In article <C5FF8E50.259E9%gus / progress.com>, gus <gus / progress.com> writes: > The fact that the base 10 rational numbers and the base 2 rational numbers > do not have the /same/ set of values that require infinite expansions means > that some numbers can be represented exactly in base 10 but not in base 2, > and vice versa. When converting from one base to the other, this will > introduce small errors because the conversion cannot be made exact. No numbers in base 2 cannot be represented exactly in base 10. 1/2**1 = 0.5 1/2**2 = 0.25 1/2**3 = 0.125 1/2**4 = 0.0625 1/2**5 = 0.03125 ... Any bit in base 2 can be represented exactly in base 10. Therefore, any number in base 2, which is a sum of some of them, is exactly representable in base 10. -- Tanaka Akira