Question

The decimal expansion of k/2^5×7^2is terminating. The value of k can be equal to

Answer 1

Given : The decimal expansion of k/2^5×7^2is terminating

To find : The value of k

Solution:

The decimal expansion of k/2^5×7^2is terminating.

Any rational number is terminating decimal expansion if written in simplest form ,  its denominator have only prime factor of 2 & 5

k/(2⁵ * 7²)

Here Denominator  Has a factor 7² other than factor of 2

Hence K must have  7² as Factor  

So k must  be  = 49n   n ∈ N

k can be  49 , 98  , 147 , , 196 and so on

so if options are provided the one option can be selected

otherwise k = 49n   n ∈ N

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