Decimal to Fraction Calculator
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About the Decimal to Fraction Calculator
Decimals and fractions are two spellings of the same number, and each has jobs the other does badly: recipes, woodworking, and tile layouts speak in eighths and sixteenths, while calculators and spreadsheets output decimals. Converting between them accurately — 0.4375 into 7/16, not 'roughly 7/16' — is what this tool does, with the simplification handled by exact GCD arithmetic rather than approximation.
Enter any terminating decimal and you get the fully reduced fraction, plus the mixed-number form when the value exceeds 1. The sections below teach the by-hand method, the conversions worth memorizing, and the one case that needs different math: repeating decimals.
Doing arithmetic on decimals themselves — rounding, place value, operations? That's our Decimal Calculator
The Place-Value Method
Three steps, works for any terminating decimal:
0.625 → 625/1000 → ÷ GCD(625,1000)=125 → 5/8
In words: count the decimal places (3), write the digits over 10 to that power (625 over 1000), and divide top and bottom by their greatest common divisor. The GCD step is what most people skip — 625/1000 is correct but unreduced, and a recipe calling for 625/1000 of a cup helps nobody.
Common Decimals as Fractions
The conversions that cover most real-world use:
| Decimal | Fraction | Where you meet it |
|---|---|---|
| 0.125 | 1/8 | Recipes, drill bits |
| 0.25 | 1/4 | Everywhere |
| 0.333… | 1/3 | Repeating — see below |
| 0.375 | 3/8 | Wrenches, lumber |
| 0.5 | 1/2 | Everywhere |
| 0.625 | 5/8 | Hardware sizes |
| 0.666… | 2/3 | Repeating |
| 0.75 | 3/4 | Everywhere |
| 0.875 | 7/8 | Hardware sizes |
| 0.0625 | 1/16 | Tape-measure ticks |
Notice the pattern in the hardware sizes: they're all halvings — 1/2, 1/4, 1/8, 1/16 — which is why imperial tools land on decimals ending in 5. A decimal ending in anything else (0.3, 0.7) will never simplify to a clean power-of-two fraction.
Repeating Decimals: The Algebra Trick
Repeating decimals can't come from the place-value method — 0.333… isn't 333/1000, it's exactly 1/3. The trick: set x = 0.333…, multiply both sides by 10 (10x = 3.333…), subtract the first equation from the second (9x = 3), solve: x = 3/9 = 1/3. The repetition cancels itself out in the subtraction.
Same machinery for longer repeats: x = 0.727272…, multiply by 100 (two repeating digits), 99x = 72, x = 72/99 = 8/11. General rule: the repeating block over as many 9s as it has digits — 0.abcabc… = abc/999 — then simplify. Every repeating decimal is exactly some fraction; only irrationals like π aren't.
Frequently Asked Questions
How do I convert a decimal to a fraction?
Write the decimal digits over a power of ten matching the decimal places, then simplify by the greatest common divisor: 0.85 = 85/100, GCD 5, so 17/20. This calculator does both steps exactly — including finding the GCD, which is the part usually done wrong by hand.
What is 0.625 as a fraction?
5/8. Working: 0.625 = 625/1000; the GCD of 625 and 1000 is 125; dividing both gives 5/8. It's one of the most-looked-up conversions because 5/8 inch is a common hardware and wrench size.
What is 0.333 as a fraction?
Exactly 0.333 (terminating) is 333/1000, which doesn't simplify. But 0.333… repeating is exactly 1/3 — the algebra: x = 0.333…, so 10x − x = 3, giving x = 3/9 = 1/3. Which answer you want depends on whether your decimal actually repeats forever or stops.
How do I convert a decimal greater than 1, like 2.75?
Two equivalent answers: the improper fraction 11/4 (from 275/100 reduced by GCD 25), or the mixed number 2 3/4 (whole part 2, plus 0.75 = 3/4). This calculator shows both forms — recipes usually want the mixed number, algebra usually wants the improper fraction.
Can every decimal be written as a fraction?
Every terminating decimal and every repeating decimal, yes — those are exactly the rational numbers. Non-repeating, non-terminating decimals like π (3.14159…) and √2 are irrational and have no exact fraction; 22/7 is only an approximation of π, good to about 0.04%.
Why does my fraction come out unsimplified elsewhere?
Most quick converters stop at the place-value step (0.375 → 375/1000) and skip the GCD reduction to 3/8. Both are mathematically equal, but unreduced fractions are useless for measurement contexts. This tool always reduces fully and reports the GCD it used, so you can check the work.
Sources & References
- [1]Weisstein, E.W. Fraction — Wolfram MathWorld
Methodology. This calculator uses standard, peer-reviewed mathematical formulas. It is reviewed and maintained by the Vast Calculators editorial team.
Last updated · July 2026
Results are estimates for general use; verify critical figures independently.