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Answer :
Sure, let's find out how far Proxima Centauri is from the Sun in kilometers (km) using the given information.
### Step-by-Step Solution:
1. Understand the problem:
- We need to calculate the distance to Proxima Centauri from the Sun.
- The distance is given as 4.3 light-years.
- We need to convert this distance to kilometers (km).
2. Know the conversion factor:
- One light-year is the distance that light travels in one year.
- The speed of light is [tex]\(9.461 \times 10^{12}\)[/tex] km/year.
3. Calculate the distance:
- Given: Distance to Proxima Centauri [tex]\(= 4.3\)[/tex] light-years.
- Speed of light [tex]\(= 9.461 \times 10^{12}\)[/tex] km/year.
To find the distance in kilometers, we multiply the number of light-years by the speed of light:
[tex]\[
\text{Distance in km} = 4.3 \, \text{light-years} \times 9.461 \times 10^{12} \, \text{km/light-year}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Distance in km} = 4.3 \times 9.461 \times 10^{12}
\][/tex]
[tex]\[
\text{Distance in km} = 40682300000000 \, \text{km}
\][/tex]
5. Express the result using two significant figures:
[tex]\[
\text{Distance in km} \approx 4.1 \times 10^{13} \, \text{km}
\][/tex]
So, the distance to Proxima Centauri from the Sun is approximately [tex]\(4.1 \times 10^{13}\)[/tex] km, expressed using two significant figures.
### Step-by-Step Solution:
1. Understand the problem:
- We need to calculate the distance to Proxima Centauri from the Sun.
- The distance is given as 4.3 light-years.
- We need to convert this distance to kilometers (km).
2. Know the conversion factor:
- One light-year is the distance that light travels in one year.
- The speed of light is [tex]\(9.461 \times 10^{12}\)[/tex] km/year.
3. Calculate the distance:
- Given: Distance to Proxima Centauri [tex]\(= 4.3\)[/tex] light-years.
- Speed of light [tex]\(= 9.461 \times 10^{12}\)[/tex] km/year.
To find the distance in kilometers, we multiply the number of light-years by the speed of light:
[tex]\[
\text{Distance in km} = 4.3 \, \text{light-years} \times 9.461 \times 10^{12} \, \text{km/light-year}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Distance in km} = 4.3 \times 9.461 \times 10^{12}
\][/tex]
[tex]\[
\text{Distance in km} = 40682300000000 \, \text{km}
\][/tex]
5. Express the result using two significant figures:
[tex]\[
\text{Distance in km} \approx 4.1 \times 10^{13} \, \text{km}
\][/tex]
So, the distance to Proxima Centauri from the Sun is approximately [tex]\(4.1 \times 10^{13}\)[/tex] km, expressed using two significant figures.
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