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On Tue, 2013-02-12 at 21:30 -0800, Richard Fateman wrote: > It is amusing to consider that [1/3, 0.1d0] could either be converted, > with some loss, > to two floats [0.3333...3, 0.1d0] > or without loss to two rationals, > > [1/3, 3602879701896397/ 2^55] > In fact, 3602879701896397/ 2^55 = 0.1000000000000000055511151231257827021181583404541015625 and not 0.1. It is impossible to get an exact rational representation of the vast majority of decimal fractions using only a power of 2 denominator. That is the mathematical reason that lead to the inclusion of decimal floating point specification in IEEE 754-2008. -- Hossam A. H. Fahmy Associate Professor Electronics and Communications Engineering Cairo University Egypt
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