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The diameter of our solar system (depending on how you define “solar system”) is about

8,980,000,000,000 kilometers.

The distance from our solar system to the nearest star, Proxima Centauri, is about

39,900,000,000,000,000 kilometers.

A light-year is the distance light travels in one year, and it is equal to about

9,460,000,000,000 kilometers.

a) Write each of these numbers in scientific notation. Explain how you got your answers, and explain why you know that your method works.
b) You’d like to both know the end-to-end distance within the solar system and the distance to Proxima Centauri in light-years. Using your scientific notation numbers, convert these distances. What is the ratio of the solar system’s length to the Proxima Centauri distance?
c) Light travels at 300,000 kilometers per second. Write this rate in scientific notation. When Proxima Centauri sends out light at that speed, how long does it take to reach our solar system? Can you convert to minutes, hours, days, or years? Does your answer in years correspond to the distance in light-years from our solar system to Proxima Centauri? Why or why not?

Jan 6, 2022