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in Number System by (41.0k points)
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Which one of the following rational numbers have non-terminating repeating decimal expansion ?

A) \(\cfrac{31}{3125}\)

B) \(\cfrac{71}{512}\)

C) \(\cfrac{23}{200}\)

D) None of these

2 Answers

+1 vote
by (57.0k points)
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Best answer

Correct option is (D) None of these

(A) \(\frac{31}{3125}\); 3125 \(=5\times5\times5\times5\times5=5^5\)

The prime factor of denominator of given ration number (3125) is 5 only.

\(\therefore\) \(\frac{31}{3125}\) has terminating decimals.

(B) \(\frac{71}{512}\); 512 \(=2\times2\times2\times2\times2\times2\times2\times2\times2=2^9\)

\(\because\) The prime factor of 512 is 2 only.

\(\therefore\) \(\frac{71}{512}\) has terminating decimals.

(C) \(\frac{23}{200}\); 200 \(=2\times2\times2\times5\times5=2^3\times5^2\)

\(\because\) The prime factor of 200 are 2 and 5 only.

\(\therefore\) \(\frac{23}{200}\) has terminating decimals.

+1 vote
by (37.4k points)

Correct option is D) None of these

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