The Four Meanings of "Accurate to 3 Places"

[Joe Horn]

What is the square root of 84, accurate to 3 places? Although this sounds like a trivial question, it is not, because it has 4 different answers, each of which is correct, depending on what "accurate to 3 places" is taken to mean. Furthermore, all 4 meanings of "accurate to 3 places" are useful and perfectly valid meanings.

This fact throws a very large monkey wrench into the design of any calculator's "decimal to fraction" feature. Hence it was the subject of a presentation at HHC 2011, which analyzed the problem, its cause, and its effects, and suggested some solutions.

Although the presentation revolved around a PowerPoint slide show, it was written up in readable form for inclusion in the HHC Proceedings. That paper can be found here: http://hhuc.us/2011/The-Four-Meanings-of...Places.pdf

This came to mind during a recent discussion regarding the differences between the outputs of the HP Prime's [a b/c] fraction button and its new QPI function.