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By the end of this section, you will be able to:
  • Identify counting numbers and whole numbers
  • Model whole numbers
  • Identify the place value of a digit
  • Use place value to name whole numbers
  • Use place value to write whole numbers
  • Round 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 , 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.

Doing the Manipulative Mathematics activity Number Line-Part 1 will help you develop a better understanding of the counting numbers and the whole numbers.

Counting numbers

The counting numbers start with 1 and continue.

1 , 2 , 3 , 4 , 5…

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

An image of a number line from 0 to 6 in increments of one. An arrow above the number line pointing to the right with the label “larger”. An arrow pointing to the left with the label “smaller”.
The numbers on the number line increase from left to right, and decrease from right to left.

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    .

Whole numbers

The whole numbers are the counting numbers and zero.

0 , 1 , 2 , 3 , 4 , 5…

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.

Which of the following are counting numbers? whole numbers?

0 , 1 4 , 3 , 5.2 , 15 , 105

Solution

  • The counting numbers start at 1 , so 0 is not a counting number. The numbers 3 , 15 , and 105 are all counting numbers.
  • Whole numbers are counting numbers and 0 . The numbers 0 , 3 , 15 , and 105 are whole numbers.

The numbers 1 4 and 5.2 are neither counting numbers nor whole numbers. We will discuss these numbers later.

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Which of the following are counting numbers whole numbers?

0 , 2 3 , 2 , 9 , 11.8 , 241 , 376

  • 2, 9, 241, 376
  • 0, 2, 9, 241, 376
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Which of the following are counting numbers whole numbers?

0 , 5 3 , 7 , 8.8 , 13 , 201

  • 7, 13, 201
  • 0, 7, 13, 201
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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 $100 bills, seven $10 bills, and four $1 bills. The amounts are summarized in [link] . How much money is in the wallet?

Practice Key Terms 7

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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