History of Zero and Place Value

Date: 02/17/99 at 12:26:35
From: Tristan
Subject: Zero/place value

I would like to know where zero and place value were invented or
discovered, and who discovered them.

Thanks.
Tristan

Date: 02/21/99 at 19:59:33
From: Doctor Reno
Subject: Re: Zero/place value

The concept of zero is surprisingly deep, and it took human thinkers 
quite a long time to come up with the notion of zero. In fact, though 
mathematicians began thinking about the concept of zero in 2000-1800 
B.C.E., it was not until about 200-300 B.C.E. that the Babylonians 
began using a symbol that would evolve into what we today know as zero.  

It turns out that mathematicians first thought of zero in the context 
of writing numbers down - zero was first a placeholder. Before 
mathematicians understood the notion of zero, there was much ambiguity 
about written numbers. For instance, if the symbol for 5 was written 
down, there was no way to tell distinguish among 5, 50, and 5,000,000. 
Zero was introduced as a placeholder to avoid these ambiguities.

In India, the concepts of 0 as a placeholder and 0 as a number were 
associated with one another much earlier than in Babylon. It is from 
the Indians that we get our present-day symbol for 0.

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 cannot write the other symbols on 
the computer), the number 4 would be expressed: |||| .  

The notion of place value was first conceived by the Babylonians 
somewhere 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 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 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 questions. If you have any more questions 
about this or anything else, please do write back. 
 
- Doctor Reno, The Math Forum
  http://mathforum.org/dr.math/