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.