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A.1.5 Numbers

Basic types of numbers.

All numbers in Mathematica can contain any number of digits. Mathematica does exact computations when possible with integers and rational numbers, and with complex numbers whose real and imaginary parts are integers or rational numbers.

There are two types of approximate real numbers in Mathematica: arbitrary precision and machine precision. In manipulating arbitrary-precision numbers, Mathematica always tries to modify the precision so as to ensure that all digits actually given are correct.

With machine-precision numbers, all computations are done to the same fixed precision, so some digits given may not be correct.

Unless otherwise specified, Mathematica treats as machine-precision numbers all approximate real numbers that lie between $MinMachineNumber and $MaxMachineNumber and that are input with less than $MachinePrecision digits.

In InputForm, Mathematica prints machine-precision numbers with $MachinePrecision digits, except when trailing digits are zero.

In any implementation of Mathematica, the magnitudes of numbers (except 0) must lie between $MinNumber and $MaxNumber. Numbers with magnitudes outside this range are represented by Underflow[ ] and Overflow[ ].