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Question

Write the condition to be satisfied by q so that a rational number pqhas a terminating decimal expansion.

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Solution

We need to find the condition to be satisfied by q so that a rational number has a non-terminating decimal expression.

For the terminating decimal expression, we should not have a multiple of 10 in the denominator.

Hence, the prime factorization of q must not be of the form, where m and n are non-negative integers.


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