Identifying counting numbers and whole numbers

Learn how to define counting numbers and whole numbers along with how to identify them including a practice problem.

Counting numbers

Counting numbers (also known as natural numbers) can be defined as numbers that start at $1$ and continue (by increments of $1$).

For example, counting numbers are often represented as:

$$1,2,3,...$$

Note

Your teacher or resource might include zero in the counting numbers as their definition, so you may want to ask your instructor if you should include zero as part of the counting numbers definition for your work.

Tip

If you know what integers are, then you can consider the counting numbers as the positive integers.

Whole numbers

Whole numbers can be defined as the natural numbers and zero, for example:

$$0,1,2,3,...$$

Practice problem

Which of the following are natural numbers, whole numbers, both, or neither?

• $0$
• $\frac{1}{4}$
• $-15$
• $3$
• $5.2$
• $105$

Solution (click here to view)

• whole number
• neither
• neither
• both
• neither
• both

Solution video

---

Here are some downloadable files based on this lesson:

• Identifying counting numbers and whole numbers - Printable.pdf
• Identifying counting numbers and whole numbers - Slides.pdf

---

Lesson content based on the “OpenStax Prealgebra 2e” textbook. Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction.