Columbia Southern University Number Theory and the Real Number System Worksheet

UNIT III STUDY GUIDEThe 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
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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
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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
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