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If the 2 repeats indefinitely, then it is 2/9. Solve like this:
- let x = 0.22222...
- then multiply by 10 --> 10x = 2.22222....
- now subtract: 10x - x = 9x, and (2.22222...) - (0.22222...) = 2 {all the other 2's cancel}
- 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.
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