What Is a Whole Number? — Definition & Examples

Whole Numbers

Whole numbers are a subset of the integers. All non-negative integers (basically, all of the natural numbers plus zero) are whole numbers. $$0, 1,2,3,4,5,\cdots$$

(Video) Whole Numbers and Place Value

by PatrickJMT

Patrick JMT has a good video on whole numbers and place value.

$\large{\text{Summary}}$

Whole numbers are all the positive integers and zero. $$0,1,2,3,...$$

Place value is the name of the place in which a number is located. $$\begin{array}{|c|c|} \hline \text{Position}&\text{Place Value}\\ \hline \#,\#\#\#,\#\#{\color{red}{\#}}&\text{Ones}\\ \#,\#\#\#,\#{\color{red}{\#}}\#&\text{Tens}\\ \#,\#\#\#,{\color{red}{\#}}\#\#&\text{Hundreds}\\ \#,\#\#{\color{red}{\#}},\#\#\#&\text{Thousands}\\ \#,\#{\color{red}{\#}}\#,\#\#\#&\text{Ten Thousands}\\ \#,{\color{red}{\#}}\#\#,\#\#\#&\text{Hundred Thousands}\\ {\color{red}{\#}},\#\#\#,\#\#\#&\text{Millions}\\ \hline \end{array}$$

Example

Patrick demonstrates a common problem encountered with place values.

Give the place value of the digit $7$ in: $$1{,}647{,}832$$

The $7$ is just before the last comma, which corresponds to the fourth spot, so the place value is the thousands place.

Whole Numbers

So what is a whole number, exactly?

The whole numbers are the numbers $0,1,2,3,4,...$

The whole numbers contain the natural numbers and $0$.

We use the symbol $\mathbb{W}$ to refer to them.

Whole numbers have some really cool properties, like the reflexive, symmetric, and transitive properties. Check them out!