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If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

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If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 04 Apr 2016, 01:01
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If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4


* A solution will be posted in two days.

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If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 04 Apr 2016, 05:40
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MathRevolution wrote:
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4


* A solution will be posted in two days.


Hi,
\(10^{n-1}< 0.000125 <10^n\)...
or \(10^{n-1}< 0.000125*\frac{1000}{1000}<10^n\)...
or \(10^{n-1}< \frac{0.125}{1000}<10^n\)...
or \(10^{n-1}*1000<0.125 <10^n*1000\)...
or \(10^{n+2}< 0.125<10^{n+3}\)...
\(10^0=1\), which >.125
so \(n+3=0\)..\(n=-3\)
B
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 04 Apr 2016, 09:00
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MathRevolution wrote:
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4


* A solution will be posted in two days.


Let's TEST some values.

Answer choice A
If n = -4, when we get: 10^(-4-1)< 0.000125 < 10^(-4)
Simplify to get: 10^(-5) < 0.000125 < 10^(-4)
Or we can say: 1/100,000 < 0.000125 < 1/10,0000
Rewrite as decimals to get: 0.00001 < 0.000125 < 0.0001
This is NO GOOD, because 0.000125 is GREATER than 0.0001
ELIMINATE A


Answer choice B
If n = -3, when we get: 10^(-3-1)< 0.000125 < 10^(-3)
Rewrite as decimals to get: 0.0001 < 0.000125 < 0.001
PERFECT!!

Answer: B

Cheers,
Brent
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 06 Apr 2016, 06:29
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4


-> Multiply 10^6- > (10^6){10^(n-1)}<125<(10^6)(10^n) -> 125 is bigger than 100
-> (10^6)(10^(n-1))=100 -> 10^(6+n-1)=10^2, n+5=2 -> n=-3
Thus, the answer is B
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 06 Apr 2016, 07:21
wouldn't 10^-4 be .0010 since you move the decimal places 4 units to the right. Do we disregard the 0 next to the 10?
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 06 Apr 2016, 10:04
bullfromist wrote:
wouldn't 10^-4 be .0010 since you move the decimal places 4 units to the right. Do we disregard the 0 next to the 10?


You are right that the decimal moves 4 places, but this is actually scientific notation, and what is omitted from the way it is written above is the 1* in front of the \(10^{-4}\). So when you see \(10^{-1}\), what you should be reading is \(1*10^{-4}\). The decimal is moved for the 1, not the 10. Similarly, what do you do if you have \(876.38*10^{-3}\) ? You move the decimal on the 876.38 to the left 3 places. \(876.38*10^{-3} = 0.87638\)

You can prove it to yourself in another way:
\(10^{-1} = \frac{1}{10} = 0.1\)
\(10^{-2} = \frac{1}{10^2} = 0.01\)
\(10^{-3} = \frac{1}{10^3} = 0.001\)
\(10^{-4} = \frac{1}{10^4} = 0.0001\)

so \(10^{-4}\) is a shorthand way of saying "divide by 10000". But what are we dividing by 10000? Whatever is multiplied in front of \(10^{-4}\). If there's nothing written in front, then it's the same as multiplying by 1, and we typically don't write it when things are multiplied by 1.

I hope that clears up the confusion

Cheers
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 17 Jul 2016, 05:08
Hi!
Expert, i tried solving this question but still unable to comprehend using values substitution method.
kindly help with some other way out please..
chetan4u i do appreciate your method but do help me with understanding that once or something different which can be recalled while following same pattern question.
thanks
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 17 Jul 2016, 05:43
Celestial09 wrote:
Hi!
Expert, i tried solving this question but still unable to comprehend using values substitution method.
kindly help with some other way out please..
chetan4u i do appreciate your method but do help me with understanding that once or something different which can be recalled while following same pattern question.
thanks


Question Says 10^(n-1)< 125*10^-6<10^n

so, if we multiply the above inequality with 10^6, we will get

10^(n-1+6)<125 *10^(-6+6)<10^(n+6)

=> 10^(n+5)<125<10^(n+6)

Now, we have 100 less than 125 and 1000 greater than 125.

So, if we put n+5=2 , we will get n=-3, which will make the above inequality as

100<125<1000.

Hence the answer.

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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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New post 06 Jun 2018, 00:28
MathRevolution wrote:
If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?

A. -4
B. -3
C. -2
D. 3
E. 4


* A solution will be posted in two days.


\(10^{(n-1)} < 0.000125 < 10^n\)

\(0.000125 = 0.0001 + 0.000025 = 10^{-4} + 0.000025\)

so \(0.000125\) = a number slightly more than \(10^{-4}\) but still less than \(10^{-3}\)

Hence \(n = -3\)

Answer B.

Thanks,
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Re: If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n?  [#permalink]

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