The following real number is expressed in decimal form. Determine whether it is rational or not. If rational,express it in the form of $\frac{p}{q}$. $5 . \overline{123456}$

(N/A) The decimal form $5 . \overline{123456}$ is non-terminating and recurring. Therefore,it is a rational number.
Let $x = 5 . \overline{123456}$.
$\therefore x = 5.123456123456 \ldots$ (Equation $1$)
Since there are $6$ repeating digits,multiply both sides by $10^6 = 1000000$:
$\therefore 1000000x = 5123456.123456123456 \ldots$ (Equation $2$)
Subtracting Equation $1$ from Equation $2$:
$1000000x - x = 5123456.123456 \ldots - 5.123456 \ldots$
$999999x = 5123451$
$\therefore x = \frac{5123451}{999999}$
Simplifying the fraction by dividing both numerator and denominator by $9$:
$x = \frac{569272.333...}{111111}$ (Note: The fraction is $\frac{5123451}{999999}$ which is the standard $\frac{p}{q}$ form).