14. A certain star is \( 4.3 \times 10^{2} \) light years from Earth. One light year is about \( 5.9 \times 10^{12} \) miles. How far from Earth (in miles) is the star? Express your answer in scientific notation.

To find the distance from Earth to the star in miles, we need to multiply the distance in light years by the conversion factor from light years to miles. Given: - Distance from Earth to the star in light years: \( 4.3 \times 10^{2} \) light years - Conversion factor: 1 light year = \( 5.9 \times 10^{12} \) miles We can calculate the distance in miles by multiplying the distance in light years by the conversion factor: Distance in miles = Distance in light years * Conversion factor Let's calculate this: Calculate the value by following steps: - step0: Calculate: \(4.3\times 10^{2}\times 5.9\times 10^{12}\) - step1: Multiply the numbers: \(25.37\times 10^{2}\times 10^{12}\) - step2: Multiply: \(25.37\times 10^{14}\) - step3: Rewrite the number: \(2.537\times 10^{15}\) The distance from Earth to the star is approximately \(2.537 \times 10^{15}\) miles. Therefore, the star is \(2.537 \times 10^{15}\) miles away from Earth.