Decimal to Fraction Calculator
Turn a decimal into the simplest fraction that matches it, or the closest fraction with a denominator up to a limit you choose — handy for measurements in eighths, sixteenths and thirty-seconds.
A terminating decimal is a fraction over a power of ten: 0.
How the decimal to fraction calculator works
A terminating decimal is a fraction over a power of ten: 0.375 = 375/1000, which simplifies to 3/8. For a decimal that does not terminate, or to match a ruler, the calculator finds the closest fraction whose denominator does not exceed your limit using continued fractions — the same method that gives 22/7 and 355/113 for π.
Formula: 0.d₁d₂…dₖ = d₁d₂…dₖ / 10ᵏ, then divide by the gcd
Worked examples
| Inputs | Fraction | Note |
|---|---|---|
| 0.375 | 3/8 | 3/8 exactly |
| 0.333333 | 333333/1000000 | 1/3 within rounding |
| 3.14159 to 1,000 | 355/113 | 355/113 |
| 0.7 to sixteenths | 7/10 | 11/16 is the closest |
FAQFrequently asked questions
How do I convert a decimal to a fraction by hand?
Write the digits after the point over 10, 100, 1000… then simplify: 0.375 = 375/1000 = 3/8.
What about repeating decimals?
Multiply to shift the repeat: x = 0.333…, 10x = 3.333…, so 9x = 3 and x = 1/3. The calculator finds the same answer numerically.
Why limit the denominator?
Rulers, drill bits and recipes use eighths and sixteenths; the closest such fraction is more useful than an exact one over a million.
What is 0.75 as a fraction?
3/4.
Is every decimal a fraction?
Every terminating or repeating decimal is. Irrational numbers like π are not, but can be approximated as closely as you like.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.