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/
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