Symbolic Manipulation 240
Using Exact, Approximate, and Auto Modes
Using Exact, Approximate, and Auto ModesUsing Exact, Approximate, and Auto Modes
Using Exact, Approximate, and Auto Modes
The Exact/Approx mode settings, which are described briefly in Operating the Handheld,
directly affect the precision and accuracy with which the TI-89 Titanium calculates a
result. This section describes these mode settings as they relate to symbolic
manipulation.
EXACT Setting
EXACT SettingEXACT Setting
EXACT Setting
When Exact/Approx = EXACT, the handheld uses exact rational arithmetic with up to
614 digits in the numerator and 614 digits in the denominator. The EXACT setting:
• Transforms irrational numbers to standard forms as much as possible without
approximating them. For example, transforms to and
ln(1000) transforms
to
3ln(10).
• Converts floating-point numbers to rational numbers. For example, 0.25 transforms
to 1/4.
The functions
solve, cSolve, zeros, cZeros, factor, ‰, fMin, and fMax use only exact
symbolic algorithms. These functions do not compute approximate solutions in the
EXACT setting.
• Some equations, such as
2
Lx
= x, have solutions that cannot all be finitely
represented in terms of the functions and operators on the handheld.
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