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Re: Confused about precision vs accuracy

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90385] Re: Confused about precision vs accuracy
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 8 Jul 2008 02:24:56 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g4smav$29$1@smc.vnet.net>

Aaron Fude wrote:

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

There are all about *uncertainty*.

<snip>

> C. On a related issue, how do I see Pi to a certain number of digits.
> I figured out this hack:
> 
> 1``100 Pi

In[1]:= N[Pi, 30]

Out[1]= 3.14159265358979323846264338328

> 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.

You must have studied some physics and/or chemistry. Do you remember the 
first few classes? Some time must have been devoted to the topic of 
measurements and uncertainties. Similar concepts applied here.

Say you are given two documents: one reports than person A is 180 m +/- 
1 cm tall, the other reports than person B is 180.5 +/- 0.1 cm tall. Can 
you tell who is the tallest (and why it is so)?

If you can answer â?? correctly! â?? the above question, you can easily 
apply the same line of though to numbers and precision in Mathematica.

Also, the following set of short tutorials is a must read.

"Numbers", tutorial/NumbersOverview,

http://reference.wolfram.com/mathematica/tutorial/NumbersOverview.html

   Types of Numbers
   Numeric Quantities
   Digits in Numbers
   Numerical Precision
   Arbitrary-Precision Numbers
   Machine-Precision Numbers
   Interval Arithmetic
   Indeterminate and Infinite Results
   Controlling Numerical Evaluation


Regards,
-- Jean-Marc


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