Symbolic Manipulation 229
AUTO Setting
When Exact/Approx = AUTO, the handheld uses exact rational arithmetic wherever all of
the operands are rational numbers. Otherwise, floating-point arithmetic is used after
converting any rational operands to floating-point. In other words, floating-point is
“infectious.” For example:
1/2 - 1/3 transforms to 1/6
but
0.5 - 1/3 transforms to .16666666666667
This floating-point infection does not leap over barriers such as undefined variables or
between elements of lists or matrices. For example:
(1/2 - 1/3) x + (0.5 - 1/3) y transforms to x/6 + .16666666666667 y
and
{1/2 - 1/3, 0.5 - 1/3} transforms to {1/6, .16666666666667}
If you do not plan to use symbolic
computations, approximate results
are similar to familiar, traditional
numeric calculators.
Symbolic operations such as limits
and integration are less likely to give
satisfying results in the
APPROXIMATE setting.
Approximate results are sometimes
less compact and comprehensible
than exact results. For example, you
may prefer to see 1/7 instead of
.142857.
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