chapter 2 – properties of real numbers 2.1 – the real number line
TRANSCRIPT
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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