Period or Comma? DecimalStyles over Time
`and Place
`
`Amelia A Williamson
`
`In the United States, decimals are notated
`with periods (for example, 1.23), whereas
`most of Europe uses decimal commas
`(1,23). Thatis just one instance in which
`style rules in the United States clash with
`those in Europe. How did this style dif-
`ference arise? Whatissues doesit cause
`for editors? How doeditors deal with the
`difference? Knowing the answers to those
`questions can help editors to avoid mis-
`understandings while working with both
`styles of decimal separators.
`
`to Barth-
`refer
`Historians sometimes
`olomaeus Pitiscus—a German mathemati-
`cian, astronomer, and theologian—as the
`first to use the decimal point. Pitiscus did
`use decimal fractions in his writing, and
`there were dots within the numbers in his
`text. Some historians argue, however, that
`the dots were not used as decimal points
`and were merely punctuationpoints written
`before and after numbers in runningtext, as
`was common in medieval manuscripts.
`Pitiscus used three other notations for
`decimal fractions: he put a zero in front of
`the decimal numbers (for example, 0123
`for our 0.123), he used a vertical stroke as
`a decimal separator(1 | 234 for our 1.234),
`and he used the common fraction form
`(1 234/1000 for our 1.234). The dots in his
`text were used for other purposes.
`John Napier, a Scottish mathematician,
`appears to have beenthefirst to intention-
`ally use the period as a decimal separator
`in his 1617 book Rabdologia. In one part of
`the book, he explicitly says that whatever
`is written after the period is a fraction.
`Later in the book, however, he uses the
`commaas a decimal separator and shows
`a division problem that illustrates his use
`of the commaas a decimal. “Thus, Napier
`vacillated between the period and the
`comma,” Cajori stated; “mathematicians
`have been vacillating in this matter ever
`since.”
`
`strength between the commaandthe dot
`as [decimal separators],” Cajori stated.
`In the early 1700s, Gottfried Wilhelm
`Leibniz, a German polymath, proposed
`the dot as the symbol for multiplication.
`Therefore, most of Europe favored the
`commaas a decimal separator. In England
`at the time, however, the preferred symbol
`for multiplication was an “X”, so the dot
`was used more frequently as a decimal
`separator there than in the rest of Europe.
`During the 19th century in England,
`the dot continued to be used as a decimal
`separator and also came to be used as the
`symbol for multiplication. That did not
`History of the Decimal Point
`cause confusion, however, because the dots
`were placed at different heights. The dot
`The history of decimal notation and the
`used to signify multiplication was placed
`style difference dates back to the 1500s,
`when decimal fractions were first used.
`on the baseline (where the United States
`currently places decimals), and the dot
`Mathematics historian Florian Cajori
`used as a decimal separator was placed mid-
`explained the history in his 1928 book A
`History of Mathematical Notations.'
`way up (where the United States currently
`places the dot for multiplication).
`Simon Stevin, a Belgian mathemati-
`In the United States, although the
`cian in the 16th century, is credited with
`comma was used occasionally as a decimal
`establishing the use of decimal fractions.
`separator, the baseline dot has always been
`He explained their use in his pamphlet
`preferred. Historians are not sure why the
`La Thiende, published in 1585. Stevin
`use of the dot raised halfway as a decimal
`understood the nature and importance of
`separator never gained general adoption in
`decimal fractions, but his notation was
`the United States.
`awkward. Stevin notated decimal fractions
`by putting superscript circled numbers after
`For a while,
`the baseline dot had two
`meanings in the United States: a deci-
`each digit
`in the number. A superscript
`mal separator and a multiplication sign.
`circled 0 was put after the units-placedigit,
`a superscript circled 1 after the tenths-
`Around 1880, however, the need arose for
`Other Decimal Notations
`place digit, a superscript circled 2 after the
`a distinction, and the decimal notation for
`the United States was clearly established
`During the 17th century, many other nota-
`hundredths-placedigit, and so on.
`as a dot on the baseline (for example,
`tions were used besides the period and the
`Franciscus Vieta, a French mathemati-
`1.234). The dot used as a multiplication
`comma. Some mathematicians put
`the
`cian in the late 1500s, came close to the
`modern notation of decimals when he used
`sign was raised to the central position, as
`decimal part in superscript and underlined
`it is today.
`it, some used an “L” shape as a separator,
`a vertical stroke to separate the integer part
`and others used the colon or an inverted
`That decision has remained the USstan-
`of the numberfrom thefractional part.
`dard ever since. The United States writes
`and raised commaasaseparator.
`By the 18th century, the notations for
`the decimal on the baseline and England in
`decimalfractionsstarted to converge. “The
`the raised position, and the United States
`chaos in notations for decimal fractions
`writes the multiplication dot in the raised
`gradually gave way to a semblance oforder.
`position and England on the baseline.
`The situation reduced itself to trials of
`In the early 1900s,
`the American
`
`AMELIA A WILLIAMSON, a graduate student
`in science and technology journalism at Texas
`A&M University, prepared this article while
`a Science Editorintern.
`
`42 © Science Editor © March — April 2008 «
`
`Vol 31 * No 2
`
`UNITED THERAPEUTICS, EX. 2116
`WATSON LABORATORIES v. UNITED THERAPEUTICS, IPR2017-01622
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`

`Period or Commacontinued
`
`Committee of Mathematicians justified
`the style decision. The committee stated
`that because the letter X is used often in
`mathematics,
`it
`is preferable to use the
`raised dot for multiplication. The commit-
`tee also stated, “Inasmuch as the period
`will continue to be used in this country
`as a decimal point,
`it
`is likely to cause
`confusion, to elementary pupils at least, to
`attempttouse it as a symbolfor multiplica-
`tion,” according to Cajori.
`
`Current Style and Issues Editors
`Face
`Currently, in European countries exceptfor
`the United Kingdom, the comma is used
`as the decimal separator. In the United
`Kingdom, the raised dot is used, and in
`the United States, the baseline dotis used.
`Australia and most Asian countries use the
`dot, South America uses the comma, and
`someparts of Africa use the dot and other
`parts, the comma.
`With regard to use of decimals in sci-
`entific writing, one would think that such
`style differences could cause some confu-
`sion. Peggy Robinson, chair of the commit-
`tee that prepared the most recent edition
`of CSE’s Scientific Style and Format, says
`that the style difference is most likely to
`cause confusion among readers who are
`not familiar with the difference in con-
`vention. An American reading a French
`article,
`for example, might misinterpret
`
`1,234 to mean one thousand, two hundred
`thirty-four instead of the decimal that was
`intended.
`Authors and editors might also find
`confusion in the style difference, Robinson
`says, and gives this advice:
`
`issues of the
`Authors: Check recent
`publication to which you are submit-
`ting your article to see what conven-
`tion is being followed and ensure that
`your submission conforms. If you are
`uncertain, check with the editorial
`office. Keep this convention in mind
`when you are checking proofs.
`
`Editors: Be alert to the possibility that
`an author from another country may
`be using a different decimal notation;
`if in doubt as to intended meaning,
`seekclarification.
`
`the
`Elise Langdon-Neuner, editor of
`European Medical Writers Association
`journal The Write Stuff, mentions another
`difficulty caused by the style difference.
`She edits reports and manuscripts written
`in English by Austrian scientists and says
`that it can be difficult to ensure thatall the
`decimal commas in the reports are changed
`to decimal points. “You can be driven mad
`by spotting the commas and changing them
`to points,” Langdon-Neunersays. “Thesoft-
`ware for the tables [the scientists] use is set
`
`. and automatic conver-
`.
`up for commas .
`sion is not possible. Therefore, comma-to-
`point changes have to be made by hand.”
`Another
`potential
`problem that
`Langdon-Neuner points out occurs when
`data files are sent
`from Europe to the
`United States. Some computer programs
`used in the United States are config-
`ured to interpret commas within numbers
`(European decimals) as thousands markers
`and will convert the decimals to thousands
`numbers. For example, some programs will
`convert 1,34 to 1,340 instead of 1.34 as was
`intended. So before sending data to the
`United States, European scientists must
`make sure thatall the decimal commasare
`changedtopoints.
`Although the style difference may be a
`bit of a nuisance sometimes,
`it does not
`appear to cause any major problems. “For
`most numbers,
`the convention can be
`discerned from the context or from other
`values in the same paper,” Robinson says.
`But authors, editors, and readers should be
`awareofthe difference. #%
`
`Reference
`1. Cajori E A history of mathematical notations.
`Chicago: The Open Court Publishing Company;
`1928. p 314-335.
`
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