Bunuel wrote:
The average distance between the Sun and a certain planet is approximately 2.3 x 10^14 inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 7.1 x 10^8
(B) 5.9 x 10^9
(C) 1.6 x 10^10
(D) 1.6 x 10^11
(E) 5.9 x 10^11
Practice Questions
Question: 65
Page: 161
Difficulty: 650
This problem is a unit conversion with an added twist of scientific notation. We need to convert 2.3 x 10^14 inches to KILOMETERS. We are given that 1 kilometer is approximately 3.9 X 10^4 inches. We also should recognize that we are being asked which of the following is CLOSEST to the average distance between the Sun and the planet, in Kilometers. Because we are being asked for an approximation, we can use some estimation here.
To convert 2.3 x 10^14 inches to kilometers, we need to multiply 2.3 x 10^14 inches by the ratio of:
1 km/(3.9 x 10^4 inches)
However, before doing this multiplication, it will make things easier to clean up each scientific notation expression. Let’s start with 2.3 x 10^14 inches.
2.3 x 10^14 inches
is equivalent to
23 x 10^13 inches
Notice that because we turn 2.3 into 23, or move the decimal one place to the right, we have to then turn 10^14 into 10^13, or move the decimal one place to the LEFT to “counterbalance” the fact that we’ve moved the decimal one place to the right for 2.3.
Next we can adjust 3.9 x 10^4 inches. However, we can simply round this value up to 4 x 10^4 inches.
Since we’ve rounded 3.9 up to 4, let’s round 23 up to 24 also. That is, we are converting 24 x 10^13 inches into kilometers given that 1 km is approximately 4 x 10^4 inches:
(24 x 10^13 inches) x 1 km/(4 x 10^4 inches)
(24 x 10^13)/(4 x 10^4) km
We can break this work up into two separate calculations:
1) 24/4 = 6
2) 10^13/10^4 = 10^9
Thus, our answer is about 6 x 10^9 km.
We see that the closest answer is B.
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