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

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<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>
  
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==Solution==
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==Solution 1==
 
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>.
 
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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 +
==Solution 2==
 +
When you multiply one number with x number of decimal places with another number with y number of decimal places, the total number of decimal places is x+y. Using this we can can we the total number of decimal places should be <math>3+2=5</math>.  Then we take <math>19200.00</math> and move the decimal place to the left 5 times, then we get <math>0.19200</math>. Therefore the answer is <math>0.19200\Rightarrow \mathrm{(B)}</math>.
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~ algebraic_algorithmic
  
 
==See Also==
 
==See Also==
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{{AJHSME box|year=1988|num-b=7|num-a=9}}
 
{{AJHSME box|year=1988|num-b=7|num-a=9}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 16:27, 1 January 2025

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 1

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 $.19200\Rightarrow \mathrm{(B)}$.

Solution 2

When you multiply one number with x number of decimal places with another number with y number of decimal places, the total number of decimal places is x+y. Using this we can can we the total number of decimal places should be $3+2=5$. Then we take $19200.00$ and move the decimal place to the left 5 times, then we get $0.19200$. Therefore the answer is $0.19200\Rightarrow \mathrm{(B)}$.

~ algebraic_algorithmic

See Also

1988 AJHSME (Problems • Answer Key • Resources)
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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC logo.png

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