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### 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
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:

__                                   __
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/

Associated Topics:
Elementary Fractions
Elementary Math History/Biography
Middle School Fractions
Middle School History/Biography

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