Decimal to Fraction Calculator
A decimal as an exact fraction in lowest terms, repeating decimals included, or as the nearest 16th, 32nd or 64th of an inch with its rounding error.
Result
Fraction: 3/8
Exact fractions are in lowest terms; the nearest-fraction modes show how far they are off.
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How to use the Decimal to Fraction Calculator
- Type the decimal. For a repeating decimal, type a few repeats and say how many final digits repeat.
- Choose the exact fraction, or the nearest 16th, 32nd or 64th for measurements.
- Read the fraction in lowest terms, as a mixed number when it is more than one, and any rounding error.
The method
A terminating decimal with n decimal places is its digits over 10ⁿ, reduced by the greatest common factor. A repeating decimal uses a small piece of algebra: if the last r of its digits repeat after n fixed ones, subtracting the number shifted by n places from the number shifted by n + r places cancels the repetition, leaving the fraction (all the digits − the fixed digits) ÷ (10ⁿ⁺ʳ − 10ⁿ).
Why the decimal is typed as text
The page reads your digits exactly as typed, so 0.1 is exactly one tenth rather than the nearest value a computer can store.
With your numbers
- Reduced by the greatest common factor: 3/8
Quick reference
Exact fractions are in lowest terms; the nearest-fraction modes show how far they are off.
| Example | Fraction |
|---|---|
| 0.375 | 3/8 |
| 0.25 | 1/4 |
| 0.333… repeating | 1/3 |
| 0.142857 repeating | 1/7 |
| 2.75 | 11/4 |
| 0.3 to the nearest 16th | 5/16 |
| 0.6875 to the nearest 16th | 11/16 |
Common questions about the Decimal to Fraction Calculator
- How do I turn a decimal into a fraction?
- Put the digits over a power of ten and reduce. 0.375 is 375/1000; the greatest common factor is 125, so it is 3/8. The page reduces every fraction to lowest terms.
- How are repeating decimals handled?
- Exactly. Tell the page which final digits repeat: 0.333333 with 1 repeating digit is 1/3, and 0.142857 with 6 is 1/7. Without that, 0.333333 would give 333333/1000000, which is only close to a third. The page does not guess which digits repeat.
- What is the nearest sixteenth for?
- Tape measures and many plans work in fractions of an inch. 0.3 inches is not an exact sixteenth; the nearest is 5/16, which is 0.0125 inches too long. The page shows that error rather than presenting the rounded fraction as exact.
- How is a fraction greater than one shown?
- Both ways: 2.75 is 11/4 as an improper fraction and 2 3/4 as a mixed number.