Question

1. If * a/b is a rational number (b ne0) in its lowest form, then what is a/b the condition on b so that the decimal representation of is terminating?​

Answer 1

Answer:

It would be a rational number

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Answer 2

Answer:

ab can be represented in a terminating decimal representation only if by multiplying both the numerator and denominator by some whole number n, you can get

ab=n×an×b=n×a10k

⟹n×b=10k

⟹n=10kb

⟹n=2k×5kb

Since n is a positive integer, 2 and/or 5 can be the only prime factors of b.

So we have our answer -

ab can be represented in a terminating decimal representation only if b=2p×5q, where p and q are non-negative integers, including zero