The decimal expansion of the rational number nbsp-145871250 nbsp-will terminate after -a- nbsp- one decimal places nbsp- nbsp- nbsp- nbsp- nbsp- -b- nbsp- nbsp-two decimal places-c- three decimal place nbsp- nbsp- nbsp- nbsp- nbsp-d- nbsp- four decimal places

Consider the rational number 145871250. Now, 1250 = 54 times; 2 The denominator can be written in the form of 2m times; 5n. So, the given number has a ...

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Standard X

Mathematics

Equations Reducible to a Pair of Linear Equations in Two Variables

The decimal e...

Question

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after :

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

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Solution

Consider the rational number $\frac{14587}{1250}$ .

Now, 1250 = 5⁴ × 2

The denominator can be written in the form of 2^m × 5ⁿ.

So, the given number has a terminating decimal expansion.

$\frac{14587}{1250} = \frac{14587}{5^{4} \times 2^{1}} = \frac{14587 \times 8}{5^{4} \times 2^{4}} = \frac{116696}{10000} = 11.6696$

The given rational number will terminate after four decimal places.

Hence, the correct answer is option D.

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Question 10
The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after

A) One decimal place
B) Two decimal places
C) Three decimal places
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A) One decimal place
B) Two decimal places
C) Three decimal places
D) Four decimal places

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The decimal expansion of the rational number 145871250 will terminate after : (a) one decimal places (b) two decimal places (c) three decimal place (d) four decimal places

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after :

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