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

1 Answer
Stefan V.
Mar 29, 2015

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

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.

http://www.bio.brandeis.edu/marderlab/orders%20of%20magnitude.html

As you can see, 1 kg contains 10^(3)"g"103g, and 1 g contains 10^(12)"pg"1012pg . In other words, you get 10^(3)"g"103g for every 1 kg and 10^(12)"pg"1012pg 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")

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