On 7/28/06, Phil M <[EMAIL PROTECTED]> wrote:
On Jul 27, 2006, at 11:21 PM, Norman Palardy wrote:

> On Jul 27, 2006, at 7:58 PM, William Squires wrote:
>
>>   I get exactly 27 on Calculator.App... :O
>
> I dont

When you refactor the expression, I also get 27 no matter what the
precision is set to.  But if I go back to the original formula ((72 /
2000) * 750) then I get the following value with Calculator precision
set to 16:

     26.9999999999999964

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Interesting discussion.  To muddy the waters further, using Mathematica:

N[72/2000, 100] (ie calculate to 100 significant digits of precision)

you get:

0.03600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

No argument here, 72/2000 is really 0.036 exactly.

As people said, this real number may not be representable exactly as a
binary floating point number, however:

N[72/2000]  (calculate to machine precision)

gives 0.036, implying that the machine is indeed able to represent
0.036 exactly.

P.


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