Certainly! Let's work through the problem step-by-step:
1. Given Data:
- Speed of light, \( c = 3.0 \times 10^8 \) meters per second.
2. Determine the number of seconds in a year:
- We know there are 60 seconds in a minute.
- There are 60 minutes in an hour.
- There are 24 hours in a day.
- There are 365 days in a year.
By multiplying these together, we get the total number of seconds in a year:
[tex]\[
\text{seconds per year} = 60 \, \text{seconds/minute} \times 60 \, \text{minutes/hour} \times 24 \, \text{hours/day} \times 365 \, \text{days/year}
\][/tex]
[tex]\[
\text{seconds per year} = 31536000 \, \text{seconds/year}
\][/tex]
3. Calculate the distance light travels in one year:
- The distance light travels in one year (often called a light-year) can be found by multiplying the speed of light by the number of seconds in a year.
[tex]\[
\text{distance light-year} = \text{speed of light} \times \text{seconds per year}
\][/tex]
[tex]\[
\text{distance light-year} = 3.0 \times 10^8 \, \text{meters/second} \times 31536000 \, \text{seconds/year}
\][/tex]
[tex]\[
\text{distance light-year} = 9.4608 \times 10^{15} \, \text{meters}
\][/tex]
4. Express the distance in scientific notation:
- The distance light travels in one year is \( 9.4608 \times 10^{15} \) meters. To express this in scientific notation with three significant figures:
[tex]\[
\text{distance light-year} \approx 9.461 \times 10^{15} \, \text{meters}
\][/tex]
So, the distance traveled by light in one year is:
[tex]\[
\boxed{9.461 \times 10^{15} \, \text{meters}}
\][/tex]
