1. The radius of the Sun is 7 X 10^5 kilometers. Use powers of ten to show that the Sun's radius is about 100 times the Earth's radius.
2. Given that an astronomical unit is 1.5 X 10^8 kilometers and a light-year is about 10^13 kilometers, how many AU are in a light-year?
1 x 10^13
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1.5 x 10^8
equals
.667 X 10^5 or 6.67 X 10^4
More exact is 63,239.4913
So if the earth is 6.4 X 10^3 radius
and the sun is 7 X 10^5 just take 6.4 X 10^3 times 109 to get 7 X 10^5
Means the sun is 109 times bigger than earth.
To show that the Sun's radius is about 100 times the Earth's radius using powers of ten, we can compare the two values in scientific notation.
The Earth's radius is given as 6.4 x 10^3 kilometers.
The Sun's radius is given as 7 x 10^5 kilometers.
To compare these two values, we need to determine the ratio of the two radii. We divide the larger radius (Sun's radius) by the smaller radius (Earth's radius):
(7 x 10^5) / (6.4 x 10^3)
To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:
(7 / 6.4) x (10^5 / 10^3)
Simplifying the exponents:
(7 / 6.4) x 10^(5-3)
Performing the division and subtracting the exponents:
1.09375 x 10^2
So, the ratio of the Sun's radius to the Earth's radius is approximately 1.09375 x 10^2. This means that the Sun's radius is about 100 times the Earth's radius.
To answer the second question, we need to convert light-years (LY) to astronomical units (AU) using the given values.
The conversion factor is:
1 light-year = 10^13 kilometers
1 astronomical unit = 1.5 x 10^8 kilometers
To find the number of AU in a light-year, we divide the light-year distance by the AU distance:
(10^13) / (1.5 x 10^8)
Again, to divide numbers in scientific notation, we divide the coefficients and subtract the exponents:
(10^13) / (1.5 x 10^8) = 6.67 x 10^(13-8) = 6.67 x 10^5
So, there are approximately 6.67 x 10^5 astronomical units in one light-year.