Which of the following rational number have non- terminating repeating

1.	Which of the following rational number have non- terminating repeating decimal expansion?A) 31/3125 B) 71/512 C) 23/200 D) none of these
Answer» We know that a rational number has a terminating decimal expansion, if the prime factorization of the denominator is of the form of 2^m5ⁿ, where m and n are non negative integers. Now solving one by one. A) 31/3125 \(=\frac{31}{5\times5\times5\times5\times5}=\frac{31}{5^52^0}\) So, given number has terminating decimal expansion. B) 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) 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.

Which of the following rational number have non- terminating repeating decimal expansion?A) 31/3125 B) 71/512 C) 23/200 D) none of these

Answer»

We know that a rational number has a terminating decimal expansion, if the prime factorization of the denominator is of the form of 2^m5ⁿ, where m and n are non negative integers.

Now solving one by one.

A) 31/3125 \(=\frac{31}{5\times5\times5\times5\times5}=\frac{31}{5^52^0}\)

So, given number has terminating decimal expansion.

B) 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) 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.

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