Calculate how far Bob is from Earth in kilometers if he is 2.3 AU away, using the conversion formula 1.5 x 10^8 km/AU.
Understand the Problem
The question is asking to convert the distance from astronomical units (AU) to kilometers using the given conversion factor of 1.5 x 10^8 kilometers per AU. Specifically, it involves calculating how far Bob is from Earth if he is 2.3 AU away.
Answer
$3.45 \times 10^8$ km
Answer for screen readers
The distance Bob is from Earth is $3.45 \times 10^8$ kilometers.
Steps to Solve
- Identify the conversion factor
We know that 1 astronomical unit (AU) is equal to $1.5 \times 10^8$ kilometers.
- Multiply the distance in AU by the conversion factor
To find the distance in kilometers, we multiply the distance in AU (2.3 AU) by the conversion factor (1.5 x $10^8$ km/AU): $$ \text{Distance in kilometers} = 2.3 , \text{AU} \times 1.5 \times 10^8 , \text{km/AU} $$
- Calculate the product
Now we perform the multiplication: $$ \text{Distance in kilometers} = 2.3 \times 1.5 \times 10^8 $$ Calculate $2.3 \times 1.5$: $$ 2.3 \times 1.5 = 3.45 $$ Now we have: $$ \text{Distance in kilometers} = 3.45 \times 10^8 , \text{km} $$
The distance Bob is from Earth is $3.45 \times 10^8$ kilometers.
More Information
The distance of 1 AU is approximately the average distance from the Earth to the Sun, about 149.6 million kilometers. Thus, being 2.3 AU away means Bob is significantly farther than the Earth, specifically over 345 million kilometers away.
Tips
- Mixing up the conversion factor units, such as using kilometers incorrectly.
- Forgetting to multiply properly, especially with scientific notation.
- Rounding prematurely before reaching the final answer.
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