Question

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

Answer 1

The numbers will be

2, 4, 8, 16, 32, 64, 128,

5, 25, 125,

10, 20, 40, 50, 80, 100, 160, 200

Therefore 18 no.

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Answer 2

As we know a number is terminating if it's denominator is either of the form $2^{m} or 5^{n} or 2^{m}\times5^{n} { \text{where m and n are positive integers.}}$

Number [2≤n≤200]  Such that 1/n has a terminating decimal expansion are =[2,4,5,8,10,16,20,25,32,40,50,64,80,100,125,128,160,200]=18 in number.

As each number can be factorized as $2^{m} or 5^{n} or 2^{m}\times5^{n}$.

Total number of numbers=18