# 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

Let $x=p/q$ be a rational number such that the prime factorization of $q$ is of the form ${2}^{m}\times {5}^{n}$ , where n, m are positive integers.

Then$x$ has a decimal expansion which terminates.

Example:

$(49/500)=(49/{2}^{2}\times {5}^{3})$

Since the denominator is of the form ${2}^{m}\times {5}^{n}$, the rational number has a terminating decimal expansion.

Any rational number its denominator is in the form of ${2}^{m}\times {5}^{n}$,where m,n are positive integers are terminating decimals.

So correct answer will be option A

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