# Ch 1: Algebra II: Real Numbers

### About This Chapter

## Algebra II: Real Numbers - Chapter Summary and Learning Objectives

Watch the video lessons included in this chapter to learn what real and rational numbers are. Our experienced instructors can show you how to plot rational figures on a number line, find a real number's absolute value and convert between different forms of notation. They can even help you discover the differences between transcendental and algebraic numbers. By the time you finish this chapter, you should be able to:

- Identify the different types of numbers
- Place rational numbers on a number line
- Convert between fraction and decimal notation
- Remove square roots from the denominators of fractions
- Identify Pythagorean triples and common transcendental numbers

Video | Objectives |
---|---|

What Are the Different Types of Numbers? | Find out which types of numbers are natural, real, irrational, rational and whole. |

Graphing Rational Numbers on a Number Line | Learn how to draw a number line and use it to graph rational numbers. |

Notation for Rational Numbers, Fractions & Decimals | Understand how to convert a rational number from decimal to fraction notation and back again. |

The Order of Real Numbers: Inequalities | Practice determining which real number in an inequality is greater. |

Finding the Absolute Value of a Real Number | Learn what absolute value is and how to find it for any real number. |

How to Rationalize the Denominator with a Radical Expression | Follow the steps required to remove radicals from the denominator of a fraction. |

Algebraic Numbers and Transcendental Numbers | Explain algebraic numbers and transcendental numbers. Familiarize yourself with well-known transcendental numbers, such as e, pi and the Liouville constant. |

Understanding Numbers That Are Pythagorean Triples | Investigate numbers that are 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. 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.

### 7. 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.

### 8. Understanding Numbers That Are Pythagorean Triples

In this video lesson, you will learn about numbers that form Pythagorean Triples. Learn why these are special numbers and what they have to do with triangles.

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### Other Chapters

Other chapters within the Algebra II: High School course

- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II