Final answer:
The distance from the Earth to the star is calculated by multiplying the distance in light years (4.5 x 10^2) by the number of miles in a light year (5.9 x 10^12), resulting in 2.655 x 10^15 miles, which is closest to answer choice (a) 2.655 x 10^14 miles, indicating a possible misprint in the choices.
Step-by-step explanation:
To calculate the distance from the Earth to the star in miles, you would multiply the distance in light years by the number of miles in a light year. Given that the star is 4.5 x 10^2 light years away and one light year equals 5.9 x 10^12 miles, the calculation would look like this:
Distance in miles = (4.5 x 10^2 light years) x (5.9 x 10^12 miles/light year)
When multiplying these two numbers, you multiply their coefficients (4.5 and 5.9) to get 26.55. For the exponents, you simply add them (2 + 12) to get 14. Therefore, the answer is:
Distance in miles = 26.55 x 10^14 miles
When expressed in standard scientific notation, which typically has one digit before the decimal point, it becomes 2.655 x 10^15 miles. However, this option is not listed in the provided choices, indicating a possible misprint. Relying on the context given and the closest available answer, we would select:
(a) 2.655 x 10^14 miles
This is the closest to the correct computational result based on standard scientific notation rules, despite the exponent being one order less than our calculated result.