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Question

# Let x=pq be a rational number, such that the prime factorisation of q is not of the form 2m5n, where n, m are non-negative integers. Then, x has a decimal expansion which is

A

Non-terminating and repeating (recurring)

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B

Terminating and non-repeating (non-recurring)

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C

Real Integer

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D

None of these

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Solution

## The correct option is A Non-terminating and repeating (recurring) A decimal is terminating only when the denominator can be prime factored in the form of 2m5n. If the denominator has any other prime factor then the decimal becomes non-terminating and repeating.

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