Representation of Numbers
The Wolfram Language handles both integers and real numbers with any number of digits, automatically tagging numerical precision when appropriate. The Wolfram Language internally uses several highly optimized number representations, but nevertheless provides a uniform interface for digit and precision manipulation, while allowing numerical analysts to study representation details when desired.
IntegerDigits — digits of an integer in any base
IntegerLength — total number of digits in any base
IntegerExponent — number of trailing 0s in a given base
BitAnd ▪ BitXor ▪ DigitCount ▪ NumberDigit ▪ Mod
RealDigits — digits and exponent of a real number in any base
Precision — total number of digits of precision
Accuracy — number of significant digits to the right of the decimal point
RealExponent — the overall scale of a number
MantissaExponent — break a number into mantissa and exponent
IntegerPart ▪ FractionalPart ▪ Floor ▪ ...
FromDigits — construct a number from its digits
NumberExpand — expand a number into its positional notation
NumberDecompose, NumberCompose — represent numbers in mixed radix form
Testing for Types
NumberQ — test whether an expression is a number
IntegerQ — test whether an expression is an integer
MachineNumberQ — test whether an expression is a machine-precision number
Head — find the symbolic head of a number
Integer ▪ Real ▪ Rational ▪ Complex
Internal Representation
$MaxNumber ▪ $MinNumber ▪ $MaxPrecision ▪ $MinPrecision
$MachinePrecision ▪ $MachineEpsilon ▪ $MaxMachineNumber ▪ $MinMachineNumber
Rational Numbers
Numerator ▪ Denominator ▪ NumeratorDenominator