Decimal calculator to fraction
A decimal is already a fraction with the bottom number hidden. Count the digits after the point, write a one with that many zeros underneath, then cancel. The calculator above checks the answer in a single step.
12 × 12 = 144
Adding 12 to itself 12 times gives the same answer.
Three steps
- Take the digits after the point as the top number. For 0.75 that is 75.
- Write a 1 with one zero for every digit you took, and put it underneath. Two digits, so 100. You now have 75/100.
- Divide top and bottom by the same number until nothing goes into both. Here 25 goes into each, and 75/100 becomes 3/4.
Checking it with the calculator above
The box multiplies two numbers and opens on 12 x 12 = 144. To test a fraction, multiply your decimal by the bottom number and see whether you land exactly on the top number. For 3/4 that is 0.75 x 4 = 3, so the fraction is right. If the result comes out at something like 2.998 instead of a whole number, the fraction is an approximation rather than the true value.
The ones worth knowing by heart
| Decimal | Fraction | The check |
|---|---|---|
| 0.5 | 1/2 | 0.5 x 2 = 1 |
| 0.25 | 1/4 | 0.25 x 4 = 1 |
| 0.75 | 3/4 | 0.75 x 4 = 3 |
| 0.2 | 1/5 | 0.2 x 5 = 1 |
| 0.4 | 2/5 | 0.4 x 5 = 2 |
| 0.125 | 1/8 | 0.125 x 8 = 1 |
| 0.625 | 5/8 | 0.625 x 8 = 5 |
| 0.05 | 1/20 | 0.05 x 20 = 1 |
When the decimal never ends
A decimal that repeats for ever is not a thousandths fraction. Writing 0.333 as 333/1000 is close but wrong: the true value is 1/3, just as 0.666 stands for 2/3 and 0.1666 for 1/6. The giveaway is the check above. Multiplying the rounded 0.333 by 3 gives 0.999 rather than a clean 1, which means you have caught a repeating decimal and should name the fraction instead of building one.
Going the other way
A fraction becomes a decimal by dividing the top by the bottom, which is the job of the division into fraction calculator. Whole numbers mixed with fractions are handled on the whole number fraction calculator, and tape-measure sixteenths on the fraction inch calculator. Everything else is listed under calculators.