A.2.5 Numbers

Input forms for numbers.

Numbers can be entered with the notation base^^digits in any base from 2 to 36. The base itself is given in decimal. For bases larger than 10, additional digits are chosen from the letters a-z or A-Z. Upper- and lower-case letters are equivalent for these purposes. Floating-point numbers can be specified by including . in the digits sequence.

In scientific notation, mantissa can contain ` marks. The exponent n must always be an integer, specified in decimal.

The precision or accuracy s can be any real number; it does not need to be an integer.

In the form base^^number`s the precision s is given in decimal, but it gives the effective number of digits of precision in the specified base, not in base 10.

An approximate number x is taken to be machine precision if the number of digits given in it is Ceiling[$MachinePrecision] + 1 or less. If more digits are given, then x is taken to be an arbitrary-precision number. The accuracy of x is taken to be the number of digits that appear to the right of the decimal point, while its precision is taken to be Log[10, Abs[x]] + Accuracy[x].

A number entered in the form 0``s is taken to have precision Indeterminate and accuracy s.