# Perform computations with real numbers

UNIT III STUDY GUIDE The Real Number System Continued 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. Course/Unit Learning Outcomes 3.1 3.2 3.3 Learning Activity Unit Lesson Chapter 6 Video: Irrational and Rational Numbers Unit III Homework Unit III Assessment Unit Lesson Chapter 6 Video: Computing Radicals Video: Exponents Video: Scientific Notation, Part I Video: Scientific Notation, Part II Video: Scientific Notation, Part III Unit III Homework Unit III Assessment Unit Lesson Chapter 6 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 Unit III Homework Unit III Assessment Reading Assignment Chapter 6: Number Theory and the Real Number System, pp. 270–272; 274; 281–288; 292–296 NOTE: The following videos can be viewed here as well as in your homework assignment within MyMathLab. Please click the titles below to view the videos. Arithmetic and Geometric Sequences, Part I: Click here to view the transcript for this video. Arithmetic and Geometric Sequences, Part II: Click here to view the transcript for this video. Arithmetic and Geometric Sequences, Part III: Click here to view the transcript for this video. Arithmetic and Geometric Sequences, Part IV: Click here to view the transcript for this video. Computing Radicals: Click here to view the transcript for this video. Exponents: Click here to view the transcript for this video. Irrational and Rational Numbers: Click here to view the transcript for this video. Scientific Notation, Part I: Click here to view the transcript for this video. Scientific Notation, Part II: Click here to view the transcript for this video. Scientific Notation, Part III: Click here to view the transcript for this video. MAT 1301, Liberal Arts Math 1 Unit Lesson UNIT x STUDY GUIDE Title Chapter 6: Number Theory and the Real Number System 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 learn about rational and irrational numbers. Rational numbers are numbers that can be expressed as a fraction. 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, use scientific notation, and be introduced to number patterns known as sequences. To complete the unit, read the unit lesson, and begin your unit assignments in MyMathLab. 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 e-mail 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. Click here to learn about the real number system. 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 here to learn about exponents and scientific notation. 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 here to learn about arithmetic and geometric sequences. MAT 1301, Liberal Arts Math 2 Looking Forward UNIT x STUDY GUIDE Title After you review sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in MyMathLab. 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. Click here to download and print the Unit III Reference Sheet. Click here to download and print the Unit III Note-Taking Guide. MAT 1301, Liberal Arts Math 3

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