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Which of the following is closest to 1/1.001?
A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001
A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001
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15 Aug 2023, 04:00
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Which of the following is closest to \(\frac{1}{1.001}\)?
A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001
\(\frac{1}{1.001} = \frac{1}{1 + 0.001}\).
Multiply the above by \(\frac{1 - 0.001}{1 - 0.001}\):
\(\frac{1 - 0.001}{(1 + 0.001)(1 - 0.001)} =\frac{1 - 0.001}{1 - 0.001^2} \).
Now, because \(0.001^2\) is very small, \(1 - 0.001^2\) is very close to 1. Therefore, \(\frac{1 - 0.001}{1 - 0.001^2} \approx \frac{1 - 0.001}{1} = 1 - 0.001 = 0.999\).
Answer: C
A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001
\(\frac{1}{1.001} = \frac{1}{1 + 0.001}\).
Multiply the above by \(\frac{1 - 0.001}{1 - 0.001}\):
\(\frac{1 - 0.001}{(1 + 0.001)(1 - 0.001)} =\frac{1 - 0.001}{1 - 0.001^2} \).
Now, because \(0.001^2\) is very small, \(1 - 0.001^2\) is very close to 1. Therefore, \(\frac{1 - 0.001}{1 - 0.001^2} \approx \frac{1 - 0.001}{1} = 1 - 0.001 = 0.999\).
Answer: C
General Discussion
abhijitatprepitt
10 May 2017, 13:09
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Cez005
Which of the following is closest to (1)/(1.001)?
A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001
This question has been posted previously; however, the thread is short and discontinued. I'm looking for a clear approach for solving this type of problem besides back-solving. Thanks!
A. 0.997
B. 0.998
C. 0.999
D. 1.000
E. 1.001
This question has been posted previously; however, the thread is short and discontinued. I'm looking for a clear approach for solving this type of problem besides back-solving. Thanks!
Back solving seems the best way. Since you can eliminate D and E from the get go start with C. Back-solving should be easy because multiplications are with 1.
Another approach could be a little bit of factoring:
1/1.001 = 1000/1001 = (1001-1)/1001 = 1 - 1/1001 ~ 1 - 0.001 ~ 0.999. Since there is approximation inherent in the last two steps of this approach, I would be cautious.
