1990 AMC 8 Problem 5

Attempt Problem 5 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

Which of the following is closest to the product (0.48017)(0.48017)(0.48017)?(0.48017)(0.48017)(0.48017)?
0.0110.011
0.1100.110
1.101.10
11.011.0
110110
Answer: B
Concepts:estimationexponent
Small hint:
0.480170.48017 is very close to 12\dfrac12
Big hint:
Estimate the product as (12)3\left(\dfrac12\right)^3
Solution:
Since 0.480170.48017 is close to 12\dfrac12, the product is close to
(12)3=18=0.125.\left(\dfrac12\right)^3 = \dfrac18 = 0.125.
The choice closest to 0.1250.125 is 0.1100.110.
Thus, the correct answer is B .
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