To determine the distance from Earth to the star in miles using scientific notation, we should multiply the distance in light-years by the distance light travels in one light-year.
Given:
- One light-year ≈ 5,880,000,000,000 miles
- Distance to the star = 13.6 light-years
First, write the distance of one light-year in scientific notation:
\[ 5,880,000,000,000 \text{ miles} = 5.88 \times 10^{12} \text{ miles} \]
Next, multiply the distance in light-years by the distance one light-year in scientific notation:
\[ 13.6 \times (5.88 \times 10^{12}) \]
We'll perform the calculation in two steps:
1. Multiply the base numbers:
\[ 13.6 \times 5.88 = 79.968 \]
2. Apply the rules of exponents (add the exponents when multiplying):
\[ 79.968 \times 10^{12} \]
Finally, convert the result to proper scientific notation:
\[ 79.968 \times 10^{12} = 7.9968 \times 10^{13} \]
So, in scientific notation, the star is:
\[ 7.9968 \times 10^{13} \text{ miles away from Earth} \]
Therefore, the correct answer is:
\[ 7.9968 \times 10^{13} \text{ miles} \]
This matches the first option in the provided choices.
18.
Simplify the expression. Write the answer using scientific notation.
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?
7.9968 x 1013 miles
5.88 x 1012 miles
1.36 x 1012 miles
5.88 x 1013 miles
1 answer