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 afterthreedecimal places.

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