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Built-in Mathematica Symbol

MantissaExponent

MantissaExponent[x]
gives a list containing the mantissa and exponent of a number x.

MantissaExponent[x, b]
gives the base-b mantissa and exponent of x.

Integers:

Base 2:

Exact numeric quantities:

The precision of the mantissa will depend on the precision of the inputs:

The fundamental identity

RealDigits gives the mantissa in terms of digits:

The mantissa is given by

This is equal to the values given by MantissaExponent:

Where r=RealExponent[x, b],

and

are the mantissa and exponent of

These are the same values given by MantissaExponent: