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Transcript
Numbers, Data, and Problem Solving Lesson 1.1 Sets of Numbers Natural Numbers The whole numbers The counting numbers { 1, 2, 3, 4, … } The counting numbers with zero included { 0, 1, 2, 3, 4, … } The integers The whole numbers and their additive opposites, their negatives { . . . , -4, -3, -2, -1, 0, 1, 2, 3, 4, … } Sets of Numbers Rational numbers Any number expressed as the quotient of two integers – and the denominator is NOT zero Note: these can be written as terminating or repeating decimals p q where p and q Integers, and q 0 Irrational numbers Numbers that cannot be represented by quotient of two integers 2 e sin 37 Try it Out … Classify the following numbers as Natural numbers Whole numbers Rationals Irrationals 17 3 17 5280 3.14 Order of Operations 1. 2. 3. Work from innermost parentheses, out Evaluate all exponents Multiplications, divisions from left to right Additions and subtractions from left to right 10 6 4 2(4 5) 2 53 13 9 16 57 3 Calculating Percent Change If a quantity changes from c1 to c2 the percent of change is given by: c2 c1 100 c1 Gasoline changed from $1.19 to $1.43 in one week's time … what was the percent of increase? Calculating Percent Change What if you are told the percentage of increase and the original value … now find the new value! c2 c1 100 c1 Enter the values you know Solve for the value you don't know What kinds of numbers did we use in these calculations? What if gas was at $1.47 and went down by 12% a week later. What is the new price? Problem Solving Important strategies … Draw a sketch Write formulas involved Determine values in the formulas that you know Solve for the values you are searching for The Milky Way has a diameter of 6 x 1017 miles. If the speed of light is 186,000 miles/sec, how many years does it take for light to travel across the galaxy? Assignment Lesson 1.1 Page 10 Exercises 1 – 27 odd, 77 - 87odd