1989 AJHSME Problems/Problem 4

Problem

Estimate to determine which of the following numbers is closest to $\frac{401}{.205}$ .

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

Solution 1

$401$ is around $400$ and $.205$ is around $.2$ so the fraction is approximately $\frac{400}{.2}=2000\rightarrow \boxed{\text{E}}$

Solution 2

Using scientific notation estimated to the first significant digit, we see the numerator rounds to $\frac{4*10^2}{2*10^{-1}}$ . Subtracting the exponents gives $2-(-1)=3$ . The answer choice that has $3$ zeros to the right of the significant digit is $\boxed{\text{E}}$

1989 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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1989 AJHSME Problems/Problem 4

Contents

Problem

Solution 1

Solution 2

See Also