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Convert decimals to simplified fractions and mixed numbers, fractions to decimals with repeating digits, and find the nearest ruler fraction.
Also covers: Decimal to fraction · Fraction to decimal · Repeating decimal to fraction · Inch fraction converter
For decimals that are really rounded values — 3.14159 with ≤ 1000 gives 355/113.
Write a repeating decimal with the repeating part in brackets: 0.(3) is 0.333…, 0.1(6) is 0.1666…. Typed decimals are converted exactly.
As a fraction
5/8
Forms
Working
Nearest ruler fractions
| Precision | Fraction | Error |
|---|---|---|
| 1/2 | 1/2 | −0.125 |
| 1/4 | 3/4 | 0.125 |
| 1/8 | 5/8 | 0 |
| 1/16 | 5/8 | 0 |
| 1/32 | 5/8 | 0 |
| 1/64 | 5/8 | 0 |
0.625, 0.(3) for a repeating decimal, 5/8, or a mixed number like 1 3/8 — the direction is detected from the “/”.
Write it over a power of ten and simplify: 0.625 = 625/1000, and dividing both by 125 gives 5/8.
Put the repeating part in brackets: 0.(3) is 1/3 and 0.1(6) is 1/6. The converter does the algebra exactly.
Set the largest denominator: 3.14159 with a limit of 1,000 gives 355/113, and 0.333 with 10 gives 1/3.
The nearest 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64 — how inch measurements are marked on tape measures.
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