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

Question

The number of positive integers n in the set 2,3,..., 200 such that (1/n) has a terminating decimal expansion is (A) 16 (B) 18 (C) 40 (D) 100

Tardigrade Admin · Accepted Answer

We have, n ∈ 2, 3, 4, 5, 6, 200 (1/n) has terminating decimal of n = 2a × 5b ∴ n = 2,4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200 Total number of n = 18

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

16

18

40

100

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

Q. The number of positive integers n in the set {2,3,...,200} such that n1​ has a terminating decimal expansion is

16

18

40

100

We have, n∈{2,3,4,5,6,200} n1​ has terminating decimal of n=2a×5b ∴n=2,4,5,8,10,16,20,25,32,40,50, 64,80,100,125,128,160,200 Total number of n=18

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

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