# Ch 2: Real Numbers

### About This Chapter

## Real Numbers - Chapter Summary

Begin your study of real numbers by learning how these can be further classified as natural, whole, rational and irrational numbers and integers. Discover their commutative, associative and distributive properties, among others, and find out how to work with decimals. If you're wary of performing mathematical operations with these numbers, instructors can show you tips for maintaining place value when adding, subtracting, multiplying and dividing. You can even learn techniques for converting decimals to fractions and percentages with ease.

Additional topics of study cover the significance of origin and identifying points on a number line and their usefulness in solving addition and subtraction problems or comparing decimals, fractions and whole numbers. When you're ready to work with exponents, instructors can also show you how to represent large numbers using scientific notation. A lesson on finding square roots concludes the chapter, which is designed to teach you the following main topics:

- Classifications and properties of real numbers
- Methods for converting among fractions, decimals and percentages
- Techniques for working with square roots and exponents

Our video lessons are taught by experienced instructors who use sample problems, examples and illustrations to help you discern between types of real numbers. If you need something to supplement the lesson content, there are corresponding self-assessment quizzes you can take as many times as you'd like. The lesson transcripts also include links to supplementary text lessons that you can use to bolster your understanding of key terms.

### 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. What are Real Numbers? - Definition & Properties

There are many definitions of real numbers, but they all lead to the same conclusion. Real numbers are numbers that have a measurable value. Learn more about real numbers with some examples and a quiz to test your knowledge.

### 3. 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.

### 4. What is a Decimal Place Value?

In this video lesson, you will see how a decimal, a simple dot, can change the place value of all the digits in a number. You will also learn how to read decimals using place values.

### 5. Arithmetic with Decimal Numbers

Watch this video lesson and see how our little professor goes about adding, subtracting, multiplying, and dividing decimal numbers all without the use of a calculator!

### 6. Relating Fractions and Decimals

Watch this video lesson to learn how to use both fractions and decimals to help you solve problems. Learn how to change between the two to use the best one for your problem.

### 7. Using the Number Line to Compare Decimals, Fractions, and Whole Numbers

Watch this video lesson to learn how useful the number line can be when you need to compare two different numbers, be they whole numbers, decimals or even fractions. Learn how to plot these numbers on the number line so you can compare them.

### 8. What is a Percent? - Definition & Examples

Thinking in terms of pizza is an excellent way to think about percentages. Learn how it can help you understand percentages in this video lesson. You will also learn about the uses of percentages in the real world.

### 9. Changing Between Decimals and Percents

Watch as we go on a rollercoaster ride in changing from a decimal to percent and then back again. Learn to master this technique so you can get as fast as a rollercoaster going downhill on tests and quizzes when you have to convert between the two.

### 10. Changing Between Decimals and Fractions

In this video lesson, you will learn about the usefulness of knowing how to change quickly between decimals and fractions. You will also learn how changing from a decimal to a fraction is different than changing from a fraction to a decimal.

### 11. Scientific Notation: Definition and Examples

Scientific notation is a special way of writing numbers so they are easier to work with. This lesson will define scientific notations and show some examples of how to convert numbers from standard notation to scientific notation and back.

### 12. Exponent: Definition & Properties

An exponent tells you how many times to use a number in a multiplication problem. This lesson will define the properties of exponents and how to interpret them. There will also be a quiz at the end of the lesson.

### 13. How to Find the Square Root of a Number

What is a square root? In this lesson, we'll learn what a square root is and how to find it. We'll review a variety of examples in order to master the concept.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards