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Difference between revisions of "1955 AHSME Problems/Problem 1"

(Created page with "== Problem == Which one of the following is not equivalent to <math>0.000000375</math>? <math> \textbf{(A)}\ 3.75\times 10^{-7}\qquad\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}...")
 
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Which one of the following is not equivalent to <math>0.000000375</math>?  
 
Which one of the following is not equivalent to <math>0.000000375</math>?  
  
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<math> \textbf{(A)}\ 3.75\times 10^{-7}\qquad\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}\qquad\textbf{(C)}\ 375\times 10^{-9}\\ \textbf{(D)}\ \frac{3}{8}\times 10^{-7}\qquad\textbf{(E)}\ \frac{3}{80000000} </math>  
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<math> \textbf{(A)}\ 3.75\times 10^{-7}\qquad\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}\qquad\textbf{(C)}\ 375\times 10^{-9}\qquad \textbf{(D)}\ \frac{3}{8}\times 10^{-7}\qquad\textbf{(E)}\ \frac{3}{80000000} </math>
  
 
==Solution==
 
==Solution==
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First of all, <math>0.000000375 = 3.75 \times 10^{-7}</math> in scientific notation. This eliminates <math>\textbf{(A)}\ 3.75\times 10^{-7}</math>, <math>\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}</math>, and <math>\textbf{(C)}\ 375\times 10^{-9}</math> immediately. <math>\textbf{(E)}\ \frac{3}{80000000}</math> is a bit harder, but it can be rewritten as <math>\frac{3}{8} \cdot 10^{-7}</math>, which is the same as <math>3.75 \times 10^{-7}</math>, so the answer is \frac{3}{8}\times 10^{-7}.
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First of all, <math>0.000000375 = 3.75 \times 10^{-7}</math> in scientific notation. This eliminates <math>\textbf{(A)}\ 3.75\times 10^{-7}</math>, <math>\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}</math>, and <math>\textbf{(C)}\ 375\times 10^{-9}</math> immediately. <math>\textbf{(E)}\ \frac{3}{80000000}</math> is a bit harder, but it can be rewritten as <math>\frac{3}{8 \times 10^{7}} = \frac{3}{8} \times 10^{-7}</math>, which is the same as <math>\textbf{(D)}</math>. Thus, the answer is either <math>\textbf{(D)}</math> or <math>\textbf{(E)}</math>.  The original contest had this error in it, although the desired answer was D.  It is likely that they intended option E to be <math>\frac{3}{8000000}</math>, but misprinted it.
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==See Also==
 
==See Also==
  

Latest revision as of 19:26, 4 October 2023

Problem

Which one of the following is not equivalent to $0.000000375$?

$\textbf{(A)}\ 3.75\times 10^{-7}\qquad\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}\qquad\textbf{(C)}\ 375\times 10^{-9}\qquad \textbf{(D)}\ \frac{3}{8}\times 10^{-7}\qquad\textbf{(E)}\ \frac{3}{80000000}$

Solution

First of all, $0.000000375 = 3.75 \times 10^{-7}$ in scientific notation. This eliminates $\textbf{(A)}\ 3.75\times 10^{-7}$, $\textbf{(B)}\ 3\frac{3}{4}\times 10^{-7}$, and $\textbf{(C)}\ 375\times 10^{-9}$ immediately. $\textbf{(E)}\ \frac{3}{80000000}$ is a bit harder, but it can be rewritten as $\frac{3}{8 \times 10^{7}} = \frac{3}{8} \times 10^{-7}$, which is the same as $\textbf{(D)}$. Thus, the answer is either $\textbf{(D)}$ or $\textbf{(E)}$. The original contest had this error in it, although the desired answer was D. It is likely that they intended option E to be $\frac{3}{8000000}$, but misprinted it.

See Also

1955 AHSC (Problems • Answer Key • Resources)
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First Question 		Followed by
Problem 2
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All AHSME Problems and Solutions


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