Why do 60S & 40S ribosomal subunits make an 80S ribosome (not 100S)?
That's not a simple mathematical addition!

If those units were mass, for instance, you could (and should) add them: a 60g Lego piece combined with a 40g Lego piece will, of course, form a combo that has 100g.

However, those numbers are Svedberg units, which is...


  a non-metric unit for sedimentation rate [...] The Svedberg coefficient is a nonlinear function. A particle's mass, density, and shape will determine its S value. (emphasis mine)


Funnily enough, most of my students thought that that S stands for Sedimentation. However, it's a tribute to Theodor Svedberg, winner of the Nobel Prize for Chemistry in 1926.

Thus, in a oversimplified explanation, the prokaryotic ribosome has two sub-units. The large sub-unit sediments at 50s, the small sub-unit sediments at 30s, but the two together (that is, the whole ribosome) sediments at 70s, not 80s.  

The same way an eukaryotic ribosome has a large sub-unit that sediments at 60s, a small one that sediments at 40s, but the whole structure sediments at 80s, not 100s.

Also, the rRNAs that constitute the sub-units have their own sedimentation rates (in svedberg units) as well:



For a detailed explanation with all math you need, the other answers here and here explain it beautifully.