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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, 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 why you know your method works.

b) You'd like to know both 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?

Answer :

Answer:

Step-by-step explanation:

Place a decimal point to the right of the first real number. write the real number with decimal point

Then count the number of places after the decimal point and this with the power of ten. For example, in diameter of solar system, after keeping decimal after 8, there are 12 places. so power of 10 is 12

a) 8,980,000,000,000 kilo meters. = 8.98 * 10¹² km

39,900,000,000,000,000 kilo meters = 3.99* 10¹⁶ km

9,460,000,000,000 kilo meters = 9.46 * 10¹² km

b)the distance to Proxima Centauri in light-years = 3.99* 10¹⁶ 9.46 * 10¹²

= 0.4218 * 10⁽¹⁶⁻¹²) = 0.4218 * 10⁴

= 4.218 * 10³ light year

c) Speed of light= 3 * 10⁵ km per second

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Rewritten by : Barada

Final answer:

The diameter of our solar system can be written as 8.98 x 10^12 kilometers, the distance to Proxima Centauri can be written as 3.99 x 10^16 kilometers, and a light-year is approximately 9.46 x 10^12 kilometers. To convert the distances to light-years, divide by the distance light travels in one year. The time it takes for light to travel from Proxima Centauri to our solar system can be calculated by dividing the distance by the speed of light.

Explanation:

a) The diameter of our solar system can be written in scientific notation as 8.98 x 1012 kilometers. The distance to Proxima Centauri can be written as 3.99 x 1016 kilometers, and a light-year is approximately 9.46 x 1012 kilometers.

b) To convert the solar system's length to light-years, we divide the diameter of the solar system by the distance in one light-year. The ratio of the solar system's length to the distance to Proxima Centauri in light-years can be found by dividing the two distances in light-years.

c) The rate at which light travels, 300,000 kilometers per second, can be written in scientific notation as 3 x 105 kilometers per second. To find the time it takes for light to reach our solar system from Proxima Centauri, we can divide the distance in kilometers by the speed of light in kilometers per second.

Learn more about Calculating Distances in the Solar System here:

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