Question

How do you convert $0.6$ ( $6$ being repeated) to a fraction?

Answer 1

$0.\overline{6}=\frac{2}{3}$
Multiply by $10$ to shift one place to the left and subtract the starting number to cancel out the repeating decimal.
To do this multiply by $(10-1)$
$(10-1)\dot{}0.\overline{6}=6.\overline{6}-0.\overline{6}=6$
To do divided both sides $(10-1)$ to find :
$0.\overline{6}=\frac{6}{10-1}=\frac{6}{9}=\frac{3\times 2}{3\times 3}=\frac{2}{3}$