Answer
$134.066\text{ inches}$.
Work Step by Step
From the given information, we can observe that it is a geometric series
$16,0.96\left( 16 \right),{{0.96}^{2}}\left( 16 \right),{{0.96}^{3}}\left( 16 \right),\cdots $
Here ${{a}_{1}}=16$ and common ratio $r=0\cdot 96$ and $n=10$.
We use the formula for the sum of a geometric series with finite terms ${{S}_{n}}=\frac{{{a}_{1}}\left( 1-{{r}^{n}} \right)}{\left( 1-r \right)}$.
Thus
$\begin{align}
& {{S}_{n}}=\frac{16\left( 1-0\cdot {{96}^{10}} \right)}{\left( 1-0\cdot 96 \right)} \\
& =\frac{16\left( 1-0\cdot 6648 \right)}{\left( 0\cdot 04 \right)} \\
& =134.066
\end{align}$
