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.

<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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