Which one of the following rational numbers have non-terminating repeating decimal expansion ?

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.

Correct option is D) None of these