AMC 8 1986 Problem 20

AMC8 1986 年第 20 题

表达式与运算★★★☆☆

The value of the expression

\displaystyle \frac{(304)^5}{(29.7)(399)^4}

is closest to

表达式

\displaystyle \frac{(304)^5}{(29.7)(399)^4}

的值最接近

A.0.003
B.0.03
C.0.3
D.3
E.30

正确答案 · Correct Answer

D

解析 · Solution

Solution 1

By rounding,

\displaystyle \frac{(304)^5}{(29.7)(399)^4} \approx \frac{300^5}{30\cdot400^4} = \frac{3^5 \cdot 10^{10}}{3\cdot 4^4 \cdot 10^9} = \frac{3^4\cdot 10}{4^4} = \frac{810}{256} \approx 3

.

Note: The actual value of this expression, rounded to 8 decimal places, is 3.44921198.

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