Answer
$\dfrac{5}{11}$
Work Step by Step
The term $0.\overline{45}$ can be written as $0.45+0.0045+...$
Here, $r=0.01$ and $a_1=0.45$; which is an infinite geometric sequence.
Their sum is $S_{\infty}=\dfrac{a_1}{1-r}$
Thus,
$S_{\infty}=\dfrac{0.45}{1-0.01}$
or, $=\dfrac{45}{99}$
Hence,
$=\dfrac{5}{11}$
