The mass of a proton is 1.67*10^(-27) kg. What is the mass of a proton in picograms?

Mar 29, 2015

The mass of a proton in picograms is $1.67 \cdot {10}^{- 12} \text{pg}$.

This is a basic unit conversion problem in which you must go from one order of magnitude, in your case kilograms, to another order of magnitude, picograms.

As you can see, 1 kg contains ${10}^{3} \text{g}$, and 1 g contains ${10}^{12} \text{pg}$ . In other words, you get ${10}^{3} \text{g}$ for every 1 kg and ${10}^{12} \text{pg}$ for every 1 gram.

So, set up two conversion factors to take you from kg to grams, and then from grams to picograms

$1.67 \cdot {10}^{- 27} \cancel{\text{kg") * (10^(3)cancel("g"))/(1cancel("kg")) * (10^(12)"pg")/(1cancel("g")) = color(green)(1.67 * 10^(-12)"pg}}$