Final answer:
The distance from the Earth to a star 4.3 x 10² light years away is 2.54 x 10¹µ miles, which is obtained by multiplying the number of light years by the miles in one light year, following the rules of significant figures and powers of 10.
Step-by-step explanation:
To calculate the distance from the Earth to a star that is 4.3 x 10² light years away, we need to multiply the number of light years by the distance that light travels in a year. One light year is approximately 5.9 x 10¹² miles. Using multiplication of powers of 10, the calculation would be (4.3 x 10²) x (5.9 x 10¹²) = (4.3 x 5.9) x 10²¹´.
When you multiply 4.3 by 5.9, you get 25.37. To follow the rules of significant figures, we round it to 25.4, and then we multiply it by 10²¹´ to obtain the distance in miles. Therefore, the distance is 2.54 x 10¹µ miles, which matches option c. 2.54 x 10¹µ miles.
The star is 4.3 x 10² light years from the earth. One light year is about 5.9 x 10¹² miles. To find the distance to the star in miles, we need to multiply the number of light years by the number of miles in one light year.
4.3 x 10² light years x 5.9 x 10¹² miles/light year = 4.3 x 5.9 x 10² x 10¹² = 25.37 x 10² x 10¹² = 25.37 x 10¹⁴ miles.
So, the distance from the earth to the star is approximately 2.54 x 10¹⁵ miles (option c).