Answer
The repeated decimal $0.\bar{6}$ can be represented in lowest form as $\frac{2}{3}$
Work Step by Step
It can be an infinite geometric sequence as:
$\begin{align}
& 0.\bar{6}=0.6+0.06+0.006+\ldots \\
& {{a}_{1}}=\frac{6}{10},r=\frac{1}{10} \\
& {{S}_{\infty }}=\frac{\frac{6}{10}}{1-\frac{1}{10}}
\end{align}$
Therefore,
$\begin{align}
& {{S}_{\infty }}=\frac{\frac{6}{10}}{\frac{9}{10}} \\
& {{S}_{\infty }}=\frac{6}{9} \\
& =\frac{2}{3}
\end{align}$
Hence, the repeated decimal can be represented in the lowest form as $\frac{2}{3}$.
