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Definition of Vinculum

Date: 10/21/2004 at 15:49:43
From: Stephen
Subject: the name of the bar used to indicate a repeating decimal

What is the name (if it has one) of the bar placed over the set of 
repeated digits in a repeating decimal?

Someone thought it was called a "vinculum", but the definition of 
vinculum is a horizontal bar that could be used in the same manner as 
grouping symbols (parentheses and such).

Date: 10/21/2004 at 23:25:22
From: Doctor Peterson
Subject: Re: the name of the bar used to indicate a repeating decimal

Hi, Stephen.

I would call it a vinculum.  The fact that it is being used in a
slightly different way than the old usage for grouping does not mean
it isn't the same symbol.  (That usage for grouping, by the way, now
exists mostly in radicals,
  \/ 2+3

where the bar holds together the expression under it, and possibly as
a fraction bar.)  In decimals, the vinculum just indicates repetition
in addition to grouping, and can still be called a vinculum.

On the other hand, I have to admit that it is hard to find 
confirmation of that; dictionaries I have looked at refer the vinculum
only to its use as a grouping symbol, and math history sources I have
don't cover the origin of the repeating decimal usage or say what it
is or was called.  (I do, however, find historians using the word
vinculum, as well as titulus, for the bar used over Roman numerals to
multiply them by 1000, which is definitely more than just grouping.)

Here is one source, which may or may not be authoritative enough:


If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum 
Associated Topics:
Elementary Definitions
Elementary Division
Middle School Definitions
Middle School Division

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