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16 Sep 2014, 01:25
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If \(n\) is an integer and \(\frac{1}{10^{n+1} } \lt 0.00737 \lt \frac{1}{10^n}\), what is the value of \(n\)?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
16 Sep 2014, 01:25
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Official Solution:
If \(n\) is an integer and \(\frac{1}{10^{n+1} } \lt 0.00737 \lt \frac{1}{10^n}\), what is the value of \(n\)?
A. 1
B. 2
C. 3
D. 4
E. 5
There is no need for algebraic manipulation to answer this question.
\(\frac{1}{10^{n+1} }\) is 10 times smaller than \(\frac{1}{10^n}\). When expressed as decimals, both have the form 0.001 (with a varying number of zeros preceding the 1). For the given expression to be valid, we should have: \(0.001 < 0.00737 < 0.01\). This implies that \(n=2\) (since \(\frac{1}{10^n}=0.01\), then \(n=2\)).
Answer: B
If \(n\) is an integer and \(\frac{1}{10^{n+1} } \lt 0.00737 \lt \frac{1}{10^n}\), what is the value of \(n\)?
A. 1
B. 2
C. 3
D. 4
E. 5
There is no need for algebraic manipulation to answer this question.
\(\frac{1}{10^{n+1} }\) is 10 times smaller than \(\frac{1}{10^n}\). When expressed as decimals, both have the form 0.001 (with a varying number of zeros preceding the 1). For the given expression to be valid, we should have: \(0.001 < 0.00737 < 0.01\). This implies that \(n=2\) (since \(\frac{1}{10^n}=0.01\), then \(n=2\)).
Answer: B
General Discussion
