We can re write as : \(\frac{1}{2^n} < \frac{1}{100}\)

Now to satisfy the equation \(\frac{1}{2^n}\) > 100 (Since greater the denominator the smaller the number)

So \(2^7\) = 128 which is greater than 100

Hence \(\frac{1}{2^n} < 0.01\) holds correct when the least value of n = 7
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We can rewrite the equation as 1/2^(n) < 1/100, which is 2^(n) > 100. We may see 100 as (2*5)^2 = 2^2 * 5^2.
Thus 2^(n)/2^2 = 5^2 or 2^(n-2) = 25. We are looking for the least value of 2^(n-2) which is greater than 25. The least power of 2 greater than 25 is 2^5 = 32.
Therefore n-2 = 5 or n=7.
Answer is A.

Regards.
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1/2^n<0.01
= 1/2^n < 1/100
= 2^n>100
When, 2^7 then it will be 64, Again when 2^8 then it will be 128
so that n must be 7 to meet the criteria