Difference between revisions of "1988 AJHSME Problems/Problem 8"

(New page: ==Problem== Betty used a calculator to find the product <math>0.075 \times 2.56</math>. She forgot to enter the decimal points. The calculator showed <math>19200</math>. If Betty had e...)
 
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==Problem==
 
==Problem==
  
Betty used a calculator to find the product <math>0.075 \times 2.56</math>.  She forgot to enter the decimal points.  The calculator showed <math>19200</math>.  If Betty had entered the decimal points correctly, the answer would have been
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Betty used a calculator to find the [[product]] <math>0.075 \times 2.56</math>.  She forgot to enter the decimal points.  The calculator showed <math>19200</math>.  If Betty had entered the decimal points correctly, the answer would have been
  
 
<math>\text{(A)}\ .0192 \qquad \text{(B)}\ .192 \qquad \text{(C)}\ 1.92 \qquad \text{(D)}\ 19.2 \qquad \text{(E)}\ 192</math>
 
<math>\text{(A)}\ .0192 \qquad \text{(B)}\ .192 \qquad \text{(C)}\ 1.92 \qquad \text{(D)}\ 19.2 \qquad \text{(E)}\ 192</math>
  
 
==Solution==
 
==Solution==
The decimal point of 0.075 is three away from what Betty punched in, and that of 2.56 is two away. The decimal point is therefore <math>3+2=5</math>. units to the left of where it should be, so we would want <math>.19200\Rightarrow \mathrm{(B)}</math>.
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The [[decimal point]] of 0.075 is three away from what Betty punched in, and that of 2.56 is two away. The decimal point is therefore <math>3+2=5</math> units to the left of where it should be, so we would want <math>.19200\Rightarrow \mathrm{(B)}</math>.
  
 
==See Also==
 
==See Also==
  
[[1988 AJHSME Problems]]
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{{AJHSME box|year=1988|num-b=7|num-a=9}}
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[[Category:Introductory Algebra Problems]]

Revision as of 17:45, 2 June 2009

Problem

Betty used a calculator to find the product $0.075 \times 2.56$. She forgot to enter the decimal points. The calculator showed $19200$. If Betty had entered the decimal points correctly, the answer would have been

$\text{(A)}\ .0192 \qquad \text{(B)}\ .192 \qquad \text{(C)}\ 1.92 \qquad \text{(D)}\ 19.2 \qquad \text{(E)}\ 192$

Solution

The decimal point of 0.075 is three away from what Betty punched in, and that of 2.56 is two away. The decimal point is therefore $3+2=5$ units to the left of where it should be, so we would want $.19200\Rightarrow \mathrm{(B)}$.

See Also

1988 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions
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