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Algebra Level pending

If k k is an integer and 0.0010101 × 1 0 k > 1001 0.0010101 \times 10^k > 1001 , the smallest value of k k is:

0 0 5 5 − 5 -5 − 6 -6 6 6

Aleksa Radovanović by Aleksa Radovanović , 25, Serbia

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1 solution

Kay Xspre
Nov 1, 2015

As 0.0010101 = 10101 1 0 7 0.0010101 = \frac{10101}{10^7} , we can write this inequality as 10101 × 1 0 k − 7 > 1001 10101 \times 10^{k-7} > 1001 , or 1 0 k − 7 > 1001 10101 10^{k-7} > \frac{1001}{10101} or 1 0 k − 6 > 0.990... 10^{k-6} > 0.990... . Here, as 1 > 0.990... 1 > 0.990... , the smallest k k is k = 6 k = 6 so as to make 1 0 k − 6 = 1 10^{k-6} = 1

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That is a complete answer. Nice :)

Aleksa Radovanović - 5 years, 7 months ago

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