Difference between revisions of "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 $20\Rightarrow \mathrm{(E)}$.