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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 • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
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
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