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Which of the following is closest to 10^180 – 10^30 ?

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Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 01 Mar 2011, 09:55
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Which of the following is closest to \(10^{180} – 10^{30}\) ?


A. \(10^{210}\)

B. \(10^{180}\)

C. \(10^{150}\)

D. \(10^{90}\)

E. \(10^6\)
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 01 Mar 2011, 09:58
you can rewrite it as \(10^30\)*(\(10^150\) - 1). Now \(10^150\) - 1 is ~\(10^150\) so expression is closest to 10^180.

Answer B
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 01 Mar 2011, 10:10
banksy wrote:
Which of the following is closest to 10^180 – 10^30 ?

A. 10^210
B. 10^180
C. 10^150
D. 10^90
E. 10^6


10^180 is much, much, much bigger number than 10^30 and as we need approximate value then it's pretty much negligible in this case, so: 10^180 – 10^30=~10^180.

Answer: B.
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 01 Mar 2011, 16:55
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banksy wrote:
Which of the following is closest to 10^180 – 10^30 ?

A. 10^210
B. 10^180
C. 10^150
D. 10^90
E. 10^6


If you have difficulty in visualizing this approximation, think about it this way:

Which of the following is closest to 10^2 – 10^1 ?

A. 1
B. 10
C. 100
D. 1000

100 - 10 is 90. Since, for a reasonably big number, a smaller power of the number is much smaller than any greater power, the answer will definitely be closer to 10^180 than any other power of 10.
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 28 Dec 2013, 04:34
banksy wrote:
Which of the following is closest to 10^180 – 10^30 ?

A. 10^210
B. 10^180
C. 10^150
D. 10^90
E. 10^6



10^180 - 10^30 can be written as 10^30*(10^150 - 1) just as the first poster said, but one other thing is worth mentioning: PEMDAS.

When you both have multiplication and parenthesis, do the operation in the parenthesis first, then the multiplication. In our case, the subtraction is extremely minescule and thus the parenthesis is almost exactly 10^150.

Now, do the multiplication: 10^30 * 10^150 = 10^180
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 18 Jun 2016, 10:21
10^180 – 10^30

10^30 * (10^150 – 1)

as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^150 – 1) would remain as 10^150.
and 10^30 * 10^150 = 10^180. Answer is B.
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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New post 24 Jun 2017, 08:19
This is a good question for approximation .
10^180 is much greater than 10^30
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Re: Which of the following is closest to 10^180 – 10^30 ?  [#permalink]

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