# Question #12f02

Aug 30, 2017

$1.3 \cdot {10}^{23}$ ${\text{s}}^{2}$

#### Explanation:

The key here is the fact that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 Gs" = 10^9color(white)(.)"s}}}}$

This means that you need ${10}^{9}$ seconds in order to have $1$ gigasecond. Consequently, $1$ second will be equivalent to $\frac{1}{10} ^ 9 \text{th}$ of a gigasecond.

This means that ${\text{1 Gs}}^{2}$ will be equal to

$\text{1 Gs" xx "1 Gs" = 10^9color(white)(.)"s" xx 10^9color(white)(.)"s}$

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{\text{1 Gs"^2 = 10^18color(white)(.)"s}}^{2}}}}$

In your case, you have $1.3 \cdot {10}^{5}$ ${\text{Gs}}^{2}$, so use the conversion factor we calculated above to convert this to seconds squared

$1.3 \cdot {10}^{5} \textcolor{red}{\cancel{\textcolor{b l a c k}{{\text{Gs"^2))) * (10^18color(white)(.)"s"^2)/(1color(red)(cancel(color(black)("Gs"^2)))) = color(darkgreen)(ul(color(black)(1.3 * 10^(23)color(white)(.)"s}}^{2}}}}$

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