Decimal ↔ Fraction Converter (with Inch-Fraction Table)

How to use

1. Edit either side — typing in the decimal box updates the fraction; typing in the fraction box updates the decimal.
2. Pick a maximum denominator to control how the decimal gets rounded to a fraction. 16 is the woodworking default; 100 is good for percent-ish; 1000 nails most everyday decimals exactly.
3. Look at the binary-fraction strip if you need a power-of-2 denominator (1/64" carpentry, 1/32" machining, etc.).
4. Use the reduced output if you need a simplified fraction; use the mixed-number form if you'd prefer '1 5/8' over '13/8'.
5. The error row tells you whether the fraction is exact or off by some tiny epsilon — pick a higher max denominator if the error matters.

Frequently asked questions

How does it pick the 'best' fraction?

For each denominator d from 1 up to your max, it computes the nearest integer numerator n = round(decimal × d) and measures the error |decimal − n/d|. The (n,d) pair with the smallest error wins, with ties broken by smaller denominator. This is exhaustive but fast — even maxDenom = 1000 finishes in microseconds. The continued-fraction algorithm would also work and is asymptotically faster, but for the denominators a human cares about, brute force is simpler and indistinguishable in speed.

Why does 0.1 not give exactly 1/10 sometimes?

0.1 in IEEE 754 binary floating point is actually 0.1000000000000000055511151231257827021181583404541015625 — there's no exact binary representation. As long as your max denominator is at least 10, the search finds 1/10 because the error there (~5.5e-18) is the smallest. With smaller maxDenom (say 8), you'll get the closest available like 1/8 or 1/9 with a visible error. The 'exact' label only shows when the difference is below 1e-12.

Why is 1/3 never exact?

1/3 = 0.333333… — a repeating decimal with no finite representation. The decimal-to-fraction side recognizes 1/3 immediately if you type the fraction directly (just 1 / 3). But typing 0.333 gives you 333/1000 if your max is 1000, or 1/3 only if your max is at least 3 AND your decimal has enough trailing 3s. To force fractions like 1/3 from a decimal, type at least 0.33333 and use a max denom of 3, 6, or higher.

What's the binary-fraction panel for?

Anywhere the denominator must be a power of 2: imperial measurements (tape measures stop at 1/16 or 1/32), pixel-snap grids, dithering kernels, audio bit-depth quantization, and any binary-fixed-point system. The panel shows all six power-of-2 denominators at once with their rounding errors, so you can see whether 1/8" is close enough or you need to step up to 1/64".

Does it handle negatives and mixed numbers?

Yes. Decimals can be negative ("-0.625" → -5/8). On the fraction side, fill the whole-number box for mixed numbers — "1" / "5" / "8" means 1 + 5/8 = 13/8 = 1.625. The decimal-to-fraction display automatically chooses mixed form when the numerator exceeds the denominator.

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