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Problem 495

AMC 12 late, AIME early

Algebra Difficulty 4.9 Find the answer

Example 8. Calculate $\frac{\pi}{4} \times 8.312$ .
(4 is an exact number, the result should be rounded to two decimal places)

Your answer

Official solution

Analysis: This problem involves multiplication and division, and we should consider the number of significant figures. However, the requirement here is based on the number of decimal places, so we need to convert this requirement into the number of significant figures.
$\frac{\pi}{4} \times 8.312 \text { is approximately } \frac{3}{4} \times 8=6 \text {, so }$
the number of significant figures for $\pi$ should be four.
$\text { Solution } \begin{aligned} & -\frac{\pi}{4} \times 8.312 \approx 3.142 \times 2.078 \\ & \approx 6.53 . \end{aligned}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.