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Question

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
151600

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Solution

we have,

151600=3320=326×52

this means that the prime factrorization of the denominator of 151600 s of the form 2m×5n.

hence, it has terminating decimal expansion which terminates after max(6,2)=6 places of decimals.

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