Question #12f02

1 Answer
Aug 30, 2017

Answer:

#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.