Check If a Given Rational No. Is Terminating or Not
Let x = p / q...
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 repeating (recurring)
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B
Terminating 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 ANon-terminating repeating (recurring) A decimal is terminating only when the denominators 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.