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1.3 Real Numbers and the Number Line Set
Objectives:
Why is it important to be able to order different values?
Real Numbers
Rational Numbers
Decimals
Irrational Numbers
Integers
Whole Numbers
Fractions
Negative Integers
Natural Numbers
0
1
Example 1: Classify
the following
numbers
Square Root of a
Number:
If b² = a, then b is the square root of a.( b = √a )
Example:
Example 2: Find
a. ± √36
b. √49
c. -√4
d. √-9
c. -√48
d. -√350
c. - ³√-125
d. ³√8
Square Root
Example 3:
a. √32
b. √103
Approximate a
Square Root to
Nearest Integer
Cube Root of a
Number:
If b³ = a, then b is the cube root of a.( b = ³√a )
Example:
Example 4: Find
a. ± ³√64
b. ³√-27
Cube Root
Example 5:
A. -√16
B. ³√-27
C. - ³√-8
D. -√25
Which of the
following has the
smallest value?
NOW YOU
TRY:
Example 6:
Evaluating
expressions
Which of the following has the greatest value?
A. √16
B. ³√27
C. - ³√-125
a. 3 + √x when x = 9
b. 11 - ³√x when x = 64
c. 4•√x when x = 49
d. _√x_ when x = 4
x
D. √26
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EXTRA
PRACTICE:
SOLVE:
VOCABULARY:
Example 7: Write
two inequalities to
compare the
numbers.
Suppose you are delivering mail in an office building. You leave the mailroom and enter
the elevator next door. You go up four floors, down seven, and up nine to the executive
offices on the top floor. Then, you go down six, up two, and down eight to the lobby on
the first floor. What floor is the mailroom on?
 Real Number Line – A horizontal line that pictures real numbers as points.
 Origin – The point 0 on the number line.
 Negative/Positive numbers – The numbers to the left and right of the origin on
the number line.
 Graph – The points on the number line that corresponds to a number. Drawing
the point is called graphing or plotting.
a. -6.4 and -6.3
b. -2.8 and ¾
c. -1/2 and -1/3
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Example 8:
1
2 2 , -3,- , 2.3, 0.75, -1, 5.1
2
a) Order the following in increasing order:
b) Order the following in decreasing order:
7, -
c) Order the following from least to greatest:
d)
1
3
1
, 2.4, - , -5.8,
2
4
3
32 ,-3, -4, - 3 , - 7, - 16,-1, 3 27, 3.4
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Which of these correctly arranges the real numbers from least to greatest:
- √2 ; 9/17; - 1.3 ; 2.37 ; 3/11
A. -1.3 ; -√2 ; 2.37; 9/17; 3/11
B. -1.3 ; -√2 ; 9/17; 2.37; 3/11
C. -√2 ; -1.3 ; 3/11 ; 9/17 ; 2.37
D. -√2 ; -1.3 ; 9/17 ; 3/11 ; 2.37
Why is it important to be able to order different values?
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Opposites:
Two points on the number line that are the same distance but on opposite sides of the
origin.
Now you try:
Give me some examples of numbers that are opposites.
Absolute Value
Example 9: Evaluate
A number’s distance from the origin on the number line. |a|
a. -4 + 7
b.12 - -4
c.
-12
3
d. - -5
1 3
e. -3 +
8 4
5 -2
f. 6 5
Example 10:
a. -3 ___- (-3)
Compare.
b. - -5 ___- (-5)
c. - (-7)___- 5
d.12 - -4 ___- (-13)
e. - (-12)___ -2 × 6
Example 11:
a. | x | = 6
b. | x | = 10
Use mental math to
solve the equation:
c. I x I = 0
Speed
The rate of movement of an object.
d. I x I = -12
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Velocity
The speed and direction an object is moving in.
Example 12:
a) An elevator is climbed 26 floors in 12 seconds what was its speed and velocity in
seconds?
b) I dropped 52 floors in 18 seconds. What was its speed and velocity in seconds?
Now You Try:
1. A diver jumps from her platform and falls 10 feet per second. What is the velocity of
the diver? At what speed is she falling? Explain.
Decide whether the statement is true or false. If it is false give a counterexample.
2. The opposite of a number is always negative. _____
3. The absolute value of a number is never negative. _____
4. The expression “ –a” is never positive. _____
5. The expression “ –a” is sometimes greater than a. _____
SUMMARY:
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Assignment:
1.3 Practice K: # 1 - 48
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