A bit of topic, but I'd like to see how practical continued fractions could be used in day to day calculations. It's mainly a matter of having decent arithmetic

A bit of topic, but I'd like to see how practical continued fractions could be used in day to day calculations. It's mainly a matter of having decent arithmetic algorithms. Continued fractions have a lot of cool properties that positional notation doesn't: * Terminating expressions are exactly the rational numbers, * All (eventually) repeating expressions are precisely the roots of some quadratic polynomial (e.g. √2 = [1;2,2,2,...]), * Truncated expressions of irrationals give best approximations to their irrationals Also, some famous irrationals have easy to remember patterns in their continued fraction representation: e = [2;1,2,1,1,4,1,1,6,1,1,8,…] Φ = [1;1,1,1,...] (the golden ratio) Bessel(1,2)/Bessel(0,2) = [0;1,2,3,4,5,...]