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0.3^20 or 0.03^50
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Updated on: 12 Sep 2018, 04:33
Updated on: 12 Sep 2018, 04:33
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Question Stats:
85% (00:38) correct
14% (00:49) wrong based on 61 sessions
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Quantity A |
Quantity B |
\((0.3)^{20}\) |
\((0.03)^{50}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: 0.3^20 or 0.03^50
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12 Sep 2018, 08:04
12 Sep 2018, 08:04
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Expert Reply
No need for any calculation.
0.3 is > 0.03 on the number line.
So when you raise 0.03 to a power you get a long list of zeroes > of when 0.3 is raised. As such. 0.03 getting smaller and smaller than 0.3.
A is the answer.
Regards
0.3 is > 0.03 on the number line.
So when you raise 0.03 to a power you get a long list of zeroes > of when 0.3 is raised. As such. 0.03 getting smaller and smaller than 0.3.
A is the answer.
Regards
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Re: 0.3^20 or 0.03^50
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13 Sep 2018, 07:44
13 Sep 2018, 07:44
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saifee wrote:
Quantity A |
Quantity B |
\((0.3)^{20}\) |
\((0.03)^{50}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Another approach is to apply a nice rule that says: (xy)^n = (x^n)(y^n)
So, 0.3 = (0.03)(10)
So, (0.3)^20 = [(0.03)(10)]^20
= (0.03^20)(10^20) [as per the rule above]
So we get:
Quantity A: (0.03^20)(10^20)
Quantity B: (0.03)^50
Divide both quantities by 0.03^20 to get:
Quantity A: (10^20)
Quantity B: (0.03)^30
At this point, we can see that Quantity A will be a HUGE number (1 followed by 20 zeros), whereas Quantity B will evaluate to be a number less than 1
Answer: A
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