Question

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

Answer 1

The mass of a proton in picograms is `1.67 * 10^(-12)"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)"g"`, and 1 g contains `10^(12)"pg"` . In other words, you get `10^(3)"g"` for every 1 kg and `10^(12)"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 * 10^(-27)cancel("kg") * (10^(3)cancel("g"))/(1cancel("kg")) * (10^(12)"pg")/(1cancel("g")) = color(green)(1.67 * 10^(-12)"pg")`