# Ch 1: Real Numbers: Types and Properties

### About This Chapter

## Real Numbers: Types and Properties - Chapter Summary and Learning Objectives

The lessons in this chapter explore many types of numbers, including real, whole and natural numbers. Several lessons look at rational numbers and how to graph them and convert them from fractions to decimals. You'll get information on how to utilize the commutative and associative properties and work out the absolute value of a real number. By the end of this chapter, you should be familiar with:

- Showing inequalities between numbers
- Find the absolute value of a real number
- The multiplication property of zero
- Pythagorean triples

Video | Objective |
---|---|

What Are the Different Types of Numbers? | In this lesson, you'll learn about the various types of numbers, such as real, whole, natural, rational and irrational. |

Graphing Rational Numbers on a Number Line | This lesson explains how to use a number line to graph rational numbers. |

Notation for Rational Numbers, Fractions and Decimals | Here, we'll examine how to change rational numbers from fractional to decimal notation. You'll be given some examples to help you understand. |

The Order of Real Numbers: Inequalities | In this lesson, we'll look at inequalities, including how to use symbols to indicate which number is greater. You'll learn to determine which inequalities have the same meaning. |

Finding the Absolute Value of a Real Number | You'll learn how to determine a real number's absolute value. |

The Commutative Property: Definition and Examples | This lesson shows you what the commutative property is and how it can be useful. |

The Associative Property: Definition and Examples | Here, you'll get information on associating expressions through the use of this property. |

The Multiplication Property of Zero: Definition and Examples | We'll explore the rules regarding multiplying by zero. |

Rationalize the Denominator | You'll learn to simplify an expression by removing a radical symbol from the denominator. |

Algebraic Numbers and Transcendental Numbers | This lesson explains what these terms mean and gives well-known examples. |

Pythagorean Triples | Here, we'll learn to identify Pythagorean triples. |

### 1. What are the Different Types of Numbers?

Learn all of the different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. This video lesson teaches you how to classify any numbers you come across.

### 2. Graphing Rational Numbers on a Number Line

Number lines have many uses both in mathematics and everyday life. This lesson will teach you how to graph numbers on a number line and give real-world examples of how to use number lines.

### 3. Notation for Rational Numbers, Fractions & Decimals

How do fractions become decimals? And how do decimals become fractions? In this lesson, we'll learn about the notation of rational numbers, fractions and decimals and learn how they're related.

### 4. The Order of Real Numbers: Inequalities

An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.

### 5. Finding the Absolute Value of a Real Number

You can find the absolute value of any real number. This lesson will define absolute value, explain what real numbers are and give the steps to finding the absolute value of any real number.

### 6. The Commutative Property: Definition and Examples

There are three major properties that deal with the addition and multiplication of numbers. One of those properties is the commutative property. This lesson will define and give examples of the commutative property and how it works.

### 7. The Associative Property: Definition and Examples

There are three basic number properties that help to form the backbone of algebra. One of those properties is the associative property. This lesson will define the associative property and give some examples of how it works.

### 8. The Multiplication Property of Zero: Definition & Examples

The number zero has different rules than other numbers; it behaves according to it's own unique properties. This lesson will define the multiplication property of zero and give some examples of how it works.

### 9. How to Rationalize the Denominator with a Radical Expression

Watch this video lesson to learn what you can do to simplify your expression when you have a radical in the denominator. Learn what the single step solution to your problem is.

### 10. Algebraic Numbers and Transcendental Numbers

Math is all about numbers. In this lesson, you'll learn about the two different categories of numbers, called algebraic and transcendental. You'll learn the definition of each type and find out how common each of them is.

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### Other Chapters

Other chapters within the Trigonometry: High School course

- Absolute Value Equations
- Working with Complex Numbers
- Coordinate Geometry Review
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Functions for Trigonometry
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Polynomial Functions Basics
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Triangle Trigonometry
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Circular Arcs, Circles & Angles
- Teaching Resources for High School Trigonometry