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Difference between revisions of "1954 AHSME Problems/Problem 34"
 
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== Solution ==
 
== Solution ==
  
−
<math>\frac{333333333}{10^8}-\frac{1}{3}\implies \frac{3\cdot 10^7+3\cdot 10^6+\dots+3\cdot 10^0}{10^8}-\frac{1}{3}\implies\frac{3(10^{8}-1)}{9\cdot 10^{8}}-\frac{1}{3}\implies\frac{10^8-1}{3\cdot 10^8}-\frac{1}{3}\implies\frac{10^8}{3\cdot 10^8}-\frac{1}{3\cdot 10^8}-\frac{1}{3}\implies\frac{-1}{3\cdot 10^8}</math>
+
<math>\frac{33333333}{10^8}-\frac{1}{3}\implies \frac{3\cdot 10^7+3\cdot 10^6+\dots+3\cdot 10^0}{10^8}-\frac{1}{3}\implies\frac{3(10^{8}-1)}{9\cdot 10^{8}}-\frac{1}{3}\implies\frac{10^8-1}{3\cdot 10^8}-\frac{1}{3}\implies\frac{10^8}{3\cdot 10^8}-\frac{1}{3\cdot 10^8}-\frac{1}{3}\implies\frac{-1}{3\cdot 10^8}</math>
−
Because we did <math>.333333333-\frac{1}{3}</math>, it is <math>\fbox{B}</math>
+
Because we did <math>.33333333-\frac{1}{3}</math>, it is <math>\fbox{D}</math>
  
 
==See Also==
 
==See Also==

Latest revision as of 16:38, 23 September 2024

Problem 34

The fraction $\frac{1}{3}$:

$\textbf{(A)}\ \text{equals 0.33333333}\qquad\textbf{(B)}\ \text{is less than 0.33333333 by }\frac{1}{3\cdot 10^8}\\ \textbf{(C)}\ \text{is less than 0.33333333 by }\frac{1}{3\cdot 10^9}\\ \textbf{(D)}\ \text{is greater than 0.33333333 by }\frac{1}{3\cdot 10^8}\\ \textbf{(E)}\ \text{is greater than 0.33333333 by }\frac{1}{3\cdot 10^9}$

Solution

$\frac{33333333}{10^8}-\frac{1}{3}\implies \frac{3\cdot 10^7+3\cdot 10^6+\dots+3\cdot 10^0}{10^8}-\frac{1}{3}\implies\frac{3(10^{8}-1)}{9\cdot 10^{8}}-\frac{1}{3}\implies\frac{10^8-1}{3\cdot 10^8}-\frac{1}{3}\implies\frac{10^8}{3\cdot 10^8}-\frac{1}{3\cdot 10^8}-\frac{1}{3}\implies\frac{-1}{3\cdot 10^8}$ Because we did $.33333333-\frac{1}{3}$, it is $\fbox{D}$

See Also

1954 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 33 		Followed by
Problem 35
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All AHSME Problems and Solutions


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