Texas Instruments TI89TITANIUM User Manual - Page 242
AUTO Setting, in the APPROXIMATE setting.
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Functions such as solve and ‰ (integrate) can use both exact symbolic and approximate numeric techniques. These functions skip all or some of their exact symbolic techniques in the APPROXIMATE setting. Advantages Disadvantages If exact results are not needed, this might save time and/or use less memory than the EXACT setting. Approximate results are sometimes more compact and comprehensible than exact results. Results with undefined variables or functions often exhibit incomplete cancellation. For example, a coefficient that should be 0 might be displayed as a small magnitude such as 1.23457E-11. 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. 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 Symbolic Manipulation 242