The problem asks to show that one light-year is $9.461 \times 10^{12}$ kilometers, correct to 4 significant figures. Here are the given values:

• Speed of light, $c = 2.9979 \times 10^5$ kilometers per second
• 1 year = 365.25 days

To calculate the distance light travels in one year (one light-year), follow these steps:

Step 1: Convert 1 year to seconds

First, calculate the number of seconds in one year.

$1 \text{ year} = 365.25 \times 24 \times 60 \times 60 \text{ seconds}$

Step 2: Multiply the speed of light by the number of seconds in a year

The distance $D$ (in kilometers) that light travels in one year is:

$D = c \times \text{(number of seconds in a year)}$

Substitute the values and solve to get the distance.

Let me calculate that for you.The distance light travels in one year (one light-year) is approximately $9.461 \times 10^{12}$ kilometers, which matches the given value in the problem.

Would you like further details on the steps or any related clarifications?

Here are five related questions:

1. How would the calculation change if we used a different value for the number of days in a year?
2. Can you convert this distance into miles?
3. How does this distance compare to the average distance between stars in our galaxy?
4. What is the relationship between a light-year and an astronomical unit (AU)?
5. How would you express this distance in terms of meters?

Tip: Always double-check your unit conversions when working with large numbers like those in astronomy.