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Topic: Low precision exponentiation
Replies: 5   Last Post: Feb 18, 2013 6:00 AM

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 Albert Retey Posts: 688 Registered: 7/15/08
Re: Low precision exponentiation
Posted: Feb 18, 2013 5:59 AM
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Hi,

> I am trying to evaluate 2.5^125 to high precision.
>
> R gives 5.527147875260445183346e+49 as the answer but Mathematica
> with N[2.5^125,30] gives 5.52715*10^49 and says that is to machine
> precision.

There are two problems here:

1) with the standard settings, Mathematica will print only 6 digits of
machine precision numbers. You can change that in the preferences tab or
with e.g.:

NumberForm[2.5^125, {16, 16}]

2) the input you are giving is interpreted to be machine precision in
the first place. You can get an exact result like this:

(5/2)^125

and a numeric result to the desired precision like this:

N[(5/2)^125,50]

alternatively you can define the precision with this syntax:

2.5`50^125

> I am inexperienced at Mathematica. Am I doing something silly?

yes and no, Mathematica handles arbitrary precision numbers in a
somewhat unusual way. You might want to read the tutorials that are
linked to the documentation of N to learn about some details. On the
other hand, I think usually you can get away with the rule that one
should try to stay with exact results as long as possible when
requesting more than machine precision...

hth,

albert

Date Subject Author
2/17/13 Blaise F Egan
2/18/13 Albert Retey
2/18/13 Bill Rowe
2/18/13 Tom D
2/18/13 svkeeley@aol.com
2/18/13 Helen Read

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