Question

Which of the following rational numbers have non terminating repeating decimal expansion A 31/3125 B) 71/512 C)23/200

D none of these

Answer 1

Hence option (D) has a non terminating repeating decimal expansion.

D none of these.

Step-by-step explanation:

Given:

A) 31/3125

B) 71/512

C)23/200

D) none of these

We know that a rational number has a terminating decimal expansion, if the prime factorisationof the denominator is of the form of $2^m 5^n$, where m and n are non negative integers.

Now solving one by one.

A) $\frac{31}{3125}=\frac{31}{5\times5\times5\times5\times5}$

                                  = $\frac{31}{5^52^0}$

So, given number has terminating decimal expansion.

B) $\frac{17}{512}=\frac{17}{2\times2\times2\times2\times2\times2\times2\times2\times2\times2}$

                                =$\frac{17}{2^95^0}$

So, given number has terminating decimal expansion.

C)$\frac{23}{200}=\frac{23}{2\times2\times2\times5\times5}$

                                 =$\frac{23}{2^35^2}$

So, given number has terminating decimal expansion.

Hence option (D) has a non terminating repeating decimal expansion.

D none of these.

                               

Answer 2

Step-by-step explanation:

i think it's answer is d none of these