# The average distance between the Sun and a certain…

## Solution:

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.

**Answer: B**