The decimal expansion of 141120 will terminate after how many places?

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Question

The decimal expansion of $\frac{141}{120}$ will terminate after how many places?

Options:

A . 3

B . 5

C . 7

D . Will not terminate

Answer: Option A
:
A

Given rational number $\frac{141}{120}$

Here, $120 = 2^{3} \times 3 \times 5$

$141 = 3 \times 47$

$\Rightarrow$ $\frac{141}{120}$ = $\frac{3 \times 47}{2^{3} \times 3 \times 5}$

= $\frac{47}{2^{3} \times 5}$

Multiply and divide by $5^{2}$ .

= $\frac{47 \times 5^{2}}{2^{3} \times 5 \times 5^{2}}$
= $\frac{47 \times 25}{(2 \times 5)^{3}}$

= $\frac{1175}{1000}$

= 1.175

Therefore, $\frac{141}{120}$ will terminate after three decimal places.

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