Question

# To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$, if $q = {2^m}{5^n}$ then m and n must belong to?(A) $Z$ (B) $N \cup \{ 0\}$ (C) $N$ (D) $R$

According to the question, the given number is $\dfrac{p}{q}$.
Further, the value of $\dfrac{p}{q}$ must be a terminating decimal. And the value of q is ${2^m}{5^n}$. From this we can conclude that m and n can have only positive values.
If m and n take negative values or zero, then we will not get the value of $\dfrac{p}{q}$ a decimal number.
So, m and n will have only positive integral values. And in the denominator we have q i.e. ${2^m}{5^n}$ which will always be a multiple of either 2 or 5 or both. Thus, the value of $\dfrac{p}{q}$ will always result in a terminating decimal number.
For ex: $\dfrac{1}{3},\dfrac{4}{{13}},\dfrac{6}{7},\dfrac{{11}}{{17}}$