Name _________________
Math 7A: Real Numbers
Date _______________
Unit 1 Lesson 1
Natural Numbers: All counting numbers, the positive integers.
Whole Numbers: All counting or natural numbers and zero.
Integers: All whole numbers and their opposites.
Rational Numbers: Any number that can be represented by a fraction whose
numerator is an integer and whose denominator is a non zero integer. (All
integers, fractions, and terminating or repeating decimals)
Irrational Numbers: An infinite, non-repeating decimal.
Real Numbers: Any positive or negative number or 0. (All Rational and Irrational
numbers)
Set: A collection of distinct elements that can be listed within braces { }.
DIAGRAM
Rational Numbers
Integers
Whole #’s
Counting #’s
Irrational Numbers
1) Decide if each statement is true or false.
a) All integers are rational numbers.
b) All rational numbers are integers.
c) All negative numbers are integers.
d) Some real numbers are integers.
e) The set of counting numbers is a finite set.
2) Which value(s) of x, when substituted into the expression x represent(s) an
irrational number?
(1) 81
(2) 49
(3) 121
(4) 12
Justify your answer(s).
3) Which of the following is not an irrational number?
(1) 
(2) 5 
(3) 25
(4)
8
Justify your answer.
4) Which number below is irrational?
1
9 ,
(Math A, 6/99)
20 ,
121
Why is the number you chose an irrational number?
5) Which of the following numbers is rational? Explain why.
169 , 27 , 
Name _________________
Math 7A: Real Numbers
1.
Date _______________
Unit 1 Lesson 1 HW
Match the words in the left hand column with the correct set of numbers in
the right hand column.
Odd Integers
Even Integers
*
G
B
N
*
N
H
Whole Numbers
* {0, 1, 2, 3 …}
E
N
S
*
* {1, 3, 5, 7 …}
P
M
Y
Counting Numbers *
Whole #’s less
than 10
O
* {2, 4, 6, 8 …}
N
*
I
Irrational Numbers*
* {0, 1, 2, 3 … 9}
* {1, 2, 3, … 9}
R
O
* { 2, 3, 5}
W
Counting #’s less
than 10
*
Letters leftover
Solution to the puzzle
Hint: This guy can really fly!
T
* {1, 2, 3, 4 …}
2.
Shade in the boxes that correspond to each description below:
Row 1: Shade in all the irrational numbers
Row 2: Shade in all even integers
Row 3: Shade in all rational numbers
Row 4: Shade in all integers
Row 5: Shade in all multiples of 3
10
14
2.5
1
16
5
18
2.2
4
7
6
.35
25
11
2
1.2
15
9
27
14
5
22
¾

4
.37
0
12
19
14
½
33
3
6
7
9
43
21
15
16
8
8
5
36
27

49
19
4
17
.33
0.25
45
18
60
In Your Own Words
3.
Please describe for me in your own words how someone can tell the
difference between a rational number and an irrational number.