+1926 Let's use a handy trick to solve this problem.
First off, let's set a variable. Let's set \(X=2.\overline{57}\)
For that value of X, then we have that
\(100 X = 257.\overline{57}\)
Now, we subtract x from 100x. Note that the repeated part of the decimal cancels out. Thus, we have
\(\eqalign{100 X &= &\hfill257.57...\cr X &= &\hfill2.57...\cr \hline 99X &= &255\cr}\)
We end up witht he equation
\(99 X = 255\)
Simplifying and isolating x, we get
\(X = \frac{255}{99}\)
Thus,
The answer is \(2.\overline{57} = 2 \frac{19}{33}\)
Thanks! :)
