1.1 Introduction to whole numbers

Identify counting numbers and whole numbers

Learning algebra is similar to learning a language. You start with a basic vocabulary and then add to it as you go along. You need to practice often until the vocabulary becomes easy to you. The more you use the vocabulary, the more familiar it becomes.

Algebra uses numbers and symbols to represent words and ideas. Let’s look at the numbers first. The most basic numbers used in algebra are those we use to count objects: $1,2,3,4,5,\dots$ and so on. These are called the counting numbers    . The notation “…” is called an ellipsis, which is another way to show “and so on”, or that the pattern continues endlessly. Counting numbers are also called natural numbers.

Counting numbers and whole numbers can be visualized on a number line    as shown in [link] .

The point labeled $0$ is called the origin    . The points are equally spaced to the right of $0$ and labeled with the counting numbers. When a number is paired with a point, it is called the coordinate    of the point.

The discovery of the number zero was a big step in the history of mathematics. Including zero with the counting numbers gives a new set of numbers called the whole numbers    .

We stopped at $5$ when listing the first few counting numbers    and whole numbers    . We could have written more numbers if they were needed to make the patterns clear.

Model whole numbers

Our number system is called a place value system    because the value of a digit depends on its position, or place, in a number. The number $537$ has a different value than the number $735.$ Even though they use the same digits, their value is different because of the different placement of the $3$ and the $7$ and the $5.$

Money gives us a familiar model of place value. Suppose a wallet contains three $\text{\$100}$ bills, seven $\text{\$10}$ bills, and four $\text{\$1}$ bills. The amounts are summarized in [link] . How much money is in the wallet?