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