Topic: The Basics
Subtopic: The Real Number System & Calculators
Overview
The graphing calculator is going to be an invaluable tool in this class. With this lesson we learn about the Real Number System as well as how to perform real number operations on a calculator. BTW, "Real numbers" are just all the numbers that you are used to dealing with -- decimals, fractions, the irrational number pi, etc. as opposed to "imaginary numbers" which we will learn about in Intermediate Algebra.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 1.2.1 Identify rational vs. irrational numbers
- 1.2.2 Convert decimal
fraction, repeating decimal fraction (by hand and on calc) - 1.2.3 Find an opposite and a reciprocal of an expression
- 1.2.4 Simplify an absolute value (by hand and on calc)
- 1.2.5 Simplify exponents and roots (mostly on calc)
- 1.2.6 Simplify expressions according to order of operations (by hand and on calc)
- 1.2.7 Perform prime factorization (by hand)
- 1.2.8 Reduce algebraic fractions (by hand)
- 1.2.9 Calculator keys: ->FRAC, NEG, x-1, ABS, ^, SQRT, XthROOT
Terminology
Define: decimal, fraction (proper and improper), mixed number, repeating decimal, integer, rational number, irrational number, Real number, opposite (of a number; of an expression), reciprocal (of a number; of an expression), absolute value (of a number; of an expression), exponent, radical, root, order of operations, prime number, composite number, prime factorization, reduce, cancel, simplify.
Text Notes
Text: Intro & Inter Algebra for CS 3ed by Blitzer, sect. 1.1-1.3, 1.5-1.7
- ch 1.1-1.2 is all review from a pre-algebra class. Skim and review as needed.
- ch 1.3 Pay particular attention to table 1.2 which describes the different types of Real numbers and provides examples of each and example 5. Particularly be able to identify rational vs. irrational numbers. We will discuss converting repeating decimals to fractions in class.
- ch 1.5-1.7 is all review from a pre-algebra class. Skim and review as needed. Particularly worth reviewing are 1.5 example 5, 1.6 examples 4-5, 1.7 examples 6-8. The rest is basically a review of arithmetic. If you have any trouble in these sections you should consider stepping back to math 030 in order to maximize your chance for success in math 089/090.