# Question #ca04a

Sep 17, 2017

$1.67 \cdot {10}^{- 33}$ $\text{Gg}$

#### Explanation:

Your tools of choice here will be the following conversion factors

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 kg" = 10^3color(white)(.)"g"))) " " and " " color(blue)(ul(color(black)("1 Gg" = 10^9color(white)(.)"g}}}}$

You can combine these two conversion factors to find a single conversion factor that takes you from kilograms to gigagrams.

$\text{1 kg"/(10^3color(red)(cancel(color(black)("g")))) * (10^9 color(red)(cancel(color(black)("g"))))/"1 Gg"= (10^6color(white)(.)"kg")/"1 Gg}$

This means that you have

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 Gg" = 10^6color(white)(.)"kg}}}}$

You can now use this conversion factor to find the mass of the proton in gigagrams

$1.67 \cdot {10}^{- 27} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{kg"))) * "1 Gg"/(10^6color(red)(cancel(color(black)("kg")))) = color(darkgreen)(ul(color(black)(1.67 * 10^(-33)color(white)(.)"Gg}}}}$

The answer will have three sig figs, the same number of sig figs you have for the mass of the proton in kilograms.