Question

what is the order of magnitude estimate for the number of steps you take in an average day? choose the correct answer below. a. the order of magnitude estimate is 3000 to 4000 steps; assuming an average person walks 2 miles per day. b. the order of magnitude estimate is 100 to 200 steps; assuming an average person walks 8 miles per day. c. the order of magnitude estimate is 375 to 575 steps; assuming an average person walks 16 miles per day. d. the order of magnitude estimate is 375 to 500 steps; assuming an average person walks \\(\frac{1}{4}\\) of a mile per day.

Explanation:

Step1: Recall step - mile conversion

On average, a person's step length is such that there are about 2000 steps in a mile (this is a common approximation, i.e., 1 mile ≈ 2000 steps).

Step2: Analyze Option A

If a person walks 2 miles per day, and 1 mile ≈ 2000 steps, then the number of steps is \(2\times2000 = 4000\) steps. The range 3000 - 4000 steps is reasonable as individual step lengths can vary a bit, so the order of magnitude estimate here makes sense.

Step3: Analyze Option B

If a person walks 8 miles per day, with 1 mile ≈ 2000 steps, the number of steps would be \(8\times2000=16000\) steps, not 100 - 200 steps. So Option B is incorrect.

Step4: Analyze Option C

If a person walks 16 miles per day, the number of steps would be \(16\times2000 = 32000\) steps, not 375 - 575 steps. So Option C is incorrect.

Step5: Analyze Option D

If a person walks \(\frac{1}{4}\) of a mile per day, the number of steps would be \(\frac{1}{4}\times2000 = 500\) steps. But the range 375 - 500 steps is too low for an average day (most people walk more than \(\frac{1}{4}\) mile a day), and the order of magnitude here is not representative of an average day. Also, the average daily walking distance for a person is more likely around 2 miles rather than \(\frac{1}{4}\) mile. So Option D is incorrect.

Answer:

A. The order of magnitude estimate is 3000 to 4000 steps; assuming an average person walks 2 miles per day.