Numbers, Data, and Problem Solving

Lesson 1.1

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, … }

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

where p and q Integers, and q 0p

q

2 sin 37e

Note: these can be written as terminating or

repeating decimals

Note: these can be written as terminating or

repeating decimals

Try it Out …

Classify the following numbers as Natural numbers Whole numbers Rationals Irrationals

17

3

17

5280

3.14

Order of Operations

Work from innermost parentheses, out

1. Evaluate all exponents

2. Multiplications, divisions from left to right

3. Additions and subtractions from left to right

210 64 2(4 5)

5 3

3

13 9 16

5 7

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?

2 1

1

100c c

c

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?

2 1

1

100c c

c

What kinds of numbers did we use in these

calculations?

What kinds of numbers did we use in these

calculations?

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