decimal expansion of a rational number is terminating if In its denominator there is a. 2 or5 b. 3 or6 c. 9 or11 d. 3or7

Dear student,

Let $x=p/q$ be a rational number such that the prime factorization of $q$ is of the form ${2}^{m}×{5}^{n}$ , where n, m are positive integers.
Then has a decimal expansion which terminates.
Example:

$\left(49/500\right)=\left(49/{2}^{2}×{5}^{3}\right)$

Since the denominator is of the form ${2}^{m}×{5}^{n}$, the rational number has a terminating decimal expansion.
Any rational number its denominator is in the form of ${2}^{m}×{5}^{n}$,where m,n are positive integers are terminating decimals.
So correct answer will be option A

Regards

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