MantissaExponent
gives a list containing the mantissa and exponent of a number x.
MantissaExponent[x,b]
gives the base‐b mantissa and exponent of x.
Details
- The mantissa always lies between
and 
or 
and 
. - MantissaExponent works with exact as well as approximate numeric quantities.
Examples
open all close allBasic Examples (1)
MantissaExponent[3.4 10 ^ 30]MantissaExponent[456.1414]Scope (4)
MantissaExponent[123451]MantissaExponent[1027, 2]MantissaExponent[Exp[Pi], 2]The precision of the mantissa will depend on the precision of the inputs:
{m, e} = MantissaExponent[N[Pi, 20], E]Precision[m]{m, e} = MantissaExponent[Pi, N[E, 20]]Precision[m]{m, e} = MantissaExponent[Pi, E]Precision[m]Properties & Relations (3)
{b = RandomInteger[{2, 20}],
x = RandomReal[] 10 ^ RandomInteger[{-9, 9}]}{m, e} = MantissaExponent[x, b]m b ^ e == xMantissaExponent is related to RealExponent:
b = RandomInteger[{2, 20}];
x = RandomReal[]b ^ RandomInteger[{-9, 9}]If r=RealExponent[x,b] then ![e=TemplateBox[{r}, Floor]+1](Files/MantissaExponent.en/6.png "e=TemplateBox[{r}, Floor]+1"){kind=small}
and 
:
r = RealExponent[x, b];
e = Floor[r] + 1;{x b ^ -e, e} == MantissaExponent[x, b]RealDigits gives the mantissa in terms of digits:
x = 12345.6789;{d, e} = RealDigits[x]
m = Sum[d[[i]] 10^-i, {i, Length[d]}]This is equal to the values given by MantissaExponent:
{m1, e1} = MantissaExponent[x]{m1 == m, e1 == e}Text
Wolfram Research (1991), MantissaExponent, Wolfram Language function, https://reference.wolfram.com/language/ref/MantissaExponent.html (updated 2002).
CMS
Wolfram Language. 1991. "MantissaExponent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2002. https://reference.wolfram.com/language/ref/MantissaExponent.html.
APA
Wolfram Language. (1991). MantissaExponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MantissaExponent.html