Features Period or Comma? Decimal Styles over Time and Place Amelia A Williamson Historians sometimes refer to Barth- strength between the comma and the dot olomaeus Pitiscus—a German mathemati- as [decimal separators],” Cajori stated. In the United States, decimals are notated cian, astronomer, and theologian—as the In the early 1700s, Gottfried Wilhelm with periods (for example, 1.23), whereas first to use the decimal point. Pitiscus did Leibniz, a German polymath, proposed most of Europe uses decimal commas use decimal fractions in his writing, and the dot as the symbol for multiplication. (1,23). That is just one instance in which there were dots within the numbers in his Therefore, most of Europe favored the style rules in the United States clash with text. Some historians argue, however, that comma as a decimal separator. In England those in Europe. How did this style dif- the dots were not used as decimal points at the time, however, the preferred symbol ference arise? What issues does it cause and were merely punctuation points written for multiplication was an “X”, so the dot for editors? How do editors deal with the before and after numbers in running text, as was used more frequently as a decimal difference? Knowing the answers to those was common in medieval manuscripts. separator there than in the rest of Europe. questions can help editors to avoid mis- Pitiscus used three other notations for During the 19th century in England, understandings while working with both decimal fractions: he put a zero in front of the dot continued to be used as a decimal styles of decimal separators. the decimal numbers (for example, 0123 separator and also came to be used as the for our 0.123), he used a vertical stroke as symbol for multiplication. That did not History of the Decimal Point a decimal separator (1|234 for our 1.234), cause confusion, however, because the dots The history of decimal notation and the and he used the common fraction form were placed at different heights. The dot style difference dates back to the 1500s, (1 234/1000 for our 1.234). The dots in his used to signify multiplication was placed when decimal fractions were first used. text were used for other purposes. on the baseline (where the United States Mathematics historian Florian Cajori John Napier, a Scottish mathematician, currently places decimals), and the dot explained the history in his 1928 book A appears to have been the first to intention- used as a decimal separator was placed mid- History of Mathematical Notations. 1 ally use the period as a decimal separator way up (where the United States currently Simon Stevin, a Belgian mathemati- in his 1617 book Rabdologia. In one part of places the dot for multiplication). cian in the 16th century, is credited with the book, he explicitly says that whatever In the United States, although the establishing the use of decimal fractions. is written after the period is a fraction. comma was used occasionally as a decimal He explained their use in his pamphlet Later in the book, however, he uses the separator, the baseline dot has always been La Thiende, published in 1585. Stevin comma as a decimal separator and shows preferred. Historians are not sure why the understood the nature and importance of a division problem that illustrates his use use of the dot raised halfway as a decimal decimal fractions, but his notation was of the comma as a decimal. “Thus, Napier separator never gained general adoption in awkward. Stevin notated decimal fractions vacillated between the period and the the United States. by putting superscript circled numbers after comma,” Cajori stated; “mathematicians For a while, the baseline dot had two each digit in the number. A superscript have been vacillating in this matter ever meanings in the United States: a deci- circled 0 was put after the units-place digit, since.” mal separator and a multiplication sign. a superscript circled 1 after the tenths- Around 1880, however, the need arose for place digit, a superscript circled 2 after the Other Decimal Notations a distinction, and the decimal notation for hundredths-place digit, and so on. During the 17th century, many other nota- the United States was clearly established Franciscus Vieta, a French mathemati- tions were used besides the period and the as a dot on the baseline (for example, cian in the late 1500s, came close to the comma. Some mathematicians put the 1.234). The dot used as a multiplication modern notation of decimals when he used decimal part in superscript and underlined sign was raised to the central position, as a vertical stroke to separate the integer part it, some used an “L” shape as a separator, it is today. of the number from the fractional part. and others used the colon or an inverted That decision has remained the US stan- and raised comma as a separator. dard ever since. The United States writes By the 18th century, the notations for the decimal on the baseline and England in AMELIA A WILLIAMSON, a graduate student decimal fractions started to converge. “The the raised position, and the United States in science and technology journalism at Texas chaos in notations for decimal fractions writes the multiplication dot in the raised A&M University, prepared this article while gradually gave way to a semblance of order. position and England on the baseline. a Science Editor intern. The situation reduced itself to trials of In the early 1900s, the American 42 • Science Editor • March – April 2008 • Vol 31 • No 2 Features Period or Comma continued Committee of Mathematicians justified 1,234 to mean one thousand, two hundred up for commas . and automatic conver- the style decision. The committee stated thirty-four instead of the decimal that was sion is not possible. Therefore, comma-to- that because the letter X is used often in intended. point changes have to be made by hand.” mathematics, it is preferable to use the Authors and editors might also find Another potential problem that raised dot for multiplication. The commit- confusion in the style difference, Robinson Langdon-Neuner points out occurs when tee also stated, “Inasmuch as the period says, and gives this advice: data files are sent from Europe to the will continue to be used in this country United States. Some computer programs as a decimal point, it is likely to cause Authors: Check recent issues of the used in the United States are config- confusion, to elementary pupils at least, to publication to which you are submit- ured to interpret commas within numbers attempt to use it as a symbol for multiplica- ting your article to see what conven- (European decimals) as thousands markers tion,” according to Cajori. tion is being followed and ensure that and will convert the decimals to thousands your submission conforms. If you are numbers. For example, some programs will Current Style and Issues Editors uncertain, check with the editorial convert 1,34 to 1,340 instead of 1.34 as was Face office. Keep this convention in mind intended. So before sending data to the Currently, in European countries except for when you are checking proofs. United States, European scientists must the United Kingdom, the comma is used make sure that all the decimal commas are as the decimal separator. In the United Editors: Be alert to the possibility that changed to points. Kingdom, the raised dot is used, and in an author from another country may Although the style difference may be a the United States, the baseline dot is used. be using a different decimal notation; bit of a nuisance sometimes, it does not Australia and most Asian countries use the if in doubt as to intended meaning, appear to cause any major problems. “For dot, South America uses the comma, and seek clarification. most numbers, the convention can be some parts of Africa use the dot and other discerned from the context or from other parts, the comma. Elise Langdon-Neuner, editor of the values in the same paper,” Robinson says. With regard to use of decimals in sci- European Medical Writers Association But authors, editors, and readers should be entific writing, one would think that such journal The Write Stuff, mentions another aware of the difference. style differences could cause some confu- difficulty caused by the style difference. sion. Peggy Robinson, chair of the commit- She edits reports and manuscripts written Reference tee that prepared the most recent edition in English by Austrian scientists and says 1. Cajori F. A history of mathematical notations. of CSE’s Scientific Style and Format, says that it can be difficult to ensure that all the Chicago: The Open Court Publishing Company; that the style difference is most likely to decimal commas in the reports are changed 1928. p 314-335. cause confusion among readers who are to decimal points. “You can be driven mad not familiar with the difference in con- by spotting the commas and changing them vention. An American reading a French to points,” Langdon-Neuner says. “The soft- article, for example, might misinterpret ware for the tables [the scientists] use is set Science Editor • March – April 2008 • Vol 31 • No 2 • 43.