1985 AJHSME Problems/Problem 3

Problem

$\frac{10^7}{5\times 10^4}=$

$\text{(A)}\ .002 \qquad \text{(B)}\ .2 \qquad \text{(C)}\ 20 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 2000$

Solution

We immediately see some canceling. We see powers of ten on the top and on the bottom of the fraction, and we quickly make quick work of this.

$\frac{10^7}{5 \times 10^4} = \frac{10^3}{5}$ . We know that $10^3 = 10 \times 10 \times 10$ . We also know that $\frac{10}{2} = 5$ . So we have $\frac{10^3}{5} = \frac{10 \times 10 \times 10}{5} = 2 \times 10 \times 10 = 200$

So the answer is (D)

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1985 AJHSME Problems/Problem 3

Problem

Solution

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