Decimals

We can use variables and equations to solve this problem. 

First, let's let $x=2.\overline{57}$

If we have that for the value of x, we have $100x = 257.\overline{57}$

This is extremely important for our solution. 

Now, we subtract x from 100x. We have

$100x-x=257.\overline{57}-2.\overline{57}$

Notice the repeating decimal cancels out. We get

$99x=255\\ x=255/99\\ x=\frac{85}{33}\\ x=2\frac{19}{33}\\$

So our final answer is $x=2\frac{19}{33}$

Thanks! :)