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  4. The number of positive integers n in the set 2,3,..., 200 such that (1/n) has a terminating decimal expansion is

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Q. The number of positive integers $n$ in the set $\{2,3,..., 200\}$ such that $\frac{1}{n}$ has a terminating decimal expansion is

KVPYKVPY 2017

Solution:

We have, $n \in \{2, 3, 4, 5, 6, 200\}$
$\frac{1}{n}$ has terminating decimal of $n = 2^a \times 5^b$
$\therefore n = 2,4, 5, 8, 10, 16, 20, 25, 32, 40, 50$,
$ 64, 80, 100, 125, 128, 160, 200$
Total number of $n = 18$