Final answer:
The distance in miles from Mercury to the Sun is 3.6 × 10^7, while the number of miles from the Sun to Proxima Centauri is 2.5 × 10^12. The distance from the Sun to Proxima Centauri is about 7 × 10^5 times greater than the distance from the Sun to Mercury.
Step-by-step explanation:
The distance in miles from Mercury to the Sun in scientific notation is 3.6 × 10^7 miles. To convert 36 million miles to scientific notation, we move the decimal point one place to the left, giving us 3.6 million. As 3.6 million is greater than 1 million and less than 10 million, we use 10^7 as the exponent.
The number of miles from the Sun to Proxima Centauri in scientific notation is 2.5 × 10^12 miles. Given that a light year is 5.9 × 10^12 miles, we divide the distance from the Sun to Proxima Centauri by a light year in miles. The resulting value is approximately 4.24 light years, so the number of miles is 4.24 multiplied by 5.9 × 10^12, resulting in 2.5 × 10^13 miles. To convert this number to scientific notation, we move the decimal point one place to the left, giving us 2.5 × 10^12.
The distance from the Sun to Proxima Centauri is about 7 × 10^5 times greater than the distance from the Sun to Mercury. We can calculate this by dividing the number of miles from the Sun to Proxima Centauri (2.5 × 10^13) by the number of miles from Mercury to the Sun (3.6 × 10^7), resulting in approximately 6.94 × 10^5. Therefore, the distance from the Sun to Proxima Centauri is about 7 × 10^5 times greater than the distance from the Sun to Mercury.