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

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

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Solution

We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is of the form, where m and n are non-negative integers.

Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.

This is given that the prime factorization of the denominator is of the form.

Hence, it has terminating decimal expansion which terminates after places of decimal.

Hence, the correct choice is (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
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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 place (b) two decimal place (c) three decimal place (d) four decimal place

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

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