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If 0 < 10^n < 1,000,000, where n is a non-negative integer,
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Bunuel
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If 0 < 10^n < 1,000,000, where n is a non-negative integer, [#permalink] New post  01 Oct 2017, 22:17
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If \(0 < 10^n < 1,000,000\), where n is a non-negative integer, what is the greatest value of \(\frac{1}{2^n}\)?


A. 1/2
B. 1
C. 5
D. 32
E. 64

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pranab223
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Re: If 0 < 10^n < 1,000,000, where n is a non-negative integer, [#permalink] New post  01 Oct 2017, 23:10
Bunuel wrote:
If \(0 < 10^n < 1,000,000\), where n is a non-negative integer, what is the greatest value of \(\frac{1}{2^n}\)?


A. 1/2
B. 1
C. 5
D. 32
E. 64

Kudos for correct solution.


In the fraction, the greater the value of n the lower the \(\frac{1}{2^n}\).

here the value of n should be between 0 to 5

so \(\frac{1}{2^0}\) = 1

\(\frac{1}{2^1}\) = 0.5

\(\frac{1}{2^2}\) = 0.25

similarly \(\frac{1}{2^5}\) = 0.031.

Hence option B is correct.
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G
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Re: If 0 < 10^n < 1,000,000, where n is a non-negative integer, [#permalink] New post  09 Feb 2021, 22:50
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Given that n is non-negative integer and 0<10^n<1000000
Asking what is the greatest value of (1/2^n).
so here n must be positive, and an increase in n will reduce the fraction further.
Example, 1/2^1= 1/2 and 1/2^2=1/4.
here only zero works fine. 1/2^0 = 1 and hence this is the greatest value.
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