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Chapter 1: Problem 47

What is the order of magnitude of the height (in meters) of a 40 -story building?

Short Answer

Expert verified
Answer: The order of magnitude of the height of a 40-story building is 2.

Step by step solution

01

Estimate the height of a typical story

Assuming an average height of 3 meters per story, a 40-story building will have a height of 3 meters * 40 stories.
02

Calculate the height of the building

To find the total height of the building, multiply the height per story by the number of stories. 3 meters * 40 stories = 120 meters.
03

Find the order of magnitude

To find the order of magnitude of 120, we will use the base-10 logarithm. Let the order of magnitude be n. Then, 10^n ≈ 120. To find n, take the base-10 logarithm of both sides: n ≈ log10(120). Calculate log10(120) using a calculator or logarithm table: n ≈ 2.08 Since the order of magnitude is an integer, we will round n to the nearest integer: n ≈ 2 Thus, the order of magnitude of the height of a 40-story building in meters is 2.

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