Solution
We are given
[tex]0.2\bar{\text{ 46}}=0.246464646....[/tex]So we have
[tex]\begin{gathered} 0.2464646...=0.2+0.046464646 \\ 0.2464646...=\frac{2}{10}+\frac{46}{990} \\ 0.2464646...=\frac{122}{495} \end{gathered}[/tex]Therefore, the answer is
[tex]\frac{122}{495}[/tex]