History of Zero and Place ValueDate: 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/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/