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Re: Using N function

On 5/18/07 at 6:31 AM, kkwweett at (kkwweett) wrote:

>Can anyone tell me, please, which of a),b) or c) is wrong :

>a) <MathematicaHelp> <quote>

>N[expr] is equivalent to N[expr, MachinePrecision].

></quote> </MathematicaHelp>

>b) In[1]:=N[Exp[Sqrt[163 ]Pi] - 640320^3] Out[1]=256.

>c) In[2]:=N[Exp[Sqrt[163 ]Pi] - 640320^3,$MachinePrecision]

a) and c) are correct.

The problem with b is the order in which things are being done.
In b, first all of the constants are made machine precision
numbers then the expressions are evaluated. In c, the expression
is being evaluated with the specified precision.

This can be verified as follows:

In[1]:= Exp[Sqrt[163.] Pi] - 640320^3

Out[2]= 256.

which results since

In[2]:= {Exp[Sqrt[163.] Pi], 640320^3.}

Out[2]= {2.6253741264076826*^17, 2.62537412640768*^17}

using arbitrary precision we get

In[3]:= N[Exp[Sqrt[163] Pi] - 640320^3, 4]

Out[3]= 744.0

which verifies c) is correct
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