Editing Decimal (section)

=== History of decimal fractions ===
[[File:Rod fraction.jpg|thumb|right|150px|counting rod decimal fraction 1/7]]
Starting from the 2nd century BCE, some Chinese units for length were based on divisions into ten; by the 3rd century CE these metrological units were used to express decimal fractions of lengths, non-positionally.<ref name=jnfractn1>{{Cite book | author=Joseph Needham | author-link=Joseph Needham | chapter = 19.2 Decimals, Metrology, and the Handling of Large Numbers |pages=82–90 | title = Science and Civilisation in China |volume=III, "Mathematics and the Sciences of the Heavens and the Earth" | title-link=Science and Civilisation in China | year = 1959 | publisher = Cambridge University Press}}</ref> Calculations with decimal fractions of lengths were [[Rod calculus#Decimal fraction|performed using positional counting rods]], as described in the 3rd–5th century CE ''[[Sunzi Suanjing]]''. The 5th century CE mathematician [[Zu Chongzhi]] calculated a 7-digit [[approximations of π|approximation of {{mvar|π}}]]. [[Qin Jiushao]]'s book ''[[Mathematical Treatise in Nine Sections]]'' (1247) explicitly writes a decimal fraction representing a number rather than a measurement, using counting rods.<ref>Jean-Claude Martzloff, A History of Chinese Mathematics, Springer 1997  {{isbn|3-540-33782-2}}</ref> The number 0.96644 is denoted

:{{lang|zh|寸}}
:[[File:Counting rod 0.png|frameless|18px]] [[File:Counting rod h9 num.png|frameless|18px]] [[File:Counting rod v6.png|frameless|18px]] [[File:Counting rod h6.png|frameless|18px]] [[File:Counting rod v4.png|frameless|18px]] [[File:Counting rod h4.png|frameless|18px]].

Historians of Chinese science have speculated that the idea of decimal fractions may have been transmitted from China to the Middle East.<ref name=Lam>[[Lam Lay Yong]], "The Development of Hindu–Arabic and Traditional Chinese Arithmetic", ''Chinese Science'', 1996 p. 38, Kurt Vogel notation</ref>

[[Al-Khwarizmi]] introduced fractions to Islamic countries in the early 9th century CE, written with a numerator above and denominator below, without a horizontal bar. This form of fraction remained in use for centuries.<ref name=Lam/><ref>{{cite journal | last1 = Lay Yong | first1 = Lam | author-link = Lam Lay Yong | title = A Chinese Genesis, Rewriting the history of our numeral system | journal = Archive for History of Exact Sciences | volume = 38 | pages = 101–08 }}</ref>

Positional decimal fractions appear for the first time in a book by the Arab mathematician [[Abu'l-Hasan al-Uqlidisi]] written in the 10th century.<ref name=Berggren>{{cite book | first=J. Lennart | last=Berggren | title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook | chapter=Mathematics in Medieval Islam |editor-first=Victor J.|editor-last=Katz|publisher=Princeton University Press | year=2007 | isbn=978-0-691-11485-9 | page=530 }}</ref> The Jewish mathematician [[Immanuel Bonfils]] used decimal fractions around 1350 but did not develop any notation to represent them.<ref>[[Solomon Gandz|Gandz, S.]]: The invention of the decimal fractions and the application of the exponential calculus by Immanuel Bonfils of Tarascon (c. 1350), Isis 25 (1936), 16–45.</ref> The Persian mathematician [[Jamshid al-Kashi]] used, and claimed to have discovered, decimal fractions in the 15th century.<ref name=Berggren />

<div style="float: right;">[[File:Stevin-decimal notation.svg]]</div>
A forerunner of modern European decimal notation was introduced by [[Simon Stevin]] in the 16th century. Stevin's influential booklet ''[[De Thiende]]'' ("the art of tenths") was first published in Dutch in 1585 and translated into French as ''La Disme''.<ref name=van>{{Cite book | author = B. L. van der Waerden | author-link = Bartel Leendert van der Waerden | year = 1985 | title = A History of Algebra. From Khwarizmi to Emmy Noether | publisher = Springer-Verlag | place = Berlin}}</ref>

[[John Napier]] introduced using the period (.) to separate the integer part of a decimal number from the fractional part in his book on constructing tables of logarithms, published posthumously in 1620.<ref name=constructionIA>{{cite book|title=[[Commons:File:The Construction of the Wonderful Canon of Logarithms.djvu|The Construction of the Wonderful Canon of Logarithms]]|first=John|last=Napier|translator-last1=Macdonald|translator-first1= William Rae|date=1889|orig-date=1620|publisher=Blackwood & Sons|publication-place=Edinburgh|via=Internet Archive|quote=In numbers distinguished thus by a period in their midst, whatever is written after the period is a fraction, the denominator of which is unity with as many cyphers after it as there are figures after the period.}}</ref>{{rp|p. 8, archive p. 32)}}