Free decimal to fraction calculator
Convert any decimal to a simplified fraction — enter a terminating or repeating decimal to see the exact fraction, updated live, as you type.
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Continued-fraction approximation. Best rational approximation within tolerance 1e-6.
Results are estimates. Consult a professional.
How the decimal to fraction calculator works
Converting a decimal to a fraction depends on whether the decimal terminates (ends) or repeats. Terminating decimals multiply by a power of 10 to form an integer fraction, then simplify by the GCD. Repeating decimals use an algebraic substitution to eliminate the repeating block.
Worked example: 0.75, 0.333…, and 0.625
Three conversions — two terminating and one repeating — each using its appropriate method. All results are expressed in lowest terms.
Common decimal to fraction conversions
The table below lists frequently encountered decimals with their exact fraction equivalents. Memorising these benchmarks makes mental conversion instant.
| Decimal | Fraction | Type |
|---|---|---|
| 0.1 | 1/10 | Terminating |
| 0.125 | 1/8 | Terminating |
| 0.2 | 1/5 | Terminating |
| 0.25 | 1/4 | Terminating |
| 0.333… | 1/3 | Repeating |
| 0.375 | 3/8 | Terminating |
| 0.5 | 1/2 | Terminating |
| 0.625 | 5/8 | Terminating |
| 0.666… | 2/3 | Repeating |
| 0.75 | 3/4 | Terminating |
| 0.875 | 7/8 | Terminating |
Source: standard fraction–decimal equivalences
Tips for decimal to fraction conversion
Converting decimals to fractions is essential in cooking, engineering, and mathematics. These tips prevent the most frequent errors.
- Count decimal places precisely — for terminating decimals, the power of 10 in the denominator equals the number of digits after the decimal point: 0.0625 has 4 places → 625/10000.
- Identify the repeating block first — for 0.142857142857…, the full repeating block is 142857 (6 digits). Multiply by 10⁶ and subtract to clear it: 999999x = 142857 → x = 142857/999999 = 1/7.
- Always simplify to lowest terms — 75/100 and 3/4 are equal, but 3/4 is the correct final form. Compute GCD and divide both parts.
- Negative decimals stay negative — convert the absolute value to a fraction, then reattach the negative sign: −0.75 = −3/4.
- Mixed decimals become mixed numbers — 2.5 = 2 + 0.5 = 2½. Convert only the fractional part, then combine with the whole-number part.
Accuracy and limitations
For terminating decimals, the conversion is mathematically exact provided the input has 15 or fewer significant decimal digits (the limit of IEEE 754 double precision). For repeating decimals detected by pattern, the result is exact. If you type a long non-repeating decimal that is actually a rounded form of a repeating decimal (e.g. 0.33333 instead of 0.333…), the calculator treats it as terminating and returns 33333/100000 rather than 1/3 — you must use the repeating-decimal input mode for those cases.
Key terms
About this calculator
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