Question

The distance from Earth to the sun, about 1.50 x 10^8 kilometers, is known as an astronomical unit. The nearest star, Proxima Centauri, is 2.6 x 10^8 astronomical units from Earth. How many kilometers separate Earth from the nearest star? Write you answer in Scientific Notation

Answer 1

Distance from Earth to Proxima Centauri (in scientific notation) =
`3.9*10^(16)` kilometers

Explanation:

We need the conversion between Astronomical Unit and Kilometers.

The conversion is:

1 AU = 1.496*10^8 km

or rounded, given in this problem,

1 AU =
`1.5*10^8` km

We need the distance from Earth to Proxima Centauri:

`2.6*10^8` AU *
`1.5*10^8` kilometers

When multiplying two numbers in scientific notation, we have to "multiply the coefficients" and "add the exponents".

Lets do this:

`(2.6*10^8)*(1.5*10^8)\\=(2.6*1.5)*10^(8+8)\\=3.9*10^(16)`

Distance from Earth to Proxima Centauri (in scientific notation) =
`3.9*10^(16)` kilometers