Question

1. a certain star is 4.3 x 10^2 light years from earth. one light year is about 5.9 x 10^12 miles. how far from earth (in miles) is the star? express your answer in scientific notation.

Explanation:

Step1: Set up the multiplication

Multiply the number of light - years of the star from Earth by the number of miles in one light - year. So we need to calculate $(4.3\times10^{2})\times(5.9\times10^{12})$.

Step2: Use the commutative and associative properties of multiplication

$(4.3\times5.9)\times(10^{2}\times10^{12})$.
First, calculate $4.3\times5.9 = 25.37$.
Then, use the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, so $10^{2}\times10^{12}=10^{2 + 12}=10^{14}$.

Step3: Rewrite in scientific notation

Since $25.37 = 2.537\times10^{1}$, then $25.37\times10^{14}=2.537\times10^{1}\times10^{14}$.
Using the exponent rule again, $2.537\times10^{1}\times10^{14}=2.537\times10^{1 + 14}=2.537\times10^{15}$.

Answer:

$2.537\times10^{15}$ miles