Question

a certain star is 5.6×10² light years from the earth. one light year is about 5.9×10¹² miles. how far from the earth (in miles) the star is miles from earth. (use scientific notation. use the multiplication symbol in the math palette as needed.)

Explanation:

Step1: Multiply the two numbers in scientific - notation

We know that if we have two numbers in scientific notation \(a\times10^{m}\) and \(b\times 10^{n}\), their product is \((a\times b)\times10^{m + n}\). Here, \(a = 5.6\), \(m=2\), \(b = 5.9\), and \(n = 12\).
\((5.6\times5.9)\times10^{2 + 12}\)

Step2: Calculate the product of the decimal parts

\(5.6\times5.9=33.04\)
So the expression becomes \(33.04\times10^{14}\)

Step3: Adjust to proper scientific - notation

In scientific notation, the coefficient \(a\) should satisfy \(1\leq a<10\). We rewrite \(33.04\times10^{14}\) as \(3.304\times10^{15}\) (since \(33.04 = 3.304\times10^{1}\) and \(3.304\times10^{1}\times10^{14}=3.304\times10^{1 + 14}=3.304\times10^{15}\))

Answer:

\(3.304\times 10^{15}\)