominator is limited.
Continued fractions give the best rational approximations: for π, 22/7 with a denominator under 100 and 355/113 under 1000.
The formula
Worked example
Using the default values shown in the calculator:
| Decimal number | 0.875 |
|---|---|
| Largest denominator allowed | 1e+06 |
- 0.875 = 7/8.
Result:
| Fraction | 7/8 |
|---|---|
| Mixed number | — |
| Difference from the decimal | 0.0000 |
Frequently asked questions
What is 0.875 as a fraction?
7/8.
Why limit the denominator?
To get a simple fraction that is close enough. For 0.3183, a limit of 10 gives 1/3 and a limit of 1000 gives 247/776.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.