Download The Real Numbers

THE REAL NUMBERS
Adapted by Mrs. Garay
Biologists classify animals based on shared
characteristics. The cardinal is an animal, a
vertebrate, a bird, and a passerine.
Animals
Vertebrates
Birds
Passerines
You already know that some
numbers can be classified as
whole numbers, integers, or
rational numbers.
The set of real numbers consists of the set of
rational numbers and the set of irrational numbers.
WHAT IS A RATIONAL NUMBER?
A
rational number is any
number that you can write in
the form a/b, where a and b
are integers and b ≠ 0.
A rational number in decimal
form is either terminating,
such as 6.27, or repeating,
such as 8.222 . . .
Examples of Rational Numbers
3
4
= 3.8
5
2
= 0.6
3
1.44 = 1.2
WHAT IS AN IRRATIONAL NUMBER?
An
irrational number cannot
be expressed in the form a/b,
where a and b are integers.
An irrational number in
decimal form is both
nonrepeating and
nonterminating.
Example of Irrational Number
2 ≈1.4142135623730950488016…
Classifying Real Numbers
Write all names that apply to each number.
A.
5 is a whole number that is
not a perfect square.
irrational, real
5
B. –12.75 –12.75 is a terminating decimal.
rational, real
C.
16
2
16
4
=
=2
2
2
whole, integer, rational, real
Your Turn! Copy and answer in your binder.
Write all names that apply to each number.
A.
9
9
=3
whole, integer, rational, real
B.
C.
–35.9
–35.9 is a terminating decimal.
rational, real
81
81
9
=
=3
3
3
3
whole, integer, rational, real
AM I RATIONAL, IRRATIONAL, OR NOT A
REAL NUMBER?
Determining the Classification of All Numbers
State if each number is rational, irrational,
or not a real number.
A.
21
irrational
B.
0
3
rational
0
=0
3
More Determining the Classification of All Numbers
State if each number is rational, irrational,
or not a real number.
C.
–4
not a real number
D.
4
9
rational
2
3
2
4
=
3
9
Your Turn! Copy and answer in binder.
State if each number is rational, irrational,
or not a real number.
A.
23
23 is a whole number that
is not a perfect square.
irrational
B.
9
0
undefined, so not a real number
Your Turn Again! Copy and answer in binder.
State if each number is rational, irrational,
or not a real number.
C.
–7
not a real number
D.
64
81
rational
8
9
8
64
=
9
81
Your Turn To Shine!
Answer practice problems from class page!
Exit Ticket
Write all names that apply to each number.
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 •
rational
9