Place Value and the Number Nine

Date: 08/31/2002 at 18:53:12
From: Jacque L.  Sievers
Subject: The number nine - place value

I am asking this for my 10-year-old grandson. Why is 9 the largest 
number you can put into any place value spot?

Date: 08/31/2002 at 23:21:02
From: Doctor Peterson
Subject: Re: The number nine - place value

Hi, Jacques.

The base-ten system is built around the idea that you can name every 
number by counting tens. Once you have ten tens, you give it a new 
name (hundreds) and write it using the hundreds place. When you get 
ten hundreds, you give that a new name (thousands) and use the 
thousands place. You never need to write a digit larger than 9, 
because ten of anything gets a new name.

Suppose we did use ten as a digit. We could talk about the number 
"tenty," meaning ten tens, and write it perhaps as X0, using X as 
the symbol for the digit ten. That would really be the same as one 
hundred; since we already have a name for it, it would be redundant. 
So we don't need an extra symbol for ten; X is written as 10, and X0 
as 100.

But occasionally you will see such ideas used humorously. In _The Lord 
of the Rings_, the story begins with Bilbo Baggins' "eleventy-first 
birthday." That would mean eleven tens and one, or 110+1, which is 
really 111. Again, we have a way to say it without using "eleventy," 
so we don't need to use eleven as a digit.

If you have any further questions, feel free to write back.

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