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Answer :
To find out how far the star is from Earth in miles, follow these steps:
1. Given the distance of the star from Earth in light years is [tex]\( 4.3 \times 10^2 \)[/tex] light years.
2. Also given, one light year is approximately [tex]\( 5.9 \times 10^{12} \)[/tex] miles.
To find the distance of the star in miles, we need to multiply these two values:
[tex]\[
\text{Distance in miles} = (\text{Distance in light years}) \times (\text{Miles per light year})
\][/tex]
Substitute the given values into the equation:
[tex]\[
\text{Distance in miles} = (4.3 \times 10^2) \times (5.9 \times 10^{12})
\][/tex]
Now, let's break down the multiplication:
[tex]\[
4.3 \times 10^2 = 430
\][/tex]
[tex]\[
5.9 \times 10^{12} = 5,900,000,000,000
\][/tex]
Multiply these values together:
[tex]\[
430 \times 5,900,000,000,000 = 2,537,000,000,000,000
\][/tex]
Hence, putting the result in scientific notation:
[tex]\[
2,537,000,000,000,000 = 2.537 \times 10^{15}
\][/tex]
Therefore, the distance of the star from Earth is:
[tex]\[
2.537 \times 10^{15} \text{ miles}
\][/tex]
So, the star is [tex]\( 2.537 \times 10^{15} \)[/tex] miles from Earth.
1. Given the distance of the star from Earth in light years is [tex]\( 4.3 \times 10^2 \)[/tex] light years.
2. Also given, one light year is approximately [tex]\( 5.9 \times 10^{12} \)[/tex] miles.
To find the distance of the star in miles, we need to multiply these two values:
[tex]\[
\text{Distance in miles} = (\text{Distance in light years}) \times (\text{Miles per light year})
\][/tex]
Substitute the given values into the equation:
[tex]\[
\text{Distance in miles} = (4.3 \times 10^2) \times (5.9 \times 10^{12})
\][/tex]
Now, let's break down the multiplication:
[tex]\[
4.3 \times 10^2 = 430
\][/tex]
[tex]\[
5.9 \times 10^{12} = 5,900,000,000,000
\][/tex]
Multiply these values together:
[tex]\[
430 \times 5,900,000,000,000 = 2,537,000,000,000,000
\][/tex]
Hence, putting the result in scientific notation:
[tex]\[
2,537,000,000,000,000 = 2.537 \times 10^{15}
\][/tex]
Therefore, the distance of the star from Earth is:
[tex]\[
2.537 \times 10^{15} \text{ miles}
\][/tex]
So, the star is [tex]\( 2.537 \times 10^{15} \)[/tex] miles from Earth.
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