Rational/ Irrational #’s
Absent Copy
Thurs/Fri 3/7,8
Whole #’s
Integers
Rational #’s
Counting #’s and zero
0,1,2,3,4,5………..
neg. and pos. numbers and 0
-5,-4,-3,-2,-1,0,1,2,3,4,5……..
Terminating/repeating decimals
0.5, 1.45, 3.9
.3333, 3.151515,
Fractions (that terminate or repeat) /perfect squares
1
√25, √81, 2 , 3
4
Rational #’s include:
All integers, all fractions and decimals that end or
repeat
Rational #’s
0 .3
3
1
5
Integers
100
 30.3
0.3
Whole #s
6
3
 0 .4
2
5
11
2
2
Irrational #’s include:
Decimals that do not end or repeat and
square roots that are not perfect squares.
1. .1823456……..,
√3 = 1.732050807
Real Numbers
Rational and irrational #’s
Non – Real #’s
 16
and 7
0
Example 1
• Write all classifications
that apply to this #.
-8
10
• This is a fraction.
• This # is also a?
• It is also a Terminating decimal.
.80
10 8.00
-80
00
Fraction, terminating
decimal, rational #
• This # is a?
• Is this #
Rational or Irrational
Why?
It is rational because
terminating decimals are
rational.
Solution
Example 2
• Write all classifications • This # is a?
• This is a sq. rt.
that apply to this #.
• What can we do to
make this sq. rt. More
32
simple to solve?
2
• We can divide 32 by 2 and get
16.
• This # is also an?
16
• This is also a whole # and an
integer.
4 • 4
Factor
Factor
4
Whole #, Integer, Rational
#
Solution
• Is this #
Rational or Irrational
Why? It is rational because
integers and whole #’s are part
of the rational family.
Example 3
• Is this # rational,
irrational, or not real.
• Is this a perfect
square?
• Yes it is.
-
16
4 • 4
factor
• What else can we call
this #?
• We can call it an integer.
factor
-4
• Is a perfect square
irrational or rational
Rational #
Solution
Example 4
• Is this # rational,
irrational, or not real.
5
29
• It is called a fraction.
• Is it a repeating
decimal or does it
terminate or is it a nonrepeating decimal?
.1724
29 5.0000
-29
210
-203
70
-58
120
-116
irrational #
• What is this # called?
• It is a non-repeating decimal.
• Is this #
irrational or rational
Solution