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Question

Which one of the following numbers is a non-terminating and repeating decimal?


A

3924

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B

4956

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C

7832

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D

311

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Solution

The correct option is D

311


The decimal expansion of a rational number, pq is terminating If q is in the form of : 2m×5n,2m,5n



3924=13×38×3=138

The denominator of 138 is 8 which is 23

Thus, the decimal expansion of 3924 is terminating


4956=7×78×7=78

The denominator of 78 is 8 which is 23

Thus, the decimal expansion of 4956 is terminating


7832=39×216×2=3916

The denominator of 3916 is 16 which is 24

Thus, the decimal expansion of 7832 is terminating

The denominator of 311 is 11 which is 111.

Thus, the decimal expansion of 311 is recurring.


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