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at its closest point, mercury is approximately 46 million kilometers from the sun. what is this distance in au? a. 0.3 au b. 2.4 au c. 30 au d. 150 million au

Verified Answer :

olemakpadu

150 Million km =  1 AU

1 Million km =  (1/150) AU

46 Million km =    (1/150) * 46 ≈ 0.3066 AU

≈ 0.31 AU

Option A.

Answer:

a. 0.3 au

Explanation:

Hello

this is a unit conversion problem,we need to know how much kilometers an au are.The astronomical unit (ua) is a unit of equal length, by definition, at 149 597 870 700 m,  which is roughly equivalent to the average distance between the Earth and the Sun.

149 597 870 700 m = 1 au

Now we can convert 46 000 000 kilometers into meter for next conver meters into au

46000000 km ⇔  x

1 km                  ⇔  1000 m

using a rule of three

\(x=\frac{46000000Km*1000m}{1km} \\x=46000000000\  m\)

Now,  meters into au

46 000 000 000m =  xau

149 597 870 700 m= 1au

\(x=\frac{46000000000m*1au}{149 597 870 700 m} \\x=0.3074 au\)

so, the correct answer is the option a

0.3 au

have a great day

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