What is the fraction form of 0.222222222?

Answer 1

If the 2 repeats indefinitely, then it is 2/9. Solve like this:

1. let x = 0.22222...
2. then multiply by 10 --> 10x = 2.22222....
3. now subtract: 10x - x = 9x, and (2.22222...) - (0.22222...) = 2 {all the other 2's cancel}
4. Now you have 9x = 2, divide by 9 --> x = 2/9.

If you had a pair of repeating digits, then multiply by 100, or in general, if you had n repeating digits, multiply by 10^n. Example: if you had y = 0.090909..., then 100y = 9.090909..., then 99y = 9, and y=1/11.