Question

select the correct answer. venus is an average distance of 108.2 million kilometers from the sun. use the conversion factor 1 au = 1.5×10^8 km to convert this distance from kilometers to astronomical units. choose the closest answer. a. 0.72 au b. 1.25 au c. 3.56 au d. 45.63 au e. 96.12 au

Explanation:

Step1: Set up conversion formula

Let $d$ be the distance in astronomical units (AU). We know that 1 AU = $1.5\times10^{8}$ km. Given the distance in km is $d_{km}=108.2\times 10^{6}$ km. We use the formula $d=\frac{d_{km}}{1.5\times 10^{8}}$.

Step2: Substitute the value of $d_{km}$

$d = \frac{108.2\times 10^{6}}{1.5\times 10^{8}}$. First, rewrite $108.2\times 10^{6}$ as $1.082\times 10^{8}$. Then $d=\frac{1.082\times 10^{8}}{1.5\times 10^{8}}$.

Step3: Calculate the value of $d$

When dividing numbers in scientific - notation with the same power of 10, we divide the coefficients. So $d=\frac{1.082}{1.5}\approx0.72$ AU.

Answer:

A. 0.72 AU