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 $q$?
$43.123456789$

(A) The given number is $43.123456789$.
Since this number has a terminating decimal expansion,it is a rational number.
It can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.
For a rational number to have a terminating decimal expansion,the prime factorization of the denominator $q$ must be of the form $2^{m} \times 5^{n}$,where $m$ and $n$ are non-negative integers.
Therefore,the prime factors of $q$ are only $2$ or $5$ or both.