Numbers, Data, and Problem Solving

1. Numbers, Data, and Problem Solving Lesson 1.1

2. Sets of Numbers • Natural Numbers • The counting numbers{ 1, 2, 3, 4, … } • The whole numbers • 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, … }

3. Sets of Numbers • Rational numbers • Any number expressed as the quotient of two integers – and the denominator is NOT zero • Irrational numbers • Numbers that cannot be represented by quotient of two integers Note: these can be written as terminating or repeating decimals

4. Try it Out … • Classify the following numbers as • Natural numbers • Whole numbers • Rationals • Irrationals

5. Order of Operations • Work from innermost parentheses, out • Evaluate all exponents • Multiplications, divisions from left to right • Additions and subtractions from left to right

6. Calculating Percent Change • If a quantity changes from c1 to c2 the percent of change is given by: • Gasoline changed from $1.19 to $1.43 in one week's time … what was the percent of increase?

7. Calculating Percent Change • What if you are told the percentage of increase and the original value … now find the new value! • Enter the values you know • Solve for the value you don't know • What if gas was at $1.47 and went down by 12% a week later. What is the new price? What kinds of numbers did we use in these calculations?

8. 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?

9. Assignment • Lesson 1.1 • Page 10 • Exercises1 – 27 odd, 77 - 87odd