Warm Up
Each square root is between two integers. Name the two integers.
119
10 and 11
15
3 and 4
Use a calculator to find each value. Round to the nearest tenth.
2
1.4
123
11.1
The Real Number System
Section 4.7
Objective:
In this lesson you’ll:
• Differentiate between rational and irrational numbers.
(NS 1.4)
Did you know????
Biologists classify animals based on shared
characteristics. The horned lizard is an animal,
a reptile, a lizard, and a gecko.
Animal
Reptile
Lizard
zzzzzz
Gecko
Words to know….
• Naturals – natural counting numbers { 1, 2, 3, ….}
• Wholes – natural counting numbers and zero
{ 0,1, 2, 3....}
• Integers – Positive or negative natural numbers
or zero
{ -2, -1, 0, 1, 2,…}
Words to know….
Rational Number – any number which can be written as a
fraction.
Irrational Number –
Any decimal number which can’t be written as a fraction.
A non-terminating and non-repeating decimal.
Example –
  3 . 1415926 ....
» Real – rational numbers and irrational numbers.
Real Numbers
4.5 27
Irrational Numbers
Rational Numbers
0 .3
4
Integers
-1

10
17
11
-3
-7
2
Whole Numbers
0
Natural Numbers
1
3
2
e

 11
Sets of Numbers – (using a tree map)
3
  3 . 1415926 ....
Let’s practice
Directions: Identify each number below as natural, whole, integer,
rational, irrational, or real. More than one answer can apply.
7
8
0
Rational,
real
Whole,
integer,
rational, real
9
integer,
rational, real
4
rational, real

5
Let’s practice
Directions: Identify each number below as natural, whole, integer, rational,
irrational, or real. More than one answer can apply.
6
8
irrational, real
Natural,
Whole,
integer,
rational, real
16

25
Natural,
Whole,
integer,
rational, real
integer,
rational, real
Use <, >, or = to compare
2
3
5
8
5
9
3
10
=
<
>
<
.6
. 65
.5
12
12

7
6
1
5
3
20
= 1
>
21
<
6
=
7
5
. 25
Lesson Quiz
Write all classifications that apply to each number.
2
real, irrational
25
0
not a real number

16
2
real, integer,
rational
4
rational
9