1988 AJHSME Problems/Problem 6

Problem

$\frac{(.2)^3}{(.02)^2} =$

$\text{(A)}\ .2 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 15 \qquad \text{(E)}\ 20$

Solution

Converting the decimals to fractions gives us $\frac{(.2)^3}{(.02)^2} =\frac{\left( \frac{1}{5}\right)^3}{\left(\frac{1}{50}\right)^2}=\frac{50^2}{5^3}=\frac{2500}{125}=20\Rightarrow \mathrm{(E)}$ .

Solution 2

We expand $\frac{(0.2)^3}{(0.02)^2}$ , and get $\frac{(0.2)*(0.2)*(0.2)}{(0.02)(0.02)}$ . The two $0.02$ 's "cancel" out with the two $0.2$ 's, leaving the fraction as: $(10)*(10)*(0.2)$ . Using basic calculations, we compute this expression to get $20\Rightarrow \mathrm{(E)}$ .

1988 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AJHSME/AMC 8 Problems and Solutions

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1988 AJHSME Problems/Problem 6

Contents

Problem

Solution

Solution 2

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