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### Numbers and Digits

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

Hi, Diana. Good question!

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/
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Associated Topics:
Elementary Definitions