Question

scientists have detected an asteroid that is 700,000,000 km from earth. about how many astronomical units is that? 0.5au 1au 3.5au 4.5au

Explanation:

Step1: Recall the conversion factor

1 astronomical unit (AU) is approximately \(150,000,000\) km.

Step2: Set up the division

Let \(x\) be the number of AU. We use the formula \(x=\frac{\text{distance in km}}{150,000,000}\). Substitute the given distance of \(700,000,000\) km. So \(x = \frac{700000000}{150000000}\).

Step3: Simplify the fraction

\(\frac{700000000}{150000000}=\frac{70}{15}\approx 4.67\). But if we consider approximate values: \(\frac{700000000}{150000000}=\frac{70}{15}=\frac{14}{3}\approx4.67\). However, if we use a simpler approximation: \(150\times0.5 = 75\) (for \(0.5\) AU: \(75,000,000\) km), \(150\times1=150\) (for \(1\) AU: \(150,000,000\) km), \(150\times3.5 = 525\) (for \(3.5\) AU: \(525,000,000\) km), \(150\times4.5=675\) (for \(4.5\) AU: \(675,000,000\) km). \(700,000,000\) is closer to \(675,000,000\) (since \(700 - 675=25\) and \(750 - 700 = 50\), and \(150\times5=750\)).

Answer:

\(4.5\) AU (the closest value among the given options when using the approximation \(1\) AU \(= 150,000,000\) km)