Question

Mercury is the closet planet to the Sun at a distance of 36 million miles. The closest star to the Sun is Proxima Centauri, which is 4.24 light years away. A light year is 5.9 ­× 1012 miles.

Select the correct exponent from the drop-down menus that makes each statement true.

The distance in miles from Mercury to the Sun in scientific notation is 3.6 × 10
7
.

The number of miles from the Sun to Proxima Centauri in scientific
notation 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.

Answer 1

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.