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[Dieter]

(01-28-2016 09:54 PM)Matt Agajanian Wrote:  Given all these accuracy and reliability isses, in what ways, in what contexts are a calculator and its results practical, accurate, useful, reliable, and trustworthy?

I do not think there are any "issues" here. What a decent calculator returns is accurate and reliable. It's up to the user not to draw the wrong conclusions:

[2] [sqrt] [pi] [x] => 4,442882938

Now listen closely to your calculator and hear what it says:
"I don't know what Pi times the square root of 2 is, but I can tell you the first ten digits of 1,414213562 times 3,141592654 are 4,442882938".

Can you hear it ?-)

Dieter