Download Number Systems

Counting numbers
42
Integers
-17
0
3½
1.1
What are integers
and how are they
related to other
numbers?
The first number system you ever used as a
natural
child was the _______________
numbers or
___________________
numbers.
counting
They are made up of the numbers you used
count
to _________________
how many of
something. ( 1, 2, 3, 4, 5, 6, 7, 8, ……… )
Natural
(Counting Numbers)
1,2,3,4,5,…
As you got older you realized that you
needed a symbol to represent nothing. The
symbol used to represent nothing is
___________.
0 “zero”
As soon as you used this new symbol, you
were using a new set of numbers called the
whole
____________
numbers.
Whole
___________numbers
are all of the
zero
counting
_______________
numbers and ________.
(0, 1, 2, 3, 4, 5, 6, 7, ………)
Whole
0
Natural
(Counting Numbers)
1,2,3,4,5,…
Then, as you got even older and more
sophisticated, you began to see a need to represent
zero
numbers smaller than _______________.
integers
These numbers are called ________________.
whole
They are made up of all of the _______________
opposites
numbers and their __________________.
Opposites
__________________
numbers are numbers that
same
zero
are the __________
distance from ____________
different
on a number line in ________________directions.
( …-4,-3, -2, -1, 0, 1, 2, 3, 4, … )
Integers
Whole
-18
All whole
numbers and
their
opposites.
Includes
-3
Negatives.
0
Natural
(Counting Numbers)
1,2,3,4,5,…
Just when you thought you could not get more
sophisticated, you realized that there needed to
part
be ways to represent a _________
of
something. These numbers are called
rational
________________
numbers.
They are numbers that can be written as a
fraction
ratio
__________
or a __________________
using
integers
______________.
Examples would be…
Can you think of a number that cannot be
ratio/fraction
written as a _____________?
Rational Numbers: Numbers
that can be written as a fraction or the ratio of
two integers.
-3/4
.6
-0.3
Integers
Whole
-18
All whole
numbers and
their
opposites.
0
Natural
7/10
(Counting Numbers)
1,2,3,4,5,…
Includes
-3
Negatives.
*Includes repeating and terminating decimals
Now, just when you think there can’t be
any other numbers, SURPRISE, there are.
irrational
They are called ____________________
numbers and they are numbers that
______________
CAN NOT be written as a
ratio/fraction using only
_______________
integers
________________.
The operations that you are familiar with
are +, -, x, ÷, and exponents. Another
square
operation is finding the ________
_________of
a number. The symbol for this
root
is ___.
means what number multiplied by
________________
itself
equals 4?
Counting numbers
1
2
3
16 4
25 5
36 6
49 7
64 8
81 9
these are called perfect squares
?
This is not a perfect square
because there is no integer that
can be multiplied by itself to
equal the answer.
Can you think of some other
irrational numbers?
Irrational
Numbers
Numbers that can
NOT be written
as a fraction or
the ratio of two
integers.
Non-repeating,
non-terminating
decimals.
2
π
Rational Numbers: Numbers
that can be written as a fraction or the ratio of
two integers.
-3/4
.6
-0.3
Integers
Whole
-18
All whole
numbers and
their
opposites.
0
Natural
7/10
(Counting Numbers)
1,2,3,4,5,…
Includes
-3
Negatives.
*Includes repeating and terminating decimals
All of the numbers we have talked about
are in one BIG group called the
real
_____________
numbers.
Real Numbers:
Irrational
Numbers
Numbers that can
NOT be written
as a fraction or
the ratio of two
integers.
Non-repeating,
non-terminating
decimals.
2
π
Both Rational and Irrational Numbers
Rational Numbers: Numbers
that can be written as a fraction or the ratio of
two integers.
-3/4
.6
-0.3
Integers
Whole
-18
All whole
numbers and
their
opposites.
0
Natural
7/10
(Counting Numbers)
1,2,3,4,5,…
Includes
-3
Negatives.
*Includes repeating and terminating decimals
Please get out your
homework and your
graphic organizer.
Quietly get your
clicker.
Answer the following
75%
13%
13%
10
00
2
0%
50
A.50
B. 2
C. 100
D.10
Participant Leaders
Points
Participant
100
Chambers
100
McKim
100
Perry
100
Raifsnider
100
Renehan
100
Van de Castle
0
McClintock
0
Wine
Points
Participant
Answer the following
88%
13%
7
0%
25
.5
0%
5
A.5
B. 2.5
C. 25
D.7
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
7
75%
13%
13%
0%
0%
0%
Participant Leaders
Points
300
Participant
Chambers
300
300
300
McKim
Raifsnider
Van de Castle
200
200
200
100
McClintock
Perry
Renehan
Wine
Points
Participant
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
50%
38%
13%
0%
0%
0%
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
88%
13%
0%
0%
0%
0%
Participant Leaders
Points
Participant
500
Van de Castle
400
Chambers
400
McKim
400
Raifsnider
400
Renehan
300
McClintock
300
Perry
300
Wine
Points
Participant
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
-21
50%
25%
13%
13%
0%
0%
Fastest Responders
Seconds
7.828
Participant
McClintock
8.969
14.75
15.031
Van de Castle
Raifsnider
Renehan
Seconds Participant
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
75%
25%
0%
0%
0%
0%
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
63%
38%
0%
0%
0%
0%
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
75%
25%
0%
0%
0%
0%
Participant Leaders
Points
Participant
800
Van de Castle
600
Raifsnider
500
McClintock
500
Renehan
400
Chambers
400
McKim
400
Perry
300
Wine
Points
Participant
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
88%
13%
0%
0%
0%
0%
If a number is a whole number it
is ALWAYS an integer.
A.True
B.False
50%
50%
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
50%
25%
13%
0%
0%
13%
What is the BEST name of the
following number?
A. Counting number
B. Irrational number
C. Real number
D. Integer
E. Rational number
F. Whole number
3.65
88%
13%
0%
0%
0%
0%
If a number is a counting
number, it is always an integer.
A.True
B.False
50%
50%
Participant Leaders
Points
1200
Participant
Van de Castle
900
700
700
Renehan
Perry
Raifsnider
600
Chambers
Points
Participant
If a number is an irrational number it
is never a whole number.
A.True
B.False
63%
38%
If a number is an integer it is never
a rational number.
A.True
B.False
88%
13%
Participant Leaders
Points
Participant
1200
Van de Castle
1000
Renehan
800
Perry
800
Raifsnider
700
Chambers
700
McClintock
700
Wine
600
McKim
Points
Participant