What is the name of the line that goes over a repeating number?

Answer 1

The line that goes over a repeting decimal is called Vinculum symbol.

en.wikipedia.org/wiki/Vinculum

- - - - - - - s-

Answer 2

Fun search!! New word for me!

"The repeating portion of a decimal expansion is conventionally denoted with a vinculum so, for example, 1/3==0.3333333...==0."

http://scienceworld.wolfram.com/search/index.cgi?num=&q=Decimal&start=0

Answer 3

It is called a vinculum.

Answer 4

It's called a "bar".

Answer 5

Infinite !!!

Answer 6

vinculum, fraction bar, "repeat bar" As a "Math Doctor", one of the most common questions asked by elementary school students is, "What is the name for the bar over repeating decimal fractions?" I always answer that "repeat bar" seems the best name to communicate what it does, but I know they want the classic Latin name for the bar, vinculum. The word is from the diminutive of vincere, to tie. vinculum referred to a small cord for binding the hands or feet. The meaning in math is mostly unchanged from that original meaning, as the purpose of the repeat bar is to bind together the sequence of repeating digits. The term repeating decimal has sometimes been replaced with "recurrent" or "Circulating". The sequence of digits which repeat have also been called the "circulants" and "repetends" (and sometimes "repetents"). The vinculum notation was once used in much the same way we now use parenthesis and brackets to "bind together" a group of numbers or symbols. Originally the line was placed under the items to be grouped although a bar over the grouping became the more lasting usage (and still is in the symbols for roots and the one for division).

It is in the expression for repeating decimals that students are most familiar with the use of the overbar as a symbol, yet it seems to have been the last application of the bar, and seems not to have occured until after 1930 in the US. In F. Cajori's A History of Mathematical Notations (1929) he points out two forms of marking repeating sequences in decimals but does not mention the vincula or overbar. Cajori credits John Marsh [Decimal Arithmetic Made Perfect, (London, 1742)] with being the first to use a symbol to indicate the repeat sequence. Marsh sometimes placed a single dot over the first number in the repeat sequence, and sometimes placed one on the first and last.

Although others used accents to denote the repeating digits, it seems that the use of dots over the digits became the common notation in most of the world. The dots were also used in the US and persisted into the Twentieth century. I have not yet discovered when, or why, the US opted for the use of a bar. In Public School Arithmetic by Baker and Bourne (G. Bell and Sons, London, 1961) in a section on "recurring decimals" (pg 349) he gives an example with 32/41 expressed as .78048 with the dot over the first and last digit. The exact same approach was used in America. In White's Complete Arithmetic (1870) A section on page 289 introduces "Circulating Decimals" as shown below.

He goes on on the next page to define a pure circulate as one that has no figure but the repetend, (for example 1/3); and a mixed circulate as a decimal with one or more figures before the repetend. He then follows with directions for converting both pure and mixed circulate decimals to a common fraction. I also found a use of the dots for repeating decimals in the 1940 College Algebra of Paul Rider of Washington University

The 29th yearbook of the NCTM, Topics in Mathematics for Elementary School Teaching, published in 1964, contains an example on page 320 which clearly uses the bar to show the decimal name for 3/14 with the statement, "...where the bar over 142857 indicates that the group 142857 repeats endlessly." In Dec of 2005 I was sent a copy of page 40 of the 1959 yearbook by Dave Mason, a teacher at South Tahoe High School. The page includes the use of the repeat bar as shown below

In the same year as the 29th NCTM yearbook(1964), Irving Adler obtained a copyright for A New Look At Arithmetic, and on page 220 he writes, "To indicate a repeating decimal with a minimum of writing, it is customary to write only enough decimal places to include the repeating part once, and to identify the repeating part by underlining it. Thus the repeating decimal for 211/990 is therefore represented by .213....". It is worth mentioning that William Oughtred, the 16th Century mathematician indicated all decimals by underlining.

A third example, or rather a hybrid of two of the former, also appeared in a book with a 1964 copyright. A A Klaf's Arithmetic Refresher was published a few years after his death by his family. The book is written in a question and answer style somewhat reminiscent of the classic dialogs of antiquity. On page 188 it asks, "How are recurring, circulation, or repeating decimals denoted?" It then goes on to answer, "b) by dots placed over the first and last figures of the recurring group." This is described exactly like the more common earlier usage, but the figure that follows includes dots, and then an arc above them, similar to what I have shown here. (see also "divide symbol" for more history of symbols). Similar arcs were used over groups of three numbers to indicate the periods (thousands, millions, etc) in some early use of Hindu-Arabic numerals. Gerber(980), who later became Pope Sylvester, referred to them as "Pythagorean Arcs."
Sam Koski of Miami Springs Senior High sent me a note about a 1960 text, Algebra ,ITS BIG IDEAS AND BASIC SKILLS by McGraw Hill. "Repeating decimals are written with ellipsis; .333... I don't see any indication of the "bar" notation."

In spite of the seeminly late date of apperance in textbooks, David L Renfro has found several journal articles dating back to 1920 that used the underline or overbar method for repeating decimals. I have taken snips from his post here:

Repeating decimals are indicated by the use of an overline bar in the following:
[2] Author unknown or n/a, "Problems -- Notes. 16. Skeleton Division", American Mathematical Monthly 28 #6/7 (June 1921), 278.
One of the sentences is: "The repeating digits are shown by a line over the crosses." (The crosses stand for unknown digits whose determination is the problem to be solved.)
[3] Frederik Schuh, Title unknown or n/a, Nieuw Tijdschrift Voor Wiskunde 8 (1920-21), 64.
The previous reference cites this as the source for the problem and, since quote marks are used in the statement of the problem, I would assume that the overline bar usage was also present in this slightly earlier reference. However, I did not have access to this journal, so I was not able to verify for sure that an overline bar usage appears in [3].
[4] David Raymond Curtiss, "I. Solution of a problem in skeleton division", American Mathematical Monthly 29 #5 (May 1922), 211-212.
An underline bar is used in the following for repeating decimals:
[5] James McGiffert, "Intrinsic decimals", Mathematics News Letter 7 #3 (December 1932), 7-10.
An overline bar is used in the following for repeating decimals:
[6] H. T. R. Aude, "Intrinsic decimals", Mathematics News Letter 8 #1 (October 1933), 8-12.
The overline usage is not nearly as noticeable as the underline usage in McGiffert's paper, but it does appear on p. 9.

Where today we might write (2x+3)5 the early users of the vinculum would write 2x+3 5. Cajori traces the use to Nicholas Chuquet in 1484. He attributes the use of a vinculum with the radical to indicate roots to Thomas Harriot in 1631, The more general use of the horizontal bar above the collected items was reinforced by Fr. van Schooten in his 1646 edit of the collected works of Vieta. [When I first wrote that statement, I assumed the use of the vinculum in place of parentheses for general computation such as the distribution of multiplication over addition had been limited to 15th and 16th century at the latest, but then I found the use (see below) in a 1924 edition of Practical Arithmetic by Van Tuyl. An even later example appears on page 20 of Elementary Shop Mathematics, published by the Lincoln Extension Institute in 1943 .]

The use of a vinculum to bind the names of points together, , to indicate a line was used by Cavalieri in 1647.

Some people also refer to the horizontal fraction bar as a vinculum as it binds the numerator and denominator into a single value. Leonardo of Pisa, or Fibonacci, introduced the bar to the west when he copied the Hindu-Arabic mathematicians who first used the fraction bar symbol, although he wrote his mixed numbers in the "Arabic" form, from right to left; 1/2 23 for twenty-three and one-half.