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\noindent [For section on numerical precision.]

\smallskip
The above discussion of precision is not itself completely precise. Don't
assume that your computer always truncates or rounds perfectly unless you
have studied its circuitry. Occasional departures happen like this
(assume a 3-digit decimal machine):

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\disleft 25pt:(1):
On a rounding machine, adding 123 to 0.567, it ignores the 0.567, giving
123 instead of~124.

\smallskip
\disleft 25pt:(2):
On a truncating machine, subtracting 0.0456 from 123, it ignores the
0.0456, giving 123 instead of~122.

\smallskip
\disleft 25pt:(3):
On either machine, subtracting 99.8 from 101, it discards the 0.8, giving
2.00 instead of~1.20.

\smallskip
Similarly, the assumption that products of relative errors are insignificant
has exceptions. I~can find examples where ignoring the products greatly
understates the error.

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