Equivalence of Repeating Decimal

Question

GRE exam question asks what is greater

$.\overline{717}$

or

$.\overline{71}$

I believe both are equal, but GRE says that $.\overline{717}$ is greater.

But why?

If they repeat for infinity, isn't the value the same, i.e.

$.71717171717171717171717171717171717171...$

Answer 1

The first one is $0.717,717,717\dots$ while the second is $0.717,171,717\dots$. They differ in the fourth place. Alternately, $0.\overline{717}=\frac {717}{999}$ while $0.\overline {71}=\frac {71}{99}$. You can cross multiply to find which is larger.