Question

Question #12f02

Answer 1

`1.3 * 10^(23)` `"s"^2`

Explanation:

The key here is the fact that

`color(blue)(ul(color(black)("1 Gs" = 10^9color(white)(.)"s")))`

This means that you need `10^9` seconds in order to have `1` gigasecond. Consequently, `1` second will be equivalent to `1/10^9"th"` of a gigasecond.

This means that `"1 Gs"^2` will be equal to

`"1 Gs" xx "1 Gs" = 10^9color(white)(.)"s" xx 10^9color(white)(.)"s"`

`color(blue)(ul(color(black)("1 Gs"^2 = 10^18color(white)(.)"s"^2)))`

In your case, you have `1.3 * 10^5` `"Gs"^2`, so use the conversion factor we calculated above to convert this to seconds squared

`1.3 * 10^5color(red)(cancel(color(black)("Gs"^2))) * (10^18color(white)(.)"s"^2)/(1color(red)(cancel(color(black)("Gs"^2)))) = color(darkgreen)(ul(color(black)(1.3 * 10^(23)color(white)(.)"s"^2)))`

The answer is rounded to two sig figs, the number of sig figs you have for the number of gigaseconds squared.