>>  (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.  

Not true. They don't have an exact binary representation.
If you check these numbers here..

http://www.h-schmidt.net/FloatConverter/IEEE754.html

You'll find

9.2 -> 9.199999809265137
7.8 -> 7.800000190734863

and so on. So adding these numbers doesn't generate the same answer as doing it 
in base10 maths

Andy Ling
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