Question:
The decimal expansion of $\frac{147}{120}$ will terminate after how many places of decimal?
(a) 1
(b) 2
(c) 3
(d) will not terminate
Solution:
The given number is $\frac{147}{120}$. We have to change the denominator in the form of $2^{m} \times 5^{n}$ and the given number terminates after largest of $m$ and $n$.
$\frac{147}{120}=\frac{147}{2^{3} \times 5 \times 3}$
$=\frac{49}{2^{3} \times 5^{1}}$
Here, $m=3, n=1$
Hence the given number terminates after 3 places.
Hence the correct option is $(c)$
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