About This Chapter
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.
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. 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.
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.
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.
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.
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.
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!
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!
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.
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.
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.
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.
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Other chapters within the NYSTCE CST Multi-Subject - Teachers of Middle Childhood (231/232/245): Practice & Study Guide course
- Language & Literacy Development
- Foundations of Teaching English Language Arts
- Strategies for Vocabulary Instruction
- Language Knowledge & Vocabulary
- Teaching Text Complexity & Comprehension
- Literary Devices & Meaning
- Evaluating Informational Texts
- Writing & Research Instruction
- Promoting Literacy Through Listening
- Language Arts Assessments in Early Childhood
- Numbers & Operations
- Ratios & Proportional Number Relationships
- Algebra Foundations
- Algebra Functions & Graphs
- Geometry & Measurement
- Solving Geometry Problems
- Data, Statistics & Graphs
- Math Instruction & Assessment
- Scientific Inquiry & Investigation
- Physical Science Basics
- Scientific Concepts for the Living Environment
- Science Modeling & Technology
- Major U.S. Historical Eras
- Role of New York in Shaping the U.S.
- Geography, Population & Climate
- Human Population Distribution Patterns
- Relationship Between Economics, Government & Politics
- Rights & Responsibilities of Citizenship in the U.S.
- Social Studies Research Skills
- Visual Arts Techniques
- Musical Arts Basics
- Performing Arts Overview
- Health, Safety & Community Awareness
- Physical Development & Activities in Early Childhood
- Childhood Development
- Consumer Economics & Personal Resource Management
- Career Development Resources
- NYSTCE CST Multi-Subject - Teachers of Middle Childhood Flashcards