Question

a certain star is 5.2×10² light - years from the earth. one light - year is about 5.9×10¹² miles. how far from the earth (in miles) is the star? the star is miles from earth. (use scientific notation. use the multiplication symbol in the math palette as needed.)

Explanation:

Step1: Identify given values

The star is $5.2\times10^{2}$ light - years away and 1 light - year is about $5.9\times10^{12}$ miles.

Step2: Set up multiplication

To find the distance in miles, we multiply the number of light - years by the number of miles in one light - year. So we have $(5.2\times10^{2})\times(5.9\times10^{12})$.

Step3: Use multiplication property of exponents

$(a\times10^{m})\times(b\times10^{n})=(a\times b)\times10^{m + n}$. Here $a = 5.2$, $b = 5.9$, $m = 2$ and $n=12$. So $(5.2\times5.9)\times10^{2 + 12}$.

Step4: Calculate coefficient

$5.2\times5.9 = 30.68$.

Step5: Write in scientific notation

$30.68\times10^{14}=3.068\times10^{15}$ miles.

Answer:

$3.068\times10^{15}$ miles