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

Announcements Calter Textbook with WileyPLUS Register for class in WileyPLUS Online Assignment – Due next week Advanced Standing in Course Quiz – Next Thursday, Sept 11 th Signed Numbers, Decimals, Sig Digs, Exponents, Radicals, Scientific Notation Sept 2008 MTH173 - Numbers 2

Whole & 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 Sept 2008 MTH173 - Numbers 3

Lecture Outline What is Mathematics The Real Numbers Definitions Addition & Subtraction Multiplication Division Sept 2008 MTH173 - Numbers 4

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 American mathematician and physicist. Sept 2008 MTH173 - Numbers 5

The 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 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. 1872–1970 British philosopher, mathematician. Sept 2008 MTH173 - Numbers 6

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 English philosopher, scientist. Sept 2008 MTH173 - Numbers 7

The Real Numbers Number Line Sept 2008 MTH173 - Numbers 8

The 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 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 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 Numbers Symbols of Equality and Inequity a = bequals a ≠ bnot equal a > bgreater than a < bless than a ≈ bapproximately equal Absolute Value Numbers magnitude regardless of its sign |n| Sept 2008 MTH173 - Numbers 12

The 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 & Subtraction Horizontal & Vertical Addition Adding Signed Numbers Subtracting Signed Numbers Sept 2008 MTH173 - Numbers 14

Laws for Addition Commutative Law for Addition Associative Law for Addition Sept 2008 MTH173 - Numbers 15

Multiplication Factors & Product Commutative Law for Multiplication Associate Law for Multiplication Distributive Law for Multiplication Sept 2008 MTH173 - Numbers 16

Multiplying Signed Numbers Rule of Signs for Multiplication Multiplying a string of numbers Multiplying negative numbers Sept 2008 MTH173 - Numbers 17

Division Definitions Dividing Signed Numbers Rule of Signs for Division Sept 2008 MTH173 - Numbers 18

Division Zero Reciprocals Sept 2008 MTH173 - Numbers 19

Powers & Roots Base & Exponent Negative Base Fractional Exponents Sept 2008 MTH173 - Numbers 20

Combined Operations Order of Operations BEDMAS Brackets Exponents Division & Multiplication Addition & Subtraction Sept 2008 MTH173 - Numbers 21