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 $\frac{p}{q}$. $0.\overline{001}$

(A) Let $x = 0.\overline{001}$.
This means $x = 0.001001001...$ (Equation $1$).
Since there are $3$ repeating digits,multiply both sides by $10^3 = 1000$:
$1000x = 1.001001001...$ (Equation $2$).
Subtract Equation $1$ from Equation $2$:
$1000x - x = 1.001001001... - 0.001001001...$
$999x = 1$.
Therefore,$x = \frac{1}{999}$.
Since the number can be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$,it is a rational number.