Question

a light - year is the distance light travels in one year, about 5.9 × 10^12 mi. earth is located about 25,000 light - years from the milky ways rim. what is the approximate distance, in miles, from earth to the rim of the milky way? o 8.5 × 10^16 o 8.5 × 10^48 o 1.5 × 10^17 o 1.5 × 10^51

Explanation:

Step1: Convert 25,000 to scientific - notation

$25000 = 2.5\times10^{4}$

Step2: Multiply by distance of 1 light - year

The distance of 1 light - year is $5.9\times 10^{12}$ miles. Multiply the number of light - years by the distance of 1 light - year: $(2.5\times10^{4})\times(5.9\times 10^{12})$.
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 $(2.5\times5.9)\times(10^{4}\times10^{12})$.
$2.5\times5.9 = 14.75\approx15$ and $10^{4}\times10^{12}=10^{4 + 12}=10^{16}$.
So, $15\times10^{16}=1.5\times10^{17}$.

Answer:

C. $1.5\times 10^{17}$