Chapter 1: The Real Number System
1.4 Real Numbers and the Number Line
Learning Objectives
1. Use Real Numbers to Express Change
2. Find a Number Satisfying Conditions
3. Judge Truth of Real Number Statements
4. List Numbers in Specified subset of Real Numbers
5. Graph Numbers on Number Line
6. Find Opposite (Additive Inverse) of Number
7. Evaluate Absolute value Expression
8. Select the Smaller of Two Numbers
9. Determine Truth of Inequality
10. Solve Applications
11. Find Value Satisfying Conditions
Objective 1: Use Real Numbers to Express Change
Use an integer to express the number.
1) A football team gained 22 yards on one play.
2) On a cloudy day, the water temperature in the swimming pool drops 9 degrees.
Objective 2: Find a Number satisfying Conditions
Give a number that satifies the given condition.
3) An integer greater than -8.3 and less than -7.3
4) A whole number greater than 3.5
5) A whole number less than 3.5
Objective 3: Judge the Truth of Real Number Statements
Tell whether the statement is true or false.
6) Every rational number is an integer.
A) True
B) False
7) Every irrational number is an integer.
A) True
B) False
8) Every whole number is a real number.
A) True
B) False
9) Some rational numbers are irrational.
A) True
B) False
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10) Every integer is an irrational number.
A) True
B) False
11) Some real numbers are integers.
A) True
B) False
Objective 4: List Numbers in Specified Subset of Real Numbers
List the numbers from the set that are of the type indicated.
12) {0, 5, -24,
7
1
, - 1 , 9.2, 4}
8
7
Integers
Whole Numbers
Irrational Numbers
Integers
Natural Numbers (Counting Numbers)
Objective 4: Graph the numbers on a number line.
3
1
13) - 4 , -2, 0, 2
4
4
Objective 5: Find the opposite (additive inverse) of the number.
14) -27
Objective 7: Evalute Absolute Value Expression
Simplify.
15) -4
16) - -12
17) 8 - 4
Objective 8: Select the smaller of the two given numbers.
18) -19, -17
19) -
9 ,- 6
16 7
20) -17 , -26
2
21) 8 - 1 , 7 - 2
Objective 9: Determine Truth of Inequality
Decide if the statement is true or false.
22) -(-28) < -25
23) -(-28) > -10
Objective 10: Solve Applications: Interpret Table
Refer to the table to answer the question.
Production
Change
Change
Category
'98-'99
'99-'00
Public Relations 3.5
4.2
Training
1.7
2.8
Sales
-4.3
1.6
Catalog
2.3
-1.1
24) Which category and year shows the largest increase?
25) Which category and year shows the smallest absolute change?
Objective 11: Find Value Satisfying Conditions
Solve the problem.
26) Give one number between -8 and 8 that is a negative real number but not an integer.
A) Not possible
B) -6.345
C) 6.345
D) 7
27) Give one number between -6 and 6 that is a rational number but not an irrational number.
10
A) Not possible
B) 13
C) - 10
D)
13
Provide an appropriate response.
28) Is the integer 0 positive or negative? Explain.
29) Explain what happens when an integer is multiplied by 1, -1, and 0.
30) Fill in the blanks with the correct numbers.
The opposite of -9 is _____.
The absolute value of -9 is _____.
The opposite of the absolute value of -9 is _____.
The absolute value of the opposite of -9 is _____.
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