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QUESTION

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

The mass of a proton in picograms is 1.67 * 10^(-12)"pg".

This is a basic 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")