Wow, this is better than I've ever expected: Android calculator makes use of Exact Real Arithmetic running in the background (with some tweaks to cope with the inherent undecidability and an infinite list of trailing zeros). I had been fully aware of ERA but never expected to see that in a such widespread application.
Searching for "Exact Real Arithmetic" will yield some. Specifically, a HaskellWiki page [1] is not too bad as a starting point. Or, if you are keen to academic presentations (read: presentations optimized for the maximal information density and not for the actual presentation ;-) [2] might be better.
You can also take a look at the actual source code for the Android ExactCalculator app [3]. For some reason, however, it is deprecated after Android 9.0.0; don't know why.
