2017 AMC 8 Problem 4

Attempt Problem 4 of the 2017 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 8 solutions, or check the answer key.

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

4.

When 0.0003150.000315 is multiplied by 7,928,5647{,}928{,}564 the product is closest to which of the following?
210 210
240 240
2,1002{,}100
2,4002{,}400
24,00024{,}000
Answer: D
Concepts:estimation
Small hint:
Round each factor to one significant digit.
Big hint:
Think of 0.0003150.000315 as about 3⋅10−43\cdot10^{-4} and 7,928,5647{,}928{,}564 as about 8⋅1068\cdot10^6.
Video solution:
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Written solution:
We can approximate the product as (3⋅10−4)(8⋅106)=24⋅102=2,400. \begin{align*} (3 \cdot 10^{-4})(8 \cdot 10^6) &= 24 \cdot 10^2 \\ &= 2{,}400. \end{align*}
Thus, D is the correct answer.
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