Question

the speed of light is about 1.86×10^5 miles per second. the star sirius is about 5.062×10^13 miles from earth. about how many seconds does it take light to travel from sirius to earth? write your answer in scientific notation, using significant digits

Explanation:

Step1: Recall the time - distance - speed formula

We know that time $t=\frac{d}{v}$, where $d$ is distance and $v$ is speed. Here, $d = 5.062\times10^{13}$ miles and $v=1.86\times 10^{5}$ miles per second.

Step2: Perform the division of numbers in scientific notation

When dividing numbers in scientific notation $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. So, $\frac{5.062\times10^{13}}{1.86\times 10^{5}}=\frac{5.062}{1.86}\times10^{13 - 5}$.

Step3: Calculate the coefficient and the exponent

$\frac{5.062}{1.86}\approx2.72$, and $13-5 = 8$. So the result is $2.72\times10^{8}$ seconds.

Answer:

$2.72\times 10^{8}$