Question

voyager 1, a spacecraft launched in 1977, left the solar system in 2012 and is now 21.7 billion kilometres from the earth. 1 astronomical unit (au) is the distance from the earth to the sun, or 150 billion meters. how many au is the voyager 1 from earth?

Explanation:

Step1: Convert distances to same unit

First, convert 21.7 billion kilometers to meters. 1 billion = $10^{9}$, so 21.7 billion kilometers = $21.7\times10^{9}\times10^{3}$ meters = $21.7\times 10^{12}$ meters. 1 AU = 150 billion meters = $150\times10^{9}$ meters.

Step2: Calculate number of AU

To find the number of AU, divide the distance of Voyager 1 from Earth in meters by the distance of 1 AU in meters. Let $n$ be the number of AU. Then $n=\frac{21.7\times 10^{12}}{150\times10^{9}}$.
Simplify the expression: $\frac{21.7\times 10^{12}}{150\times10^{9}}=\frac{21.7}{150}\times10^{12 - 9}=\frac{21.7}{150}\times10^{3}$.
$\frac{21.7}{150}\approx0.145$, and $0.145\times10^{3}=145$.

Answer:

145 AU