Quick start
- Type a normal decimal such as 0.625 or 3.2.
- For a repeating decimal, put the repeating digits in brackets: 0.(6) means 0.666… and 0.2(7) means 0.2777…
- Read the fraction, the mixed number if it is above 1, and the percent.
Terminating decimals
Write the digits over a power of ten and simplify. 0.625 has three decimal places, so it is 625/1000. Dividing top and bottom by 125 gives 5/8.
Repeating decimals: the subtraction trick
Let x = 0.666… Multiplying by 10 gives 10x = 6.666… The tails match, so subtracting removes them: 10x − x = 6, so 9x = 6 and x = 2/3.
If the repeat starts later, multiply by two different powers of ten. For x = 0.2777…, 100x = 27.777… and 10x = 2.777… Subtracting gives 90x = 25, so x = 25/90 = 5/18.
Patterns to remember
| You type | Means | Fraction |
|---|---|---|
| 0.(6) | 0.666… | 2/3 |
| 0.(18) | 0.1818… | 2/11 |
| 0.(27) | 0.2727… | 3/11 |
| 0.2(7) | 0.2777… | 5/18 |
| 0.58(3) | 0.58333… | 7/12 |
| 0.(037) | 0.037037… | 1/27 |
Common questions
How do I convert 0.666… to a fraction?
Type 0.(6). The answer is 2/3.
Does 0.999… equal 1?
Yes. With x = 0.999…, 10x − x = 9, so x = 1. Type 0.(9) to see it.
What about numbers bigger than 1?
They work too. 1.(3) = 4/3 = 1 1/3.