Hi there,
In this specific problem, I was wondering if someone could explain to me how exactly the answer is C? By using a calculator you can get 1/14400 = 6.94 x 10^-5 which we can rewrite as 0.0000694, thus being 3 distinct digits I presume. Can someone confirm if this is the right way to approach this problem?
Secondly, lets assume we don’t use a calculator as mentioned in the video, In that scenario it was solved as follows:
While the 0.0625 is present, why doesn’t the 0.111 contribute to the number of digits as well? Any clarification on the thought process behind the logic would be much appreciated.
Are you asking whether using a calculator could qualify as a right approach? That’s your choice isn’t it? I don’t consider that an approach cuz then u learn nothing from the question.
You can see why the recurring part doesn’t contribute to the “distinct digits” if u solve the problem this way:
First rewrite \frac{1}{2^2 \cdot 3^2 \cdot 4^2 \cdot 5^2} as \frac{1}{10^6} \cdot \frac {5^4}{3^2}. Now you know that you can express \frac{5^4}{3^2} as 69 + \frac 49, where \frac 49 is a recurring decimal (in particular, it’s just a fractional representation of 0.\overline{4}). Owing to that, you quickly arrive at the answer of the fraction having 3 distinct nonzero digits.
