What is 0.222222222 as a fraction?

If you mean 0.222.... recurring to infinity.

Then the answer is 2/9

How do we go there?

Let

P = 0.222.... &

10P = 2.2222....

Subtract

9P = 2.0

P = 2/9

NB Notice what the multiplication by '10' does.

NNB Notice also that subtraction of recurring decimals to infinity reduces to zero.