Numbers and Digits

Date: 09/21/2000 at 23:45:34
From: Diana Avila
Subject: Numbers and Digits

What is a digit?  Why can't we call a digit a number?        

This is the question my first grade class came up with today during 
math. I was explaining to them that numbers are made up of digits.  
Some numbers have one digit, some have two digits, and so on. We 
wrote numbers on the board and pointed out the digits before going 
into our ArithmeTwists (workbook). After the lesson, my students 
still wanted to call digits numbers. They didn't really understand 
the concept of "digit."  They wanted to know what it was and why it 
wasn't just called a number.

Thanks, Dr. Math.

Date: 09/22/2000 at 15:11:41
From: Doctor Peterson
Subject: Re: Numbers and Digits

Hi, Diana. Good question!

I occasionally see questions from students asking about "how to divide 
three numbers by two numbers," or "how many numbers there are in pi," 
and their use of "number" in place of "digit" makes me feel as if they 
were scraping chalk on a blackboard. Why does it bother me so much?

A digit is PART of a number (or rather, of a numeral). A number is an 
actual quantity, whereas a digit is only discussed within the context 
of the numeral in which it is used. The important thing is that 
numbers are not made up of other numbers, but of digits. There are 
only ten different digits, but infinitely many numbers; there is only 
one way to combine digits (by writing them next to one another), but 
there are many ways to combine numbers (add, subtract, multiply, ...). 
Some numbers are written with only one digit, it's true; but when we 
write a bigger number, we use digits, not numbers, to write it.

It's similar to the situation with words and letters. "A" in "BAT" 
is a letter, specifically the second letter in the word. "A" in 
"A student asked an interesting question" is a word, which just 
happens to be written with only one letter, namely "A." The two "A"s 
are different things, and it can be important to distinguish between 
words and letters; we don't say "BAT is made up of three words," do 
we? Similarly, "312" is made up of three digits, not three numbers. 
(Of course, "B" and "T" aren't words; but "bee" and "tea" are!)

To put it simply, distinguishing the two words allows us to say what 
we mean more clearly. When we are talking about putting symbols 
together to form numbers, we call "2" a digit, and it's clear what we 
are talking about. When we count the number of boys in my family, we 
call "2" a number. I can't put the number of boys and the number of 
girls together and get 21, but I can add them and get 3. 

Since numbers and digits are used in different ways, they have 
different names.

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