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Confused about precision vs accuracy

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90359] Confused about precision vs accuracy
  • From: Aaron Fude <aaronfude at gmail.com>
  • Date: Mon, 7 Jul 2008 05:06:51 -0400 (EDT)

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?)

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;

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

1``100 Pi

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.

Many thanks in advnce!

Aaron


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