OneTaskBy Tim King · Updated
Decimal to Fraction Calculator
Simplified Fractions From Repeating Decimals, Plus Decimal to Inch Fractions
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How the Decimal to Fraction Calculator works
This decimal to fraction calculator turns a decimal into a fraction in lowest terms and shows the working. It handles recurring decimals too: type 0.1(6) for 0.1666… and get 1/6. For tape measures and drill bits, round instead to the nearest half, quarter, eighth, sixteenth, thirty-second or sixty-fourth.
A terminating decimal is already a fraction in disguise. The digits after the point are a numerator, and the place value of the last digit is the denominator, so 0.375 means 375 thousandths. All that is left is simplifying.
How the decimal to fraction calculator works
For a terminating decimal the formula is: fraction = digits ÷ 10ⁿ, where n is the number of decimal places, then divide top and bottom by their greatest common factor. For a recurring decimal the calculator multiplies by powers of 10 so that the repeating tails line up, subtracts to cancel them, and divides by the matching run of 9s and 0s. In nearest mode it multiplies the decimal by the chosen denominator, rounds to a whole number and simplifies, and reports how far off that is.
First example. 0.375 has three decimal places, so it is 375/1000. Both divide by 125, giving 3/8.
Second example. 0.1(6) means 0.1666… Multiply by 100 and by 10 to get 16.666… and 1.666…; subtracting leaves 15, which is 90 times the number. So it is 15/90, which simplifies to 1/6.
How many sixteenths is a 0.3125 inch drill bit? 0.3125 × 16 = 5 exactly, so it is a 5/16 inch bit.
Common fractions between 0 and 1 as a decimal, a fraction in lowest terms and a percentage
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.0833… | 1/12 | 8.33% |
| 0.1 | 1/10 | 10% |
| 0.125 | 1/8 | 12.5% |
| 0.1667… | 1/6 | 16.67% |
| 0.2 | 1/5 | 20% |
| 0.25 | 1/4 | 25% |
| 0.3 | 3/10 | 30% |
| 0.3333… | 1/3 | 33.33% |
| 0.375 | 3/8 | 37.5% |
| 0.4 | 2/5 | 40% |
| 0.4167… | 5/12 | 41.67% |
| 0.5 | 1/2 | 50% |
| 0.5833… | 7/12 | 58.33% |
| 0.6 | 3/5 | 60% |
| 0.625 | 5/8 | 62.5% |
| 0.6667… | 2/3 | 66.67% |
| 0.7 | 7/10 | 70% |
| 0.75 | 3/4 | 75% |
| 0.8 | 4/5 | 80% |
| 0.8333… | 5/6 | 83.33% |
| 0.875 | 7/8 | 87.5% |
| 0.9 | 9/10 | 90% |
| 0.9167… | 11/12 | 91.67% |
Tips
- Brackets mark the repeat. Write 0.(3) for 0.333… and 0.58(3) for 0.58333…
- Rounded decimals give odd fractions. 0.33 is 33/100, not 1/3. Use 0.(3) if you mean a third.
- Imperial sizes. Most rulers stop at 1/16 inch; machinists and drill charts go to 1/64.
FAQ
How do you convert a decimal to a fraction?
Write the digits after the point over 10, 100, 1000 and so on, one zero for each decimal place. Then divide the top and bottom by their greatest common factor. 0.45 becomes 45/100, and both divide by 5, so 0.45 is 9/20. A whole-number part stays in front as a mixed number.
How do you turn a repeating decimal into a fraction?
Let x be the number, multiply it by 10 for each repeating digit, and subtract x so the endless tail cancels. For 0.(27), 100x is 27.2727… and x is 0.2727…, so 99x is 27 and x is 27/99, which simplifies to 3/11. Type the repeating part in brackets and the calculator does this for you.
What is 0.625 as a fraction?
0.625 is 625/1000. Both numbers divide by 125, leaving 5/8. It is one of the eighths, which are all worth learning: 0.125, 0.25, 0.375, 0.5, 0.625, 0.75 and 0.875 are 1/8 up to 7/8 in order.
How do I convert a decimal measurement to the nearest 1/16 inch?
Multiply the decimal part by 16 and round to the nearest whole number; that is how many sixteenths. 2.7 inches gives 0.7 × 16 = 11.2, so it is about 2 11/16 inches. Choose Nearest 1/16 to get the fraction in lowest terms and the size of the rounding error.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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