Real Number System

1. Warm Up
Each square root is between two integers. Name the two integers.
Use a calculator to find each value. Round to the nearest tenth.
10 and 11
3 and 4
1.4
11.1
119
15
2
123

2. Section 4.7
The Real Number System

3. Objective:
In this lesson you’ll:
• Differentiate between rational and irrational numbers.
(NS 1.4)

4. Did you know????
Animal
Reptile
Biologists classify animals based on shared
characteristics. The horned lizard is an animal,
a reptile, a lizard, and a gecko.
Lizard
zzzzzz
Gecko

5. 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,…}

6. 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 –
» Real – rational numbers and irrational numbers.
....
1415926
.
3



7. Real Numbers
Rational Numbers Irrational Numbers
11
2
17


e
4
27 3
.
0
11
10

4.5
Integers
Whole Numbers
Natural Numbers
-7
-1 -3
0
1
2
3

8. Sets of Numbers – (using a tree map)
3 ....
1415926
.
3



9. Let’s practice
Directions: Identify each number below as natural, whole, integer,
rational, irrational, or real. More than one answer can apply.
5
4

8
7
0
9

Rational, real
Whole, integer,
rational, real
integer, rational, real
rational, real

10. Let’s practice
Directions: Identify each number below as natural, whole, integer, rational,
irrational, or real. More than one answer can apply.
25

6
8
16
irrational, real
Natural, Whole,
integer, rational, real
Natural, Whole,
integer, rational, real
integer, rational, real

11. Use <, >, or = to compare
3
2
6
.
8
5
< 65
.
9
5
5
.
10
3
3
1
12
12
1
 7
21
6
7
5
6
25
.
20
5
=
>
<
=
>
<
=

12. Lesson Quiz
2 2
16

Write all classifications that apply to each number.
real, irrational
real, integer,
rational
0
25
9
4 
not a real number rational