The mass of a proton is #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"#.

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"#, 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")#

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