Decimal to Fraction Converter
Two modes, because two different people search this. Exact reduced fractions for math, and nearest tape-measure fractions for anyone holding a tool.
Enter a number.
Which mode do you want? Exact mode gives the true fraction, so 0.4 becomes 2/5. Inch mode gives the nearest fraction your tape actually has, so 0.4 becomes 13/32 with the rounding error shown. Neither is more correct; they answer different questions.
How exact conversion works
Write the decimal over a power of ten, then reduce. 0.375 becomes 375/1000, and dividing both by 125 gives 3/8.
Repeating decimals need a different approach, since 0.333 repeating isn't 333/1000. This tool recognises the common repeating patterns and returns 1/3 rather than a close approximation.
Inch fraction reference
| Decimal inch | Nearest 1/16 | Nearest 1/32 | Millimeters |
|---|---|---|---|
| 0.0625 | 1/16 | 1/16 | 1.59 |
| 0.1250 | 1/8 | 1/8 | 3.17 |
| 0.1875 | 3/16 | 3/16 | 4.76 |
| 0.2500 | 1/4 | 1/4 | 6.35 |
| 0.3125 | 5/16 | 5/16 | 7.94 |
| 0.3750 | 3/8 | 3/8 | 9.52 |
| 0.4375 | 7/16 | 7/16 | 11.11 |
| 0.5000 | 1/2 | 1/2 | 12.70 |
| 0.5625 | 9/16 | 9/16 | 14.29 |
| 0.6250 | 5/8 | 5/8 | 15.88 |
| 0.6875 | 11/16 | 11/16 | 17.46 |
| 0.7500 | 3/4 | 3/4 | 19.05 |
| 0.8125 | 13/16 | 13/16 | 20.64 |
| 0.8750 | 7/8 | 7/8 | 22.22 |
| 0.9375 | 15/16 | 15/16 | 23.81 |
| 1.0000 | 1 | 1 | 25.40 |
Why a tape measure can't show 0.4
Imperial tapes are divided into halves, quarters, eighths, sixteenths and sometimes thirty-seconds. Those are all fractions with a power of two on the bottom. A decimal like 0.4 is 2/5, and 5 isn't a power of two, so it has no exact position on the tape.
The practical answer is the nearest available mark plus a note saying how far off it is. 0.4 inches sits between 6/16 and 7/16, closer to 13/32 at 0.40625. Inch mode shows that error rather than hiding it.
The same logic drives the fractional output on the length converters, where a millimeter value rarely lands on a clean fraction.
Common questions
What is 0.375 as a fraction?
0.375 is exactly 3/8. Written as 375/1000 and reduced by the greatest common divisor of 125, it becomes 3/8. This one is exact because 0.375 terminates in binary as well as decimal, so nothing is lost.
What is 2.5 as a fraction?
2.5 is 5/2 as an improper fraction, or 2 1/2 as a mixed number. Multiply by 2 to clear the single decimal place, giving 5/2, which is already in lowest terms.
How do I convert a repeating decimal to a fraction?
A repeating decimal is a rational number, so it has an exact fraction. 0.333 repeating is exactly 1/3, and 0.166 repeating is 1/6. This tool recognises common repeating patterns rather than treating 0.3333 as 3333/10000.
What is 0.4 inches on a tape measure?
There is no exact fraction for 0.4 on a standard tape. The nearest sixteenth is 6/16, which reduces to 3/8 and equals 0.375, about 0.025 inches under. The nearest thirty-second is 13/32, or 0.40625, which is closer.
Related converters and guides
Sources
- Decimal to fraction conversion is arithmetic rather than a measured conversion, so there is no external factor to cite. Exact mode reduces the fraction to lowest terms using the greatest common divisor. Inch mode rounds to the nearest multiple of the selected denominator and reports the resulting error.
- NIST Guide to the SI, Appendix B. Source for the exact inch-to-millimeter relationship of 25.4 mm used in the reference table.