# Classifying Real Numbers

### Learning Outcomes

- Classify real numbers as counting, whole, rational, irrational, or integers

### Real Numbers

Real numbers are numbers that are either rational or irrational.*imaginary numbers.*You won't encounter imaginary numbers in this course, but you will later on in your studies of algebra.

### example

Determine whether each of the numbers in the following list is a 1. whole number, 2. integer, 3. rational number, 4. irrational number, and 5. real number. [latex-display]-7,\Large\frac{14}{5}\normalsize ,8,\sqrt{5},5.9,-\sqrt{64}[/latex-display] Solution: 1. The whole numbers are [latex]0,1,2,3\dots[/latex] The number [latex]8[/latex] is the only whole number given. 2. The integers are the whole numbers, their opposites, and [latex]0[/latex]. From the given numbers, [latex]-7[/latex] and [latex]8[/latex] are integers. Also, notice that [latex]64[/latex] is the square of [latex]8[/latex] so [latex]-\sqrt{64}=-8[/latex]. So the integers are [latex]-7,8,-\sqrt{64}[/latex]. 3. Since all integers are rational, the numbers [latex]-7,8,\text{and}-\sqrt{64}[/latex] are also rational. Rational numbers also include fractions and decimals that terminate or repeat, so [latex]\Large\frac{14}{5}\normalsize\text{and}5.9[/latex] are rational. 4. The number [latex]5[/latex] is not a perfect square, so [latex]\sqrt{5}[/latex] is irrational. 5. All of the numbers listed are real. We'll summarize the results in a table.Number | Whole | Integer | Rational | Irrational | Real |
---|---|---|---|---|---|

[latex]-7[/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | ||

[latex]\Large\frac{14}{5}[/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | |||

[latex]8[/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | |

[latex]\sqrt{5}[/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | |||

[latex]5.9[/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | |||

[latex]-\sqrt{64}[/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] | [latex]\quad\checkmark [/latex] |

### try it

[ohm_question]145962[/ohm_question]## Licenses & Attributions

### CC licensed content, Shared previously

- Identifying Sets of Real Numbers.
**Authored by:**James Sousa (Mathispower4u.com).**License:**CC BY: Attribution. - Question ID 145962.
**Authored by:**Harbaugh,Gregg, mb Lippman,David.**License:**CC BY: Attribution.

### CC licensed content, Specific attribution

- Prealgebra.
**Provided by:**OpenStax**License:**CC BY: Attribution.**License terms:**Download for free at http://cnx.org/contents/[email protected].