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A company wishes to distill a 0.830 mole fraction ethanol (0.170 mole fraction water) solution. To aid in the distillation process, a 0.950 mole fraction benzene (0.050 mole fraction water) mixture containing fresh benzene and a recovered benzene solution is added.
Have people verify that 355/113 is a good rational approximation. You can also point out that 355/113 is very easy to remember, since it consists of the digits 113355 in some order! The theory of continued fractions allows one to find good rational approximations of any irrational number.