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If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n?

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If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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New post 15 Aug 2017, 00:32
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If \(10^n< 0.000025 <10^{n+1}\), what is the value of an integer n?

A. -5
B. -4
C. -3
D. 4
E. 5
[Reveal] Spoiler: OA

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If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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New post 15 Aug 2017, 00:59
To find the exact value of the expression, simplify the expression:
\(0.000025 = 25*10^{-6} = \frac{100*10^{-6}}{4} = \frac{10^{2-6}}{4} = \frac{1}{4}*10^{-4}\)

Since this value must be between the range \(10^n\) and \(10^{n+1}\),
n must take the value of -5 as the value is between \(10^{-5}\) and \(10^{-4}\) (Option A)
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Re: If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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New post 15 Aug 2017, 01:02
MathRevolution wrote:
If \(10^n< 0.000025 <10^{n+1}\), what is the value of an integer n?

A. -5
B. -4
C. -3
D. 4
E. 5

0.000025 = 2.5*10^(-5)
also,
1<2.5<10
therefore
10(-5)<2.5*10^(-5)<10^(-4)
On comparing, we get
n = -5
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Re: If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n? [#permalink]

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New post 16 Aug 2017, 23:53
=>\(0.00001 < 0.000025 < 0.0001\)
\(10^{-5} < 0.000025 < 10^{-4}\)

Ans: A
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Re: If 10^n< 0.000025 <10^{n+1}, what is the value of an integer n?   [#permalink] 16 Aug 2017, 23:53
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