If a planet is 13 billion kilometers from the Sun, and the distance of an Astronomical Unit (AU) is 1.496x10^8 km, how many AU is this planet from the Sun?

1 Answer
Ernest Z.
Feb 13, 2014

A planet that is 13 × 10⁹ km from the Sun is 87 AU away.

13 × 10⁹ km = ? km

For this problem, we can use the conversion factors

#(1 AU)/(1.496 × 10⁸ km) = 1# or #(1.496 ×10⁸ km)/(1 AU) = 1#

Both are equivalent, but only the first has “km” in the denominator. By choosing the first conversion factor, we can cancel units in the conversion and end up with AU as the units for the answer.

13 × 10⁹ km × #(1 AU)/(1.496 ×10⁸ km)# = 87 AU

Note that we are allowed to have only two significant figures in our answer.

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