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Place Value

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Date: Wed, 16 Nov 1994 12:42:14 -0500 (EST)
From: Kacey
Subject: place value

What is place value? where did it come from?

Kyle
RSK@Nando.net
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Date: Mon, 21 Nov 1994 20:43:51 -0500 (EST)
From: Dr. Sydney
Subject: Re: place value

Dear Kyle:

Thanks for writing Dr. Math!  You have a GREAT question!
In fact, place value is very interesting to think about.  Believe it or not,
place value is a relatively new notion in mathematics. It took humans
28,000 years to come up with the notion of place value.  Before the place
value system was invented, symbols had to be repeated to express the right
amount.  For instance, using the original hieroglyphic script of Egyptian
numerals where | = 1 (I can't write the other symbols on the computer!!),
the number 4 would be expressed: |||| .

The notion of place value was first conceived by the Babylonians some-
where between 2000 B.C.E. and 1000 B.C.E.  Their place value system was
different from the one we use today because it was base 60 rather than base
10.  Do you know what bases are?  Basically (ha!) it means that if you have,
say, the number 628 in base 60 then that means 628 (base 60) = 6 x (60)^2 +
2 x (60) + 8 x (1).  In base 10, we have:  628 (base 10) = 6 x (10)^2 + 2 x
(10) + 8 x (1).  Anyway, this Babylonian system was all very fine except
initially it lacked a symbol for zero.  However, as time passed, ideas
evolved, and by 500 A.D., Indians had invented a base 10 system that had
unique symbols for the numbers 1 through 9, employed a place value notation,
and it used a zero.  This is the system that evolved into the way we
express numbers today.

So that's where place value came from.  What is it, though?
Place-value is the notion that where a digit sits in a number says something
about its value.  Take the example I used above, 628, means 6 x 100 + 2 x
10 + 8 x 1.  The 6 sits in the hundreds place so we multiply it by one
hundred or 10^2, the 2 sits in the tens place, so we multiply it by ten,
and the 8 sits in the ones place so we multiply it by 1.  This is a good
thing because it makes addition and multiplication easy.  We can just line
up numbers so that their place values line up and add accordingly.

If we didn't have this notion of place value, addition would be a big
pain.  Are you familiar with Roman Numerals?  They are written without a
notion of place value, and consequently, it is hard to add them together
without first converting to our base 10 notation for numbers.  Try adding XIII
and IX, for instance.  There is no easy, systematic way to do it unless you
convert them to base 10  numerals and then convert back after adding.

I hope this helps answer your question.  If you have any more

--Sydney
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