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????

>

>

> Aaron

>

--

Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

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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