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Question

Without actually performing the long division state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

133125.


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Solution

If the denominator has factors of the form of 2m×5n then it has a terminating decimal expansion.

If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.

Now, factorizing the denominator.

3125=5×5×5×5×5=55

As the denominator has only 5 as its factor.

Hence, 133125 has a terminating decimal expansion.


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