SOL 8.2 Notes
The Real Number System
Number set
Definition
Examples
NonExamples
Natural numbers
Whole numbers
Integers
Rational numbers
Irrational numbers
The set of rational numbers and the set of irrational numbers together make up the set of
real numbers. The Venn diagram below shows the relationship among the real numbers.
Real Numbers
Rational Numbers
Irrational Numbers
1) The sum of two rational numbers is ___________________________.
Examples:
2) The product of two rational numbers is _________________________.
Examples:
3) The sum of a rational number and an irrational number is ____________.
Examples:
4) The product of a nonzero rational number and an irrational number is
____________________________.
Examples:
Identify all of the subsets of real number system to which each number belongs:
1) 15
2) -28
3) 0.3
7
4) -81
5)
67
7) 0.10110111….
8) 0.235235
6)
2
9) - 196
Name _____________________________________ Block _____________________
SOL 8.2 Homework: The Real Number System
Name all of the sets of numbers to which each real number belongs. Use natural numbers,
whole numbers, integers, rational numbers, and irrational numbers.
1) 0.212121…
2) -41
3) 1
4
4) -42
5
5) 0.090090009…
6)
7) 45
8) 36
9
2.31
Determine whether each statement is sometimes, always, or never true.
13) A decimal number is an irrational number. _____________________
14) An integer is a whole number. _______________________________
15) A natural number is an integer. _______________________________
16) An integer is a natural number. _______________________________
Choose the letter which best answers the question.
17) Which of the following is a whole number?
A) 3.6
B) 16
C) 8
D) Both B and C
18) Which category does 81 not belong to?
A) Irrational #’s
B) Integers C) Natural #’s
D) Whole numbers
_________________________________________________________________________________
Give an example and a non-example for each of the following subsets:
Example Non-example
Example Non-example
Integer
Rational Number
Whole Number
Irrational Number
Name ____________________________________________
Real Number System Practice
I. Classify Numbers - Complete the chart. Place an “X” in the box for each correct classification.
Example
0
4
-7
25
41
3
4
0.121212…
0.010110111…
Natural
Whole
Integer
Rational
Irrational
Real
II. Describe each subset of the real numbers. Give an example and a non-example.
Subset
Description
Example
NonExample
Whole Numbers
Irrational Numbers
Natural Numbers
Integers
Rational Numbers
IV. True or False. Determine if the following statements are true or false. Then, explain your answer.
__________ 1) The number 0 is a counting number. Explain your answer. ________________________________________
__________ 2) The number
2
is rational. Explain your answer. _________________________________________________
9
__________ 3) The number 0.33333… is irrational. Explain your answer. _________________________________________
__________ 4) The number -2.5 is an integer. Explain your answer. ______________________________________________
V. Determine whether each statement is sometimes, always, or never true.
1) A rational number is an irrational number _________________
2) A fraction is an integer. ____________________
3) A negative number is an integer. ________________________
4) A counting number is a whole number. ________
0
1
2
0.7
0.121212…
–3
2
–0.9
π
5
17
14.8
0.010110111…
–4.267
–