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Re: Confused about precision vs accuracy

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90403] Re: Confused about precision vs accuracy
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 8 Jul 2008 02:28:19 -0400 (EDT)
  • References: <g4smav$29$1@smc.vnet.net>


Hi Aaron,

see below.

Daniel



Aaron Fude wrote:

> Hi,

> 

> I can't figure out how the precision and accuracy concepts work in

> Mathematica.

> 

> A. First of all, what's the difference? (Is it only total number of

> digits vs digits after decimal?)

exactly, for a banker the accuracy makes sense, but the accuracy does 

not make much sense for numbers near zero.

> 

> B. Secondly, could someone talk through the logic of why.

> 

> N[Tanh[100000] - 1]

> 

> equals 0, while

> 

> N[Tanh[100000``1] - 1]

> 

> equals -3.*10^-86859;

100000``1 means the number is somwhere between 99999.5 and 100000.5,

the result must therefore be between: 

{1.3803010643*10^-86858,1.8680343549*10^-86859},

no mistery here.

> 

> C. On a related issue, how do I see Pi to a certain number of digits.

> I figured out this hack:

> 

> 1``100 Pi

hi, we have N[Pi,100] for this

> 

> D. And finally (for now) where can I read up on rules for "precision

> arithmetic". For example, my guess that

> 

> Precision[1`10 + 1`100]

> 

> ought to be 100-ish rather than 10-ish.

well, you add an inaccurate numer to a more accurate one and expect the 

result to be accurate????

> 

> Many thanks in advnce!

> 

> Aaron

> 





-- 



Daniel Huber

Metrohm Ltd.

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CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>




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