Download 4.2 Irrational Numbers

FCP 10
4.2 Irrational Numbers
Use your calculator to express each of these as decimals where necessary. How are the
numbers that are rational numbers different from the numbers that are not rational?
Rational Numbers
2
121
3
6.25
0.123123123...
4
625
81
3
Numbers that are not rational
0.125
1
36
1
27
49
81
0
π
2
135
4
20
5
5
3
100
3.6
0.101001000100001....
43
999
A rational number is any number that expressed as a _________________. As
decimals, they either ________________ or _________________.
An irrational number is any number that cannot be expressed as a ________________.
As decimals, they neither ___________________ nor ____________________.
All the numbers on the number line are called the real numbers. The real numbers are
made up of the rational numbers and the irrational numbers.
Symbol for real numbers: ___________
Real Numbers
Rational numbers – any number that
when written as a decimal terminates or
repeats
Irrational numbers –
any decimal number that
neither terminates nor
repeats
Integers
… , -3, -2, -1, 0, 1, 2, 3, …
Whole
numbers
0, 1, 2, 3, 4,
Natural
numbers
1, 2, 3, 4,
Example 1:
Put a check mark in the box that describes the number given. (Some numbers may require more
than one check.)
Types of Numbers
-5
0
0.12112111…
2
3
-0.75
13
2
1
Real
Irrational
Rational
Integer
Whole
Natural
Example 2: Using the following list of numbers, identify
2
3
0.73
5
2
49
0
0.476
π
3
9
6
5
12345
a) the integers
b) the rational numbers
c) the irrational numbers
d) the real numbers
Example 3:
What type of number is
A)
B)
C)
D)
36 ?
I.
Natural
II.
Integer
III.
Rational
IV.
Irrational
I. & II.
I. & III.
I. & II. & IV.
II. & III.
Example 3:
a) Is every natural number a whole number? ______________
b) Is every integer a whole number? _______________
c) Is every whole number a natural number? _______________
d) Is every integer a whole number? ______________
e) Is every integer a real number? _______________
3
1
4
3
1
4
3
27
8