Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth. In scientific notation, how many miles away is it?

Given : Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles. Suppose a star is 13.6 light-years from Earth.

To find : In scientific notation, how many miles away is it?

Solution :

According to question,

The distance can travel in 1 light year is

[tex]1 \text{ light year} = 5,880,000,000,000 \text{ miles}[/tex]

We have to find the distance traveled in 13.6 light-years.

[tex]13.6 \text{ light year} =13.6\times 5,880,000,000,000 \text{ miles}[/tex]

[tex]13.6 \text{ light year} =79,968,000,000,000 \text{ miles}[/tex]

In scientific notation,

[tex]13.6 \text{ light year} =7.9968\times 10^{13}\text{ miles}[/tex]

Therefore, The distance traveled in 13.6 light year is [tex]7.9968\times 10^{13}\text{ miles}[/tex]