1985 AJHSME Problems/Problem 3

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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 make quick work of this: \[\frac{10^7}{5 \times 10^4} = \frac{10^3}{5}\]

We know that $10^3 = 10 \times 10 \times 10$, so

\begin{align*} \frac{10^3}{5} &= \frac{10\times 10\times 10}{5} \\ &= 2\times 10\times 10 \\ &= 200 \\ \end{align*}

So the answer is $\boxed{\text{D}}$

See Also

1985 AJHSME Problems

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