MATH 173 GI Whole & Signed Numbers Sept 2008MTH173 - Numbers1

MATHMATH173 GI173 GI

Whole & Signed Numbers

Sept 2008 MTH173 - Numbers 1

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


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


Lecture OutlineLecture Outline

What is Mathematics The Real Numbers Definitions Addition & Subtraction Multiplication Division


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.


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.


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.



Number Line



Natural Numbers

• Counting numbers

Whole Numbers

• Natural numbers including Zero

Integers

• Whole numbers including zero and negative values



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



Exact Numbers

• Have no uncertainty

• 24 hours / day, 4 wheels / car, 25.4 mm

Approximate Numbers

• Measured quantities, Fractions, Irrational Numbers

Significant Digits



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|



Signed Numbers

• Positive number is greater than Zero

• Negative number is less than Zero

• Place a negative sign (-) in front of a negative number


Addition & SubtractionAddition & Subtraction

Horizontal & Vertical Addition

Adding Signed Numbers

Subtracting Signed Numbers


Laws for AdditionLaws for Addition

Commutative Law for Addition

Associative Law for Addition


MultiplicationMultiplication

Factors & Product

Commutative Law for Multiplication

Associate Law for Multiplication

Distributive Law for Multiplication


Multiplying Signed NumbersMultiplying Signed Numbers

Rule of Signs for Multiplication

Multiplying a string of numbers

Multiplying negative numbers


DivisionDivision

Definitions

Dividing Signed Numbers

Rule of Signs for Division


DivisionDivision

Zero

Reciprocals


Powers & RootsPowers & Roots

Base & Exponent

Negative Base

Fractional Exponents


Combined OperationsCombined Operations

Order of Operations

• BEDMAS

• Brackets

• Exponents

• Division & Multiplication

• Addition & Subtraction


Documents

MATH 173 GI Whole & Signed Numbers Sept 2008MTH173 - Numbers1