Which of the following numbers has


Which of the following numbers has terminating decimal expansion?

(a) $\frac{37}{45}$

(b) $\frac{21}{2^{3} 5^{6}}$

(C) $\frac{17}{49}$

(d) $\frac{89}{2^{2} 3^{2}}$


Here we have to check terminating decimal expansion.

We know that if the numerator can be written in the form  where and are non negative positive integer then the fraction will surely terminate. We proceed as follows to explain the above statement

$\frac{21}{2^{3} \times 5^{6}}=\frac{2^{2} \times 21}{2^{2} \times 2^{3} \times 5^{3}}$

$=\frac{84}{(2 \times 5)^{5}}$




Hence the correct option is (b).

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