The value of the expression ((304)^5)/((29.7)(399)^4) is closest to

1986 AMC 8 Problem 20 — Solution

1986 AMC 8 Problem 20

Below is the professionally curated solution for Problem 20 of the 1986 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 8 solutions, or check the answer key.

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Concepts:estimation exponent

Difficulty rating: 980

20.

The value of the expression

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

is closest to

$.003$

$.03$

$.3$

$3$

$30$

Solution:

Estimating,

$\begin{aligned} \dfrac{300^5}{30 \cdot 400^4} &= 10 \left(\dfrac{300}{400}\right)^4 \\ &= 10 \left(\dfrac34\right)^4 \\ &= 10 \cdot \dfrac{81}{256} \approx 3. \end{aligned}$

Thus, the correct answer is D .

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