convert recurring decimal 2,232323 to to common fraction

Question

unklerhaukus · Answer

$$\qquad x=2.232323...$$$$100x=223.232323...$$

$$99x=$$

tyteen4a03 · Answer

I assume that you mean $$2.2323232323...$$ in the question.

Let x be 2.232323....
Then 100x would be 223.232323...
Now this is the tricky part, we subtract x from 100x. Visualization is:
223.232323...
002.232323...
-------------
221 <- This is 99x.
Now that we have 99x = 221, just solve this equation.

Because x and 100x have this common part .232323..., it is safe to subtract each other to get rid of this part.

unklerhaukus · Answer

tyteen4a03 has explained this very well