RATIONAL AND IRRATIONAL NUMBERS
RATIONAL NUMBERS
Any number that can be written in the form
is called a rational number.
a
b
(with a and b being integers and b not being zero)
Examples
Show that each of the following numbers is a rational number: !7,!0.31,!1 25 ,!! 16,!!0.6,!0.83
a.
c.
!7 = !71
1 25 = 57
e.
!0.6 = ! 23 =
!2
3
b.
0.31 =
d.
! 16 = !4 =
e.
0.83 =
31
100
!4
1
5
6
Problems
Show that each of the following numbers is a rational number.
1.
5.
10
–14
2.
0.2
6.
!2 83
9.
0.3
10.
25
4
3.
7.
11.
5 13
0
3.125
4.
–0.15
8.
81
12.
0.1
IRRATIONAL NUMBERS
A decimal number that never repeats and never ends is called an irrational number. The most
commonly used irrational numbers are ! and the square root of any non-perfect square.
The numbers on a number line are called the real numbers. All of the rational numbers joined
with all of the irrational numbers make up the real numbers.
Examples
The following are all irrational numbers
a.
c.
e.
! = 3.141592...
1 + 24 = 5.898979...
7.30030003...
b.
d.
e.
5 = 2.236067...
! 300 = !17.320508...
!0.23571113...
Problems
Determine if each real number is rational or irrational.
13.
3 13
17.
! 100
21.
( 5)
2
14.
18.
22.
15.
10
7.121121112... 19.
23.
2+!
0.25
16.
!0.002
20
0.123123…
20.
!5 27
24.
11 19
Answers
1.
5.
9.
13.
17.
21.
10
1
!14
1
1
3
R
R
R
2.
6.
10.
14.
18.
22.
=
2
10
!19
8
5
2
I
I
I
1
5
3.
7.
11.
15.
19.
23.
16
3
0
1
3125
1000
R
I
R
=
25
8
4.
8.
!15
100
9
1
=
!3
20
12.
16.
20.
24.
1
9
=
1
3
R
R
R