On Fri, 23 Oct 2015 10:43:44 -0700
Scott Hess <shess at google.com> wrote:
> You're right, any base-2 representation right of the decimal should be
> precise to represent in base-10. But it's the kind of thing where if
> you find yourself counting on it, you probably made a grave error
> earlier in your design :-).
I'm either brave or naive enough to think I can still add to this
discussion. If we accept what you say, above, then why should
> (9.2+7.8+0+3.0+1.3+1.7)
in particular present any problem? There's no division. Each value
has an exact decimal representation. I'm prepared to assert that any
permutation of their sums also has an exact decimal representation.
Therefore they should have an exact binary representation, too.
To the OP, I want to point out that whether or not a fraction can be
presented exactly is a function of the base. Consider that 1/3 has no
finite decimal representation. But in base 3 it's just
0.1
--jkl
