Chapter 2 – Properties of Chapter 2 – Properties of Real NumbersReal Numbers

2.1 – The Real Number Line2.1 – The Real Number Line

2.1 – The Real Number Line2.1 – The Real Number Line

Today we will be:Today we will be: Graphing and comparing real numbers using the Graphing and comparing real numbers using the

number linenumber line

Finding the opposite and absolute value of a Finding the opposite and absolute value of a number in a real-life applicationnumber in a real-life application

2.1 – The Real Number Line2.1 – The Real Number Line

The numbers in this book are real numbers. They can be pictured on the real number line.

The point labeled 0 is the origin. Points to the left of zero are negative numbers. Points to the right of zero are positive numbers.

2.1 – The Real Number Line2.1 – The Real Number Line

The scale marks represent integers. The real number line has points that represent

fractions and decimals as well. The point that corresponds to a number is the

graph. Drawing the point is called graphing the

number or plotting the point.

2.1 – The Real Number Line2.1 – The Real Number Line

Example 1Graph the numbers -1 ¾ and 2.7.

2.1 – The Real Number Line2.1 – The Real Number Line

Example 2Write two inequalities that compare – ½ and – 3/2.

2.1 – The Real Number Line2.1 – The Real Number Line

Example 3Write the following numbers in increasing order:

-1.5, 1/3, -3, 2.5, 0, -1

2.1 – The Real Number Line2.1 – The Real Number Line

Two points that are the same distance from the origin but on opposite sides of the origin are opposites.

2.1 – The Real Number Line2.1 – The Real Number Line

Example 4The numbers ½ and – ½ are opposites because each

is ½ unit from the origin.

2.1 – The Real Number Line2.1 – The Real Number Line

The expression -3 can be stated as “negative 3” or “the opposite of 3”.

Do not assume that –a is a negative number. If a = -2, then –a = -(-2) = 2

2.1 – The Real Number Line2.1 – The Real Number Line

The absolute value of a real number is the distance between the origin and the point representing the real number. The symbol | a | represents the absolute value of a

number a.

2.1 – The Real Number Line2.1 – The Real Number Line

THE ABSOLUTE VALUE OF A NUMBER If a is a positive number, then | a | = a

| 3 | = 3 If a is zero, then | a | = 0

| 0 | = 0 If a is a negative number, then | a | = -a

| -3 | = 3

2.1 – The Real Number Line2.1 – The Real Number Line

Example 5Evaluate the expression | ½ |

| -1.6 |

- | 3 |

2.1 – The Real Number Line2.1 – The Real Number Line

Example 6Use mental math to solve. | x | = 4.3

| x | = ¾

2.1 – The Real Number Line2.1 – The Real Number Line

Velocity shows both speed and direction (up is positive; down is negative).

Speed is the absolute value of velocity.

2.1 – The Real Number Line2.1 – The Real Number Line

Example 7An object is dropped towards Earth’s surface. It

falls at a rate of 32 ft/sec (if air resistance is ignored). What are the object’s speed and velocity?

2.1 – The Real Number Line2.1 – The Real Number Line

Example 8Decide whether the statement is true or false. If it is

false, give a counterexample. The expression | a | is ALWAYS positive. The absolute value of a number is ALWAYS

greater than the number. The symbol –a is SOMETIMES equal to | a |.

2.1 – The Real Number Line2.1 – The Real Number Line

HOMEWORK

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