What are Whole Numbers? - Definition & Examples

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  • 0:01 Numbers
  • 0:49 What Are Whole Numbers?
  • 2:17 Examples
  • 2:45 Lesson Summary
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Lesson Transcript
Instructor
Tara Quinn
Expert Contributor
Kathryn Boddie

Kathryn earned her Ph.D. in Mathematics from UW-Milwaukee in 2019. She has over 10 years of teaching experience at high school and university level.

In this lesson, we will learn about whole numbers , including what they are and what distinguishes them from other types of numbers. We'll also take a look at a few things about whole numbers that sometimes trip students up.

Numbers

There are a lot of numbers in the world! Think about it. How many numbers are there really? Are there as many numbers as stars in the sky? Are there as many numbers as grains of sand on all the beaches in the world? No. There are actually more numbers than all of these things!

So exactly how many numbers are there in the world? There's an infinite amount of numbers; that means they go on and on and on and never end. Wow! That's a lot of numbers!

To help themselves keep track of and understand the similarities and differences between numbers, mathematicians have developed a grouping system that categorizes and describes the type of numbers that are out there. In this lesson, we will focus on whole numbers.

What Are Whole Numbers?

Whole numbers are a special category or group of numbers that:

  • Consist of the numbers: {0, 1, 2, 3, 4, 5, 6, 7, 8...}
  • Are all positive numbers, including zero, which do not include any fractional or decimal parts

Whole numbers do not have any fractional parts or any decimal parts. A few things to note here:

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Additional Activities

Extra Examples and Discussion

In the following examples, students will classify numbers as being whole numbers or not - and give reasons for their answers to help solidify the definition of the set of whole numbers. After successfully answering the example questions, students should move on to the discussion question - which will help students think more about what whole numbers are capable of representing and what they are not.

Examples

Classify the following numbers as whole numbers or not whole numbers and write your answers in a table. Give reasoning for your decision.

1) -9

2) 3/4

3) 9,876,543,210

4) 3.5

5) 0

6) 27 + 50

7) 8*6

8) -5.2

Whole Numbers Not Whole Numbers
_____ _____
_____ _____
_____ _____
_____ _____

Solutions

Whole Numbers Not Whole Numbers
9,876,543,210-9
03/4
27+503.5
8*6-5.2

1) -9 is not a whole number because it is negative.

2) 3/4 is not a whole number because it is a fraction.

3) 9,876,543,210 is a whole number because it is a positive number with no decimal or fraction parts. Even really large numbers can be whole numbers.

4) 3.5 is not a whole number because it has a decimal part.

5) 0 is a whole number because the set of whole numbers includes positive numbers with no decimal or fraction parts and 0.

6) 27 + 50 = 77, which is a whole number because it is a positive number with no decimal or fraction parts. Two whole numbers added together is always a whole number.

7) 8*6 = 48, is a whole number because it is a positive number with no decimal or fraction parts. Two whole numbers multiplied is always a whole number.

8) -5.2 is not a whole number because it is negative and has a decimal part.

Discussion

What are some examples of things that can be represented with whole numbers? What types of things cannot be represented with whole numbers?

Guide to Discussion

Students may struggle more to think of things that cannot be represented with whole numbers. Some examples of things that can be represented with whole numbers are:

  • The number of pets in a house
  • The number of children at a park
  • The number of animals at a zoo

Some examples of things that cannot be represented with whole numbers (at least not always) are:

  • The number of dollars in a bank account (where cents are treated as a fraction of a dollar)
  • Measurements in a recipe
  • Many measurements (height, weight, etc)
  • A slice of cake - if one cake is sliced into 10 slices, then one slice is represented by 1/10.
  • Interest rates on loans

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