math 173 gi whole & signed numbers sept 2008mth173 - numbers1
TRANSCRIPT
AnnouncementsAnnouncements
Calter Textbook with WileyPLUS
Register for class in WileyPLUS• Online Assignment – Due next week
Advanced Standing in Course
Quiz – Next Thursday, Sept 11th
• Signed Numbers, Decimals, Sig Digs, Exponents, Radicals, Scientific Notation
Sept 2008 MTH173 - Numbers 2
Whole & Signed NumbersWhole & Signed Numbers
Calter & Calter (2008)• Technical Mathematics with Calculus,
Canadian Edition
• Chapter 1: Numerical Computation• 1-1 The Real Numbers
• 1-2 Addition & Subtraction
• 1-3 Multiplication
• 1-4 Division
• pages 1 - 18
Sept 2008 MTH173 - Numbers 3
Lecture OutlineLecture Outline
What is Mathematics The Real Numbers Definitions Addition & Subtraction Multiplication Division
Sept 2008 MTH173 - Numbers 4
What is Mathematics?What is Mathematics?
math-e-mat-ics ... the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.
Webster's New Collegiate Dictionary
Mathematics is a language.
Gibbs, Josiah Willard. 1839-1903.American mathematician and physicist.
Sept 2008 MTH173 - Numbers 5
The Real NumbersThe Real Numbers
To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
Richard Feynman. 1918-1988.American physicist.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Bertrand Russell. 1872–1970British philosopher, mathematician.
Sept 2008 MTH173 - Numbers 6
What is Mathematics?What is Mathematics?
All science requires Mathematics. The knowledge of mathematical things is almost innate in us... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
Roger Bacon. 1214-1294English philosopher, scientist.
Sept 2008 MTH173 - Numbers 7
The Real NumbersThe Real Numbers
Natural Numbers
• Counting numbers
Whole Numbers
• Natural numbers including Zero
Integers
• Whole numbers including zero and negative values
Sept 2008 MTH173 - Numbers 9
The Real NumbersThe Real Numbers
Rational Numbers
• Integers & other numbers that can be expressed as quotient of two integers
Irrational Numbers
• Numbers that cannot be expressed as a quotient of two integers
Real Numbers
• Rational and Irrational Numbers
• Do not include Imaginary Numbers
Sept 2008 MTH173 - Numbers 10
The Real NumbersThe Real Numbers
Exact Numbers
• Have no uncertainty
• 24 hours / day, 4 wheels / car, 25.4 mm
Approximate Numbers
• Measured quantities, Fractions, Irrational Numbers
Significant Digits
Sept 2008 MTH173 - Numbers 11
The Real NumbersThe Real Numbers
Symbols of Equality and Inequity
• a = b equals
• a ≠ b not equal
• a > b greater than
• a < b less than
• a ≈ b approximately equal
Absolute Value
• Numbers magnitude regardless of its sign
• |n|
Sept 2008 MTH173 - Numbers 12
The Real NumbersThe Real Numbers
Signed Numbers
• Positive number is greater than Zero
• Negative number is less than Zero
• Place a negative sign (-) in front of a negative number
Sept 2008 MTH173 - Numbers 13
Addition & SubtractionAddition & Subtraction
Horizontal & Vertical Addition
Adding Signed Numbers
Subtracting Signed Numbers
Sept 2008 MTH173 - Numbers 14
Laws for AdditionLaws for Addition
Commutative Law for Addition
Associative Law for Addition
Sept 2008 MTH173 - Numbers 15
MultiplicationMultiplication
Factors & Product
Commutative Law for Multiplication
Associate Law for Multiplication
Distributive Law for Multiplication
Sept 2008 MTH173 - Numbers 16
Multiplying Signed NumbersMultiplying Signed Numbers
Rule of Signs for Multiplication
Multiplying a string of numbers
Multiplying negative numbers
Sept 2008 MTH173 - Numbers 17
DivisionDivision
Definitions
Dividing Signed Numbers
Rule of Signs for Division
Sept 2008 MTH173 - Numbers 18
Powers & RootsPowers & Roots
Base & Exponent
Negative Base
Fractional Exponents
Sept 2008 MTH173 - Numbers 20