# Ch 1: Real Numbers & Expressions

### About This Chapter

## Real Numbers & Expressions - Chapter Summary

This chapter simplifies the process of studying real numbers and expressions. Our instructors have developed entertaining lessons you can access anytime to improve your understanding of rational numbers, irrational numbers, the process of finding the square root of a number and more. By the end of this chapter, you will be able to:

- List properties of real numbers
- Graph rational numbers on a number line
- Compare and order decimals and fractions
- Use the number line to compare fractions, whole numbers and decimals
- Identify and order irrational numbers on a number line
- Find the square root of a number
- Simplify imperfect squares
- Find the greatest common factor and least common multiple

Navigate as many of the lessons as you need to gain full comprehension of real numbers and expressions. Revisit these lessons as often as you'd like, and take short quizzes to test your knowledge of the concepts they cover. Check your knowledge of the entire chapter by taking the practice exam. All the resources in this chapter are available around-the-clock and can be viewed using any smartphone, tablet or computer.

### 1. 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.

### 2. What are Rational Numbers? - Definition & Examples

In this lesson, we will learn about rational numbers and their characteristics. We'll discover what they are, what they aren't and how to distinguish them from other types of numbers.

### 3. 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.

### 4. Comparing and Ordering Decimals

In this video lesson, you'll find out how you can look at any two decimals and immediately tell which is greater than the other. You'll also learn how to quickly sort decimals from least to greatest or vice versa.

### 5. Comparing and Ordering Fractions

Comparing and ordering fractions is way to examine fractions that contain different-sized sets. In order to compare these fractions, you must find a common denominator and make equivalent fractions.

### 6. 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.

### 7. What are Irrational Numbers? - Definition & Examples

Irrational numbers may not be crazy, but they do sometimes bend our minds a little. Learn about common irrational numbers, like the square root of 2 and pi, as well as a few others that businessmen, artists, and scientists find useful.

### 8. Ordering & Graphing Irrational Numbers on a Number Line

This lesson will help you identify irrational numbers, order irrational numbers, and place the irrational numbers in the correct order on a number line.

### 9. 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.

### 10. Simplifying Square Roots When not a Perfect Square

Numbers that are imperfect squares are those that, when evaluated, do not give solutions that are integers. The proper mathematical way to simplify these imperfect squares is discussed in this lesson.

### 11. How to Find the Greatest Common Factor

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

### 12. How to Find the Least Common Multiple

The least common multiple of two numbers is the smallest number that can be divided evenly by your two original numbers. See some examples of what I'm talking about here!

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Pennsylvania Algebra I Keystone Exam: Test Prep & Practice course

- Understanding Exponential Expressions
- Working with Radical Expressions
- Understanding Absolute Value Expressions
- Estimation & Math Problem-Solving
- Solving Problems with Polynomials
- Solving, Writing & Graphing Linear Equations
- Solving Problems with Systems of Equations
- Solving & Graphing Linear Inequalities
- Understanding Function Basics
- Using Scatter Plots
- Understanding Basic Statistics
- Interpreting & Graphing Data
- Understanding the Probability of Compound Events
- Pennsylvania Algebra I Keystone Exam Flashcards