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

RealValuedNumberQ — test whether an expression is a number with a real value

IntegerQ — test whether an expression is an integer

MachineNumberQ — test whether an expression is a machine-precision number

ExactNumberQ   ▪ InexactNumberQ

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

Complex Numbers

Re   ▪ Im   ▪ ReIm

Abs   ▪ Arg   ▪ AbsArg

Conjugate   ▪ Sign

Related Tech Notes

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• Types of Numbers
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• Digits in Numbers
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• Numerical Precision
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• The Uncertainties of Numerical Mathematics

Related Guides

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• Numerical Functions
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• Integer Functions
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• Display of Numbers
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• Number Recognition
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• Number Digits
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• Continued Fractions
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• Diophantine Equations

Related Links

• Demonstrations related to Representation of Numbers (Wolfram Demonstrations Project)