The following real number has a decimal expansion as given below. Decide whether it is rational or not. If it is rational and of the form $\frac{p}{q}$,what can you say about the prime factors of $q$?
$0.120120012000120000 \ldots$

(N/A) The given decimal expansion is $0.120120012000120000 \ldots$
$1$. $A$ number is rational if its decimal expansion is either terminating or non-terminating recurring.
$2$. $A$ number is irrational if its decimal expansion is non-terminating and non-recurring.
$3$. In the given number $0.120120012000120000 \ldots$,the pattern of digits does not repeat in a fixed block,and it does not terminate.
$4$. Since the decimal expansion is non-terminating and non-recurring,the given number is an irrational number.
$5$. Because it is irrational,it cannot be expressed in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$.