The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $0.2\overline{35}$

(A) Let $x = 0.2\overline{35}$.
This means $x = 0.2353535...$ (Equation $1$).
Multiply both sides by $10$ to shift the decimal point: $10x = 2.353535...$ (Equation $2$).
Multiply Equation $1$ by $1000$: $1000x = 235.353535...$ (Equation $3$).
Subtract Equation $2$ from Equation $3$:
$1000x - 10x = 235.353535... - 2.353535...$
$990x = 233$.
Therefore,$x = \frac{233}{990}$.
Since the number can be expressed in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$,it is a rational number.