Number System Advantages, Disadvantages

Date: 01/24/2001 at 10:10:13
From: Milton Mui
Subject: Advantages and disadvantages of present number system

Hi Dr.Math,

I've a question to ask you for my maths project. I want to know the 
advantages and disadvantages of the present number system.

With regards,
Milton

Date: 01/24/2001 at 12:21:11
From: Doctor Peterson
Subject: Re: Advantages and disadvantages of present number system

Hi, Milton.

This is a wide-open question where you can think of many different 
things to discuss in your paper. I suggest you visit our FAQ page on 
Roman numerals (which has links on other systems at the bottom), and 
familiarize yourself with how some other systems work. 

   http://mathforum.org/dr.math/faq/faq.roman.html   

The advantages of the current system should be obvious if you try 
doing some math problems in those systems, or just try to write large 
numbers; but the disadvantages may not be so obvious.

Our number system has several features that distinguish it from other 
possible systems: the place value concept, base 10 in particular, the 
specific set of symbols we have, the way we put those symbols together 
(in a row, using a decimal point), and so on. I don't think you can 
find any disadvantages in the use of place value, but you might be 
able to see better choices than 10 for the base; look into the 
Babylonian number system, which was partly based on 60, to see how 
"decimals" work better that way. In fact, if we used base 60, or 
perhaps 12, and therefore used that for the metric system as well, we 
could eliminate one of the big problems with the metric system, the 
fact that it doesn't handle common fractions well.

Maybe you can come up with an alternative set of symbols (especially 
if you choose a larger base) that would be easier to learn than ours. 
If you have ever seen the computer game Riven, it turns out that they 
use a base 25 system of numbers with a very consistent system of digit 
symbols. You might even want to ask some young children what problems 
they're having in learning to write numbers, to see if a different 
system might help.

One disadvantage that led to early rejection of Arabic numerals in 
Europe was that numbers could be more easily forged than in Roman 
numerals - it was easier to change 0 to 6 or 9 than to change V to X. 
That's why we have to write out numbers on checks - a different system 
might eliminate that problem.

This can be a fascinating idea to think about, so enjoy the experience 
of looking at our number system as an outsider deciding which system 
to use!

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