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Chapter 1: Problem 95

The circumference of the Cornell Electron Storage Ring is \(768.4 \mathrm{~m}\). Express the diameter in inches, to the proper number of significant figures.

Short Answer

Expert verified
Answer: The diameter of the Cornell Electron Storage Ring in inches is 9628 inches.

Step by step solution

01

Find the diameter in meters

Using the formula for the circumference of a circle: \(C = \pi d\), where \(C\) is the circumference and \(d\) is the diameter. We are given \(C = 768.4 \mathrm{~m}\). To find the diameter, we can rearrange the formula as follows: \(d = \frac{C}{\pi}\) Substitute the given circumference value, and calculate the diameter in meters: \(d = \frac{768.4}{\pi} \approx 244.6 \mathrm{~m}\)
02

Convert the diameter to inches

Now that we have the diameter in meters, we need to convert it to inches. We will use the conversion factor: \(1\mathrm{~m} = 39.37\mathrm{~in}\). Multiply the diameter in meters by the conversion factor to get the diameter in inches: \(d_{in} = 244.6 \times 39.37 \approx 9628 \mathrm{~in}\)
03

Determine the correct number of significant figures

The given circumference has four significant figures, so our final answer should also have four significant figures. The calculated diameter in inches is \(9628\mathrm{~in}\), which already has the proper number of significant figures. The diameter of the Cornell Electron Storage Ring in inches, to the proper number of significant figures, is \(9628\mathrm{~in}\).

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