Question

a certain star is 3.1×10² light - years from the earth. one light - year is about 5.9×10¹² miles. how far from the earth (in miles) is the star? (use scientific notation. use the multiplication symbol in the math palette as needed.) the star is (square) miles from earth.

Explanation:

Step1: Identify the given values

The star is $3.1\times 10^{2}$ light - years away and 1 light - year is about $5.9\times 10^{12}$ miles.

Step2: Multiply the number of light - years by the number of miles per light - year

$(3.1\times 10^{2})\times(5.9\times 10^{12})$.
Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$ and $(a\times b)\times(c\times d)=(a\times c)\times(b\times d)$, we have $(3.1\times5.9)\times(10^{2}\times10^{12})$.
$3.1\times5.9 = 18.29$ and $10^{2}\times10^{12}=10^{2 + 12}=10^{14}$.
So the result is $18.29\times 10^{14}$.

Step3: Convert to proper scientific notation

In scientific notation, the coefficient should be between 1 and 10. So $18.29\times 10^{14}=1.829\times 10^{15}$ miles.

Answer:

$1.829\times 10^{15}$ miles