Decimal to Fraction Calculator
| Decimal | Exact fraction | Nearest 1/16 | Miss by |
|---|---|---|---|
| 0.125 | 1/8 | 2/16 | 0 |
| 0.25 | 1/4 | 4/16 | 0 |
| 0.333… | 1/3 (repeating) | 5/16 = 0.3125 | 0.0208 |
| 0.375 | 3/8 | 6/16 | 0 |
| 0.5 | 1/2 | 8/16 | 0 |
| 0.625 | 5/8 | 10/16 | 0 |
| 0.65 | 13/20 | 10/16 = 0.625 | 0.025 |
| 0.875 | 7/8 | 14/16 | 0 |
Every terminating decimal is a fraction in disguise: 0.375 is 375/1000 by definition, and the whole task of converting is simplifying that ratio - divide top and bottom by the greatest common divisor (125 here) and 375/1000 collapses to 3/8. This calculator shows the unsimplified form, the GCD, and the smallest-terms answer, so the mechanics stay visible instead of magic.
The second answer is the one a tape measure or drill chart actually needs: imperial tools resolve in powers of two - 1/16, 1/32, 1/64 - not in exact terms like 13/20. Pick a denominator cap and the tool finds the closest mark and states the error honestly: 0.65 sits on no sixteenth line, so it rounds to 10/16 = 5/8 and misses by exactly 0.025. Exact and practical answers, side by side.
How to use
- Type a decimal (0.375) and read the exact fraction with its simplification steps - unsimplified form, the GCD that divides it, and the smallest-terms result.
- Set a denominator cap for shop reality: 1/16 mimics a tape measure, 1/32 and 1/64 mimic precision scales and drill charts. The result shows the nearest mark and its exact error.
- Leave the cap on Exact for pure math. Repeating decimals like 0.333... are covered in the FAQ below - truncating them hides what the fraction should be.
Frequently asked questions
What is 0.375 as a fraction?
3/8. The digits after the point name the denominator: three places means 1000, so 0.375 = 375/1000. The GCD of 375 and 1000 is 125, and 375/125 = 3 while 1000/125 = 8. The same read works on any terminating decimal - 0.625 = 625/1000 = 5/8 (GCD 125), 0.65 = 65/100 = 13/20 (GCD 5).
How do I convert a repeating decimal like 0.333... to a fraction?
Use the multiply-and-subtract trick: let x = 0.333..., then 10x = 3.333..., and 10x - x = 3 exactly - the infinite tails cancel. That gives 9x = 3, so x = 1/3. This calculator reads only the digits you type, so it will treat 0.333 as 333/1000; the repeating case needs the trick, and the table below marks which anchors repeat.
Why do tape measures use 1/16 steps instead of decimals?
Imperial length descends by halving: halves, quarters, eighths, sixteenths - each mark is one more halving, which is how carpenters and machinists read a scale by eye. A sixteenth of an inch is 0.0625 (1.5875 mm) and a sixty-fourth is 0.015625. The cap selector reproduces this ladder, and it is also why the nearest-mark answer is often tidier than the exact one: 0.375 already sits exactly on 6/16.
What is 0.65 as a fraction, and why isn't it on the tape?
Exactly 13/20 (65/100 simplified by the GCD 5) - but twentieths are not on a halving tape. The nearest sixteenth to 0.65 is 10/16 = 5/8 = 0.625, off by 0.025; the nearest thirty-second is 21/32 = 0.65625, off by 0.00625. Doubling the denominator quarters the worst-case error - that is the entire reason 1/64 marks exist on precision rules.