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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 Math Behind the Fact: The theory of continued fractions allows one to find good rational approximations of any irrational number.