Express

Let $x$ be $0 . \overline{23}$

$x=0 . \overline{23}$  ...........(1)

Multiplying both sides by 100, we get

$100 x=23 . \overline{23}$     ..........(2)

Subtracting (1) from (2), we get

$100 x-x=23 . \overline{23}-0 . \overline{23}$

$\Rightarrow 99 x=23$

$\Rightarrow x=\frac{23}{99}$

Thus, simplest form of $0 . \overline{23}$ as a rational number is $\frac{23}{99}$.