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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.

Show that one light year is 9.461 × 10^12 km, correct to 4 significant figures. The speed of light is 2.9979 × 10^5 kilometers per second. One light year is the distance that light travels in a year of 365.25 days.

Learn how to show that the distance light travels in one year (one light year) is 9.461 × 10^12 km. This problem involves calculating the number of seconds in a year and multiplying by the speed of light. Suitable for high school students in Grades 9-12.

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