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Ch 11: Rational & Real Number Systems

About This Chapter

This chapter delves into rational and real number systems. The lessons within break down the components of these systems while demonstrating relevant mathematic operations and defining related terms.

Rational & Real Number Systems - Chapter Summary

The lessons in this chapter dissect the operations, terminology, and mathematic formulas involved with rational and real number systems. You'll learn about rational exponents, estimating square roots, converting decimals to mixed numbers, and more. Other topics covered in this chapter include all of the following:

  • Real, rational, and irrational numbers
  • Navigating number lines
  • Transforming repeating decimals into fractions
  • Simplifying expressions using exponents and rational exponents
  • Locating the square root of a number
  • Cube roots
  • Distinguishing numbers that are written in scientific notation

These lessons include both a video and transcript of the content, allowing you to process the material in the manner best suited to your learning style. Those who opt for the videos can use the timeline feature beneath the videos to jump around the lesson's main points, while transcript readers can look out for bolded words indicating key topics and terms.

13 Lessons in Chapter 11: Rational & Real Number Systems
Test your knowledge with a 30-question chapter practice test
What are Real Numbers? - Definition & Properties

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.

What are Rational Numbers? - Definition & Examples

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.

What are Irrational Numbers? - Definition & Examples

3. 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.

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

4. 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.

Converting Decimals to Mixed Numbers

5. Converting Decimals to Mixed Numbers

After watching this video lesson, you should be able to convert easily between decimals and mixed numbers. Learn what kinds of decimals you can and cannot convert to a mixed number.

Converting Repeating Decimals into Fractions

6. Converting Repeating Decimals into Fractions

After watching this video lesson, you will be able to convert any repeating decimal that you come across into a fraction. Learn how to write the two equations that are needed for the conversion.

Rational Exponents

7. Rational Exponents

In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.

How to Simplify Expressions with Exponents

8. How to Simplify Expressions with Exponents

In this video, we will put all of the exponent properties we have learned together. Don't let lots of numbers and letters confuse you! Simplifying exponents can be easy and fun!

Simplifying Expressions with Rational Exponents

9. Simplifying Expressions with Rational Exponents

Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!

How to Find the Square Root of a Number

10. 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.

Estimating Square Roots

11. Estimating Square Roots

Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.

Cube Root: Definition, Formula & Examples

12. Cube Root: Definition, Formula & Examples

In this lesson, we're going to discover the world of cube roots! By the time we're done, you should be able to define what a cube root is, explain how to solve for the cube root of a number, and be familiar with several common cube roots.

Comparing Numbers Written in Scientific Notation

13. Comparing Numbers Written in Scientific Notation

After watching this video lesson, you will be able to compare numbers written in scientific notation with each other. You will learn how to tell which is larger and which is smaller.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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