Question

Convert $0.\overline{6}$ into fraction.

Answer 1

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 $(10-1):$

$(10-1).0.\overline{6}=6.\overline{6}-0.\overline{6}=6$

Then divide both sides by $(10-1)$ to find:

$0.\overline{6}=\frac{6}{10-1}=\frac{6}{9}=\frac{3.2}{3.3}=\frac{2}{3}$