On Jul 28, 2006, at 8:53 AM, Peter K. Stys wrote:
In[26]:= N[72/2000*750,100]
Out[26]=
27.0000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000
In[27]:= N[72/2000*750]
Out[27]= 27.
Still suggests all these numbers and intermediate results are
representable exactly at machine precision.
I'm quite certain that 72/2000 is not.
Write it as the simple sum of powers of 2 and you find the problem.
72/2000 = 2^-2 + 2^-4 + 2^-5 + 2^-6 + 2^-11 + 2^-15 ..... and so on
and you never get exactly the result you get from 72/2000.
In the machine all you have is powers of 2
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