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Chapter 1: Problem 43

The distance from the center of the Moon to the center of the Earth ranges from approximately \(356,000 \mathrm{~km}\) to \(407,000 \mathrm{~km}\). What are these distances in miles? Be certain to round your answers to the appropriate number of significant figures.

Short Answer

Expert verified
Answer: The range of distances is approximately 221,000 miles to 253,000 miles.

Step by step solution

01

Identify the conversion factor

First, we need to find the conversion factor for kilometers to miles. The appropriate factor is 1 kilometer is equal to 0.621371 miles.
02

Convert the minimum distance from kilometers to miles

To convert the minimum distance (356,000 km) from kilometers to miles, we use the conversion factor that we have found in the previous step: Minimum distance in miles = (356,000 km) * (0.621371 miles / 1 km) Minimum distance in miles ≈ 221288.196 miles
03

Round the minimum distance to the appropriate number of significant figures

We were given the distance in kilometers as 356,000 km, which has 3 significant figures. So, we need to round our answer to 3 significant figures as well: Minimum distance in miles ≈ 221,000 miles (rounded to 3 significant figures)
04

Convert the maximum distance from kilometers to miles

Now, we'll do the same for the maximum distance (407,000 km): Maximum distance in miles = (407,000 km) * (0.621371 miles / 1 km) Maximum distance in miles ≈ 252977.677 miles
05

Round the maximum distance to the appropriate number of significant figures

Again, we were given the distance in kilometers as 407,000 km, so we need to round our answer to 3 significant figures: Maximum distance in miles ≈ 253,000 miles (rounded to 3 significant figures)
06

Final answer

So, the distances from the center of the Moon to the center of the Earth range from approximately 221,000 miles to 253,000 miles, rounded to the appropriate number of significant figures.

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