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Re: A strange precision behavior?

• To: mathgroup at smc.vnet.net
• Subject: [mg90395] Re: A strange precision behavior?
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Tue, 8 Jul 2008 02:26:48 -0400 (EDT)

On 7/7/08 at 5:07 AM, aaronfude at gmail.com (Aaron Fude) wrote:

>The following two commands result in different values:

>SetPrecision[0.01, 50] 0.01`50

That is because these are different numbers.

>Is that because in the first case, 0.01 is first represented as a
>double and then passed to SetPrecision, while in the second case,
>Mathematica gets a chance to interprete 0.01 as 1/100?

Mathematica never interprets 0.01 as 1/100. The value 0.01 is a
machine precision number.

If you want to get the equivalent of 0.01`50 using SetPrecision
you should use

SetPrecision[1/100, 50]

as

In[1]:= SetPrecision[1/100, 50] === .01`50

Out[1]= True

shows

Doing

SetPrecision[0.01, 50]

is telling Mathematica to start with a machine precision number
and increase the precision to 50. You can't do this in any
consistent manner. In general, the difference between the
closest machine number entered with a decimal point and the
exact rational value will be greater than that between a number
with a precision of 50 and the exact rational value. It is never
a good idea to attempt to increase the precision of a lower
precision number.