### Rational and Irrational Numbers

```Rational and
Irrational
Numbers
Monday, September 27th, 2010
The set of real numbers consists of the set
of rational numbers and the set of irrational
numbers.
Real Numbers
Rational numbers
Integers
Whole
numbers
Irrational numbers
RATIONAL NUMBERS
Definition: written as fractions, and as
decimals that either terminate or repeat.
 Rational numbers are nice and neat!
2
1. Fractions
3
2. Terminating Decimals
3. Repeating Decimals
4. Whole Numbers
5. Integers
3.8
0.6
0
-4
6. Perfect Squares
144 = 12
21.89
Irrational Numbers
Definition: can only be written as decimals that do
not terminate or repeat.
 Irrational numbers are crazy numbers!
1. Non-terminating and Non- repeating Decimals (go on and
on and on but don’t repeat)
65.65971059893…
0.363765489965…
2. Non- Perfect Squares
73 ≈8.54400374531753116…
2 ≈1.414213562373095048…
 HINT: If a whole number is not a perfect square, then
its square root is an irrational number.
Classify as rational or irrational and
WHY??:
1.
5
2. –12.75
3.
16
2
Classify as rational or
irrational and WHY??:
4.
9 =3
9
rational
5. –35.9 –35.9 is a terminating decimal.
rational
6.
81
3
rational
81 = 9 = 3
3
3
Non-Real Numbers
) can’t have a negative number
– If there is a negative inside the radical, then it is a
NON-REAL NUMBER
2. 0 can’t be in the denominator of a fraction
Example:
-9
-18
-49
These are ok (the negative is outside of the
- 100
81
- 49
):
Mini Quiz
Write all names that apply to each number (real, non-real
number, irrational, rational)
1.
2
2. –
real, irrational
16
2
real, integer, rational
State if each number is rational, irrational, or not a real
number.
3.
25
0
not a real number
4.
4 •
9
rational
3
3
Find
a
real
number
between
–2
and
–2
.
5.
4
8
5