Question:
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) $\frac{89}{2^{2} 3^{2}}$
Solution:
Here we have to check terminating decimal expansion.
We know that if the numerator can be written in the form 
where m and n are non negative positive integer then the fraction will surely terminate. We proceed as follows to explain the above statement
$\frac{21}{2^{3} \times 5^{6}}=\frac{2^{2} \times 21}{2^{2} \times 2^{3} \times 5^{3}}$
$=\frac{84}{(2 \times 5)^{5}}$
$=\frac{84}{10^{5}}$
$=\frac{84}{100000}$
$=0.00089$
Hence the correct option is (b).