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Answer :
To find out how far the star is from Earth in miles, we need to multiply the distance of the star in light years by the number of miles in one light year. Here's how we can do it step-by-step:
1. Understand the Given Values:
- The distance of the star from Earth is given as [tex]\(4.3 \times 10^2\)[/tex] light years.
- One light year is approximately [tex]\(5.9 \times 10^{12}\)[/tex] miles.
2. Set Up the Multiplication:
- We need to calculate the total distance in miles by multiplying the distance in light years by the number of miles per light year.
- This looks like: [tex]\((4.3 \times 10^2) \times (5.9 \times 10^{12})\)[/tex].
3. Multiply the Numbers:
- Start by multiplying the coefficients (the numbers before the powers of 10): [tex]\(4.3 \times 5.9 = 25.37\)[/tex].
- Next, use the properties of exponents to multiply the powers of 10: [tex]\((10^2) \times (10^{12}) = 10^{14}\)[/tex].
4. Combine the Results:
- Combine the results from step 3 to express the final answer in scientific notation.
- [tex]\(25.37 \times 10^{14}\)[/tex].
5. Express in Proper Scientific Notation:
- Adjust [tex]\(25.37\)[/tex] to proper scientific notation, which is [tex]\(2.537\)[/tex] by moving the decimal one place to the left. This increases the power of 10 by 1.
- Therefore, the expression becomes [tex]\(2.537 \times 10^{15}\)[/tex].
So, the distance of the star from Earth is approximately [tex]\(2.537 \times 10^{15}\)[/tex] miles.
1. Understand the Given Values:
- The distance of the star from Earth is given as [tex]\(4.3 \times 10^2\)[/tex] light years.
- One light year is approximately [tex]\(5.9 \times 10^{12}\)[/tex] miles.
2. Set Up the Multiplication:
- We need to calculate the total distance in miles by multiplying the distance in light years by the number of miles per light year.
- This looks like: [tex]\((4.3 \times 10^2) \times (5.9 \times 10^{12})\)[/tex].
3. Multiply the Numbers:
- Start by multiplying the coefficients (the numbers before the powers of 10): [tex]\(4.3 \times 5.9 = 25.37\)[/tex].
- Next, use the properties of exponents to multiply the powers of 10: [tex]\((10^2) \times (10^{12}) = 10^{14}\)[/tex].
4. Combine the Results:
- Combine the results from step 3 to express the final answer in scientific notation.
- [tex]\(25.37 \times 10^{14}\)[/tex].
5. Express in Proper Scientific Notation:
- Adjust [tex]\(25.37\)[/tex] to proper scientific notation, which is [tex]\(2.537\)[/tex] by moving the decimal one place to the left. This increases the power of 10 by 1.
- Therefore, the expression becomes [tex]\(2.537 \times 10^{15}\)[/tex].
So, the distance of the star from Earth is approximately [tex]\(2.537 \times 10^{15}\)[/tex] miles.
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