Unit III J Math

MAT 1301, Liberal Arts Math 1

Course Learning Outcomes for Unit III Upon completion of this unit, students should be able to:

3. Perform computations with real numbers. 3.1 Identify rational and irrational numbers. 3.2 Perform operations using exponents, radicals, and scientific notation. 3.3 Compute future terms of arithmetic and geometric sequences.

Required Unit Resources Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us,

Sections 6.4–6.6

Unit Lesson Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us

Unit I introduced counting numbers, integers, and whole numbers. In this unit, we will learn about other types of numbers that make up the real number system. Specifically, we will learn about rational and irrational numbers. Rational numbers are numbers that can be expressed as fractions. Whole numbers, integers, and some decimals are rational numbers. You have probably used rational numbers when shopping or cooking. Irrational numbers are numbers that cannot be expressed as a fraction. The decimal expansion of an irrational number does not end and does not repeat. An example of an irrational number is pi where pi is approximately equal to 3.141592654. This number goes on forever without a repeating pattern. The number pi is utilized in anything that has a curvature. For example, the construction of a football involves a calculation with pi. As you learn more about rational and irrational numbers, you will learn how to compute radicals, perform operations with exponents, and use scientific notation, and you will be introduced to number patterns known as sequences. To complete the unit, read the unit lesson, and begin your unit assignments in MyLab Math. Do not forget to use the reference sheet and note-taking guide located in this lesson. Also, please be aware that you will need a scientific calculator to perform some of the calculations in this unit. Please email your professor if you need assistance with your calculator.

Section 6.4: The Real Number System Mathematicians have categorized numbers into different sets. As shown previously, some sets of numbers have different rules when performing computations. For example, integer operations are dependent on the sign of the number, and fraction operations require that we manipulate the denominator when adding or subtracting. In this section, we will expand our knowledge of rational numbers and learn about another group of numbers called irrational numbers.

UNIT III STUDY GUIDE

The Real Number System Continued

MAT 1301, Liberal Arts Math 2

UNIT x STUDY GUIDE

Title

Click the link to view the Section 6.4: The Real Number System lesson.

Section 6.5: Exponents and Scientific Notation Exponential and scientific notation is used to identify very small and very large numbers. For example, these notations will help us to express a number that is 100 digits long. Exponents and scientific notation will also aid in performing calculations with very small and very large numbers. Click the link to view the Section 6.5: Exponents and Scientific Notation lesson.

Section 6.6: Sequences As children, we were taught to recognize patterns. We might have been given three shapes and been asked to provide the fourth shape based upon a recognizable pattern. As adults, we can recognize patterns or trends in things such as utility bills or gas prices. For example, we may expect an increase in our cable bill if that bill increased in previous years. In this section, we will learn how to recognize patterns in number sequences and predict the next number in a given sequence. Click the link to view the Section 6.6: Sequences lesson.

Looking Forward After you review Sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in MyLab Math. You will be instructed to watch several instructional videos before you complete your homework problems. It is recommended that you print the following reference sheet and note-taking guide to use while you watch the unit homework videos and complete the unit homework assignment.

• Unit III Reference Sheet

• Unit III Note-Taking Guide

Suggested Unit Resources In order to access the following resources, click the links below. The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please click the titles below to view the videos. Transcripts and closed captioning will be available once you access the videos.

• Rational and Irrational Numbers video

• Computations With Radicals video

• Operations With Exponents video

• Scientific Notation video

• Multiplying and Dividing Numbers in Scientific Notation, Part I video

• Multiplying and Dividing Numbers in Scientific Notation, Part II video

• Arithmetic and Geometric Sequences, Part I video

• Arithmetic and Geometric Sequences, Part II video

• Arithmetic and Geometric Sequences, Part III video

• Arithmetic and Geometric Sequences, Part IV video

MAT 1301, Liberal Arts Math 1

Course Learning Outcomes for Unit III Upon completion of this unit, students should be able to:

3. Perform computations with real numbers. 3.1 Identify rational and irrational numbers. 3.2 Perform operations using exponents, radicals, and scientific notation. 3.3 Compute future terms of arithmetic and geometric sequences.

Required Unit Resources Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us,

Sections 6.4–6.6

Unit Lesson Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us

Unit I introduced counting numbers, integers, and whole numbers. In this unit, we will learn about other types of numbers that make up the real number system. Specifically, we will learn about rational and irrational numbers. Rational numbers are numbers that can be expressed as fractions. Whole numbers, integers, and some decimals are rational numbers. You have probably used rational numbers when shopping or cooking. Irrational numbers are numbers that cannot be expressed as a fraction. The decimal expansion of an irrational number does not end and does not repeat. An example of an irrational number is pi where pi is approximately equal to 3.141592654. This number goes on forever without a repeating pattern. The number pi is utilized in anything that has a curvature. For example, the construction of a football involves a calculation with pi. As you learn more about rational and irrational numbers, you will learn how to compute radicals, perform operations with exponents, and use scientific notation, and you will be introduced to number patterns known as sequences. To complete the unit, read the unit lesson, and begin your unit assignments in MyLab Math. Do not forget to use the reference sheet and note-taking guide located in this lesson. Also, please be aware that you will need a scientific calculator to perform some of the calculations in this unit. Please email your professor if you need assistance with your calculator.

Section 6.4: The Real Number System Mathematicians have categorized numbers into different sets. As shown previously, some sets of numbers have different rules when performing computations. For example, integer operations are dependent on the sign of the number, and fraction operations require that we manipulate the denominator when adding or subtracting. In this section, we will expand our knowledge of rational numbers and learn about another group of numbers called irrational numbers.

UNIT III STUDY GUIDE

The Real Number System Continued

MAT 1301, Liberal Arts Math 2

UNIT x STUDY GUIDE

Title

Click the link to view the Section 6.4: The Real Number System lesson.

Section 6.5: Exponents and Scientific Notation Exponential and scientific notation is used to identify very small and very large numbers. For example, these notations will help us to express a number that is 100 digits long. Exponents and scientific notation will also aid in performing calculations with very small and very large numbers. Click the link to view the Section 6.5: Exponents and Scientific Notation lesson.

Section 6.6: Sequences As children, we were taught to recognize patterns. We might have been given three shapes and been asked to provide the fourth shape based upon a recognizable pattern. As adults, we can recognize patterns or trends in things such as utility bills or gas prices. For example, we may expect an increase in our cable bill if that bill increased in previous years. In this section, we will learn how to recognize patterns in number sequences and predict the next number in a given sequence. Click the link to view the Section 6.6: Sequences lesson.

Looking Forward After you review Sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in MyLab Math. You will be instructed to watch several instructional videos before you complete your homework problems. It is recommended that you print the following reference sheet and note-taking guide to use while you watch the unit homework videos and complete the unit homework assignment.

• Unit III Reference Sheet

• Unit III Note-Taking Guide

Suggested Unit Resources In order to access the following resources, click the links below. The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please click the titles below to view the videos. Transcripts and closed captioning will be available once you access the videos.

• Rational and Irrational Numbers video

• Computations With Radicals video

• Operations With Exponents video

• Scientific Notation video

• Multiplying and Dividing Numbers in Scientific Notation, Part I video

• Multiplying and Dividing Numbers in Scientific Notation, Part II video

• Arithmetic and Geometric Sequences, Part I video

• Arithmetic and Geometric Sequences, Part II video

• Arithmetic and Geometric Sequences, Part III video

• Arithmetic and Geometric Sequences, Part IV video