Answer
The repeated decimal can be represented in the lowest form as $\frac{47}{99}$.
Work Step by Step
The provided decimal can be written as:
$\begin{align}
& 0.\overline{47}=0.474747\ldots \\
& =\frac{47}{100}+\frac{47}{10000}+\frac{47}{1000000}\ldots \\
& =0.47+0.0047+0.000047+....
\end{align}$
So, it can be considered a geometric sequence such that
${{a}_{1}}=\frac{47}{100},r=\frac{1}{100}$
Thus,
$\begin{align}
& {{S}_{\infty }}=\frac{\frac{47}{100}}{1-\frac{1}{100}} \\
& =\frac{\frac{47}{100}}{\frac{99}{100}} \\
& =\frac{47}{99}
\end{align}$
