Editing Fractional part (section)

{{short description|Excess of a non-negative real number beyond its integer part}}
[[File:Parte_fraccionaria.png|thumb|right|Graph of the fractional part of real numbers]]
The '''fractional part''' or '''decimal part'''<ref>{{cite web|url=https://en.oxforddictionaries.com/definition/decimal_part|archive-url=https://web.archive.org/web/20180215143935/https://en.oxforddictionaries.com/definition/decimal_part|url-status=dead|archive-date=February 15, 2018|title=Decimal part|publisher=[[OxfordDictionaries.com|Oxford Dictionaries]]|access-date=2018-02-15}}</ref> of a non‐negative [[real number]] <math>x</math> is the excess beyond that number's [[integer part]]. The latter is defined as the largest integer not greater than {{mvar|x}}, called ''[[floor function|floor]]'' of {{mvar|x}} or <math>\lfloor x\rfloor</math>. Then, the fractional part can be formulated as a [[difference (mathematics)|difference]]:

:<math>\operatorname{frac} (x)=x - \lfloor x \rfloor,\; x > 0</math>.

The fractional part of [[Logarithm|logarithms]],<ref>{{Cite book |last=Ashton |first=Charles Hamilton |url=https://books.google.com/books?id=Yls6AQAAMAAJ |title=Five Place Logarithmic Tables: Together with a Four Place Table of Natural Functions |date=1910 |publisher=C. Scribner's Sons |pages=iv |language=en}}</ref> specifically, is also known as the [[Mantissa (logarithm)|'''mantissa''']]; by contrast with the mantissa, the integral part of a logarithm is called its ''characteristic''.<ref>{{Cite book |last=Magazines |first=Hearst |url=https://books.google.com/books?id=Ad4DAAAAMBAJ&pg=PA291 |title=Popular Mechanics |date=February 1913 |publisher=Hearst Magazines |pages=291 |language=en}}</ref><ref>{{Cite book |last=Gupta |first=Dr Alok |url=https://books.google.com/books?id=IVTvDwAAQBAJ |title=Business Mathematics by Alok Gupta: SBPD Publications |date=2020-07-04 |publisher=SBPD publications |isbn=978-93-86908-16-2 |pages=140 |language=en}}</ref> The word ''mantissa'' was introduced by [[Henry Briggs (mathematician)|Henry Briggs]].<ref>{{Cite book |last=Schwartzman |first=Steven |url=https://books.google.com/books?id=PsH2DwAAQBAJ |title=The Words of Mathematics: An Etymological Dictionary of Mathematical Terms in English |date=1994-12-31 |publisher=American Mathematical Soc. |isbn=978-1-61444-501-2 |pages=131 |language=en}}</ref>

For a [[positive number]] written in a conventional [[positional numeral system]] (such as [[binary numeral system|binary]] or [[decimal]]), its fractional part hence corresponds to the digits appearing after the [[radix point]], such as the [[decimal point]] in English. The result is a real number in the half-open [[Interval (mathematics)|interval]] [0, 1).