Question:
The value of $0.23+0.22$ is
(a) $0 . \overline{45}$
(b) $0 . \overline{43}$
(c) $0 . \overline{45}$
(d) $0.45$
Solution:
Given that $0 . \overline{23}+0 . \overline{22}$
Let $x=0 . \overline{23}+0 . \overline{22}$
Now we have to find the value of $x$
$\Rightarrow x=0 . \overline{23}+0 . \overline{22}$
$\Rightarrow x=\frac{23}{99}+\frac{22}{99}$
$\Rightarrow x=\frac{23+22}{99}$
$\Rightarrow x=\frac{45}{99}$
$\Rightarrow x=\frac{5}{11}$
$0 . \overline{23}+\overline{0.22}=0 . \overline{45}$
The correct option is 
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