Bar over a Whole Number?

Date: 06/05/2001 at 20:52:27
From: Sandy Taylor
Subject: Pre-algebra

What does a bar over a whole number indicate? I am a 6th grade 
teacher and I am using a set of problems to prepare my students for 
an algebra readiness test. For example,we were asked to arrange this 
list in order from greatest to least: 
    __          _        _
    67, 0.6, 0.67, 0.67, 6

We know that a bar over a decimal means the decimal repeats, but we 
don't know what a bar over a whole number means.

Date: 06/06/2001 at 18:23:49
From: Doctor Douglas
Subject: Re: Pre-algebra

Hi Sandy, and thanks for writing.

The notation of a bar (vinculum, or overbar) over a whole number 
doesn't seem to be very common.  Here are some possibilities as to 
what it could mean:

It is sometimes used as a grouping symbol, as in a fraction:
   _____                                __
   3 + 1  x  5     =  20             so 67  =  67

I have also seen it used to refer to the average:
                       _                __
   x = {1,2,6},   x  = 3             so 67  =  67  

   (the average of one number is itself, of course).

I have also heard that it can be used to mean "1000 times whatever is
underneath", especially with Roman numerals - see the following Web 
page, Final Answers by Gerard P. Michon:

  http://home.att.net/~numericana/answer/culture.htm#bars   
   __                                   __
   IV      = 4000   (or MMMM)        so 67  = 67000

I hope this helps.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/   

Date: 06/07/2001 at 09:16:12
From: Doctor Peterson
Subject: Re: Pre-algebra

Hi, Sandy.

I see that Dr. Douglas has answered you with several possibilities. I, 
too, have never seen this notation, but I think we should include the 
obvious possibility from the context: that the vinculum represents 
repeated decimals, as usual.
                 __                           _
My guess is that 67 means 67.67676767..., and 6 means 6.6666... . That 
is, they are extending the usage of the vinculum from its normal usage 
after the decimal point, allowing it to be used before the decimal, 
but still meaning that the digits included are to be repeated forever 
to the right.

Again, I've never seen the vinculum in this sense used to the left of 
the decimal; but if you want to define it that way, I see no problems. 
The only problem is that if a text is going to use such a notation, 
they should (a) tell you what it means, and (b) say that it is non-
standard, so you won't try to use it elsewhere and find that nobody 
understands you!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/