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Question 10
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form pq? Give reasons.

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Solution

327.7081 is terminating decimal number. So, it represents a rational number and also its denominator must have the form 2m×5n .
Thus,
327.7081=327708110000=pq
q=104=2×2×2×2×5×5×5×5=24×54=(2×5)4
Hence, the prime factorization of q contains only factors of 2 and 5.

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