\( 3.5 \times 10^{k}=3.500000000 \times 10^{14}=350000000.0 \) or 35000000 Example 3: The closest star to the Earth (other than Sun ) is Alpha Centauri, 4,35 light y from Earth. How many kilometers from Earth is Alpha Centauri" If one light year \( =9460920 \) million km . Write the answer in scientific notation.

To find the distance to Alpha Centauri in kilometers, you can multiply the distance in light years by the number of kilometers in a light year. Given that Alpha Centauri is 4.35 light years away and one light year is approximately 9,460,920 million kilometers, the calculation would be: \[ 4.35 \, \text{ly} \times 9,460,920 \, \text{million km/ly} = 41,197,062,600 \, \text{km} \] In scientific notation, this distance can be expressed as: \[ 4.12 \times 10^{10} \, \text{km} \] Now you know that the closest star to us, Alpha Centauri, is not just light years away, but in fact, about \( 4.12 \times 10^{10} \, \text{km} \) away! This is quite astonishing when you think about how vast space is! Just remember that one light year represents a tremendous distance, which can be hard to grasp. It’s also one of the key reasons why astronomers use scientific notation—it’s much easier to write and comprehend those staggering figures!