3CHAPTER1
Counting Methods
Algebra is a science of numbers. To work with numbers, you need symbols to represent them.
The way these symbols relate to actual quantities is called a numeration system. In this chap-
ter, you’ll learn about numeration systems for whole-unit quantities such as 4, 8, 1,509, or
1,580,675. Fractions, negative numbers, and more exotic numbers will come up later.Fingers and Sticks
Throughout history, most cultures developed numeration systems based on the number
of fingers and thumbs on human hands. The word digit derives from the Latin word for
“finger.” This is no accident. Fingers are convenient for counting, at least when the numbers
are small!Number or numeral?
The words number and numeral are often used as if they mean the same thing. But they’re
different. A number is an abstraction. You can’t see or feel a number. A numeral is a tangible
object, or a group of objects, that represents a number. Suppose you buy a loaf of bread cut
into eighteen slices. You can consider the whole sliced-up loaf as a numeral that represents the
number eighteen, and each slice as a digit in that numeral. You can’t eat the number eighteen,
but you can eat the bread.
In this chapter, when we write about numbers as quantities, let’s write them out fully in
words, like eighteen or forty-five or three hundred twenty-one. When we want to write down
a numeral, it’s all right to put down 18 or 45 or 321, but we have to be careful about this sort
of thing. When you see a large quantity written out in full here, keep this in mind: It means
we’re dealing with a number, not a numeral.Figuring with fingers
Imagine it’s the afternoon of the twenty-fourth day of July. You have a doctor’s appointment
for the afternoon of the sixth of August. How many days away is your appointment?Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.