Show that $0.3333... = 0.\overline{3}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

(N/A) Let $x = 0.3333...$ (Equation $1$).
Multiply both sides by $10$:
$10x = 3.3333...$ (Equation $2$).
Since $x = 0.3333...$,we can write $10x = 3 + 0.3333... = 3 + x$.
Subtracting $x$ from both sides:
$10x - x = 3$
$9x = 3$
$x = \frac{3}{9} = \frac{1}{3}$.
Thus,$0.\overline{3}$ can be expressed as $\frac{1}{3}$,where $p = 1$ and $q = 3$ are integers and $q \ne 0$.