# Question e9b89

Sep 11, 2016

$\text{0.134 s}$

#### Explanation:

The idea here is that you can use the speed of light as a conversion factor to help you calculate the time needed for light to travel a distance equal to the circumference of the Earth.

So, the speed of light is given to you in meters per second, $\text{m/s}$, so the first thing to do here is to convert the distance that light must travel from miles to meters.

24900 color(red)(cancel(color(black)("mi"))) * overbrace((1.609344color(red)(cancel(color(black)("km"))))/(1color(red)(cancel(color(black)("mi")))))^(color(blue)("miles to kilometers")) * overbrace((10^3"m")/(1color(red)(cancel(color(black)("km")))))^(color(darkgreen)("kilometers to meters")) = 4.0073 * 10^7"m"

Now set up the speed of light as a conversion factor to find

4.0073 * 10^7 color(red)(cancel(color(black)("m"))) * "1 s"/(2.998 * 10^8color(red)(cancel(color(black)("m")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("0.134 s")color(white)(a/a)|)))#

The answer must be rounded to three sig figs, the number of sig figs you have for the circumference of the Earth.