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avatar+1957 

Express 2.\overline{57} as a base 10 fraction in reduced form.

 Jun 13, 2024
 #1
avatar+1075 
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We can use a clever trick to make \( 2.\overline{57}\) a fraction. 

 

First, let's set \(x= 2.\overline{57}\)

If we multiply both sides by 100, we get \( 100x=257.\overline{57}\)

 

Subtracting x from 100x, we get \(100x-x=257.\overline{57}- 2.\overline{57}\)

 

\(99x= 257.\overline{57}-2.\overline{57}\\ 99x=257\\ x=257/99\\ x=2 \frac{19}{33}\)

 

So our final answer is \(2 \frac{19}{33}\)

 

Thanks! :)

 Jun 13, 2024

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