The decimal expansion of the rational number

Question:

The decimal expansion of the rational number $\frac{37}{2^{2} \times 5}$ will terminate after

(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places

 

Solution:

(b) two decimal places

$\frac{37}{2^{2} \times 5}=\frac{37 \times 5}{2^{2} \times 5^{2}}=\frac{185}{100}=1.85$

So, the decimal expansion of the rational number will terminate after two decimal places.

 

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