+1926 First, we can use variables to solve this problem in quite a handy way. First, let's set
\(x = 2.\overline{57}\)
For this value of x, we know that
\(100 x= 257.\overline{57}\)
Now, we do the really cool trick. We subtract the first equation from the second equation to get
\(100 x - x = 257.\overline{57} - 0.\overline{57}\)
Notice that the repeating terms cancel out. Thus, we have
\(99x =257\\ x= \frac{255}{99}\)
Dividing by a common factor, we have
\(x= 2 \frac{19}{33}\)
Thus, our final answer is \(2.\overline{57} = 2 \frac{19}{33}\)
Thanks! :)
