Classifying Real Numbers.notebook
September 02, 2014
Classifying Real Numbers
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Classifying Real Numbers.notebook
Real
Numbers
September 02, 2014
abbreviation
(R)
The set of all natural,
whole, integers, rational
and irrational numbers,
excluding imaginary
numbers.
Simon
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Classifying Real Numbers.notebook
Whole
Numbers
September 02, 2014
abbreviation
(W)
The numbers 0, 1, 2, 3, 4, ...
• starts at 0
• includes all the natural
(counting numbers)
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Classifying Real Numbers.notebook
Natural
Numbers
September 02, 2014
abbreviation
(N)
The numbers 1, 2, 3, 4, ...
• starts at 1
• includes all the numbers used in counting
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Classifying Real Numbers.notebook
September 02, 2014
abbreviation
Integers
(Z)
The numbers
..., ­3, ­2, ­1, 0, 1, 2, 3, ...
All positive and negative
whole numbers,
including zero.
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Classifying Real Numbers.notebook
Rational
Numbers
s
All positive and negative
September 02, 2014
abbreviation
(Q)
fractions, including integers
and improper fractions.
The set of all real numbers
that can be written as a ratio
of two integers (fraction) with
3/ , ‐1/ , 3.72, 7
a nonzero denominator.
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Classifying Real Numbers.notebook
Irrational
Numbers
September 02, 2014
abbreviation
(I)
Real numbers that are not
rational.
Real numbers that cannot
be written as a ratio of
integers.
Examples: ­√2, √7, √19, π, ...
√4 = 2 (rational)
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Classifying Real Numbers.notebook
September 02, 2014
Number Systems Concept Map
All of the natural numbers are whole numbers. All of the whole
numbers are integers. All of the integers are rational numbers.
All of the rational and irrational numbers are real numbers.
Real Numbers
Rational
Irrational
Integers
Whole
Natural
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Classifying Real Numbers.notebook
Q ­ Rational Numbers
Z ­ Integers
W ­ Whole Numbers
September 02, 2014
Drag the numbers into the
correct category.
Remember that each
number may go into more
than one category.
­5
12
2.2
N ­ Natural Numbers
1.33
√10
­3/4
36
I ­ Irrational Numbers
7/9
­√2
√73
√15
0
1.25
­1
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Classifying Real Numbers.notebook
September 02, 2014
­3/4 Q ­ Rational Numbers 0
12 ­5 7/9 2.2 1.33 ­1
Z ­ Integers
12
­5
36
­1
0
W ­ Whole Numbers
0
√15
­5
12
2.2
1.33
­√2
7/9
√10
­3/4
36
36
I ­ Irrational Numbers
√10
Remember that each
number may go into more
than one category.
36
12
N ­ Natural Numbers
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Drag the numbers into the
correct category.
­√2
√73
√15
0
1.25
­1
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Classifying Real Numbers.notebook
September 02, 2014
You tube video review of number sets
http://youtu.be/oEkkXE82MN0
Interactive game using number sets
http://www.softschools.com/math/classifying_numbers/real_rational_integer_whole
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Classifying Real Numbers.notebook
September 02, 2014
Taking into account the irrational numbers and the real numbers, our
classification might look like this: Figure %: Classification of Numbers If a number falls into a category, it also falls into all the categories below
that category to which it is connected by a line. For example, ­7 is an
integer, so it is also a rational and a real number. The square root of 2
is an irrational number, so it is also a real number.
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Classifying Real Numbers.notebook
September 02, 2014
The chart below will help you with the classification of numbers a lot. It will makes things crystal clear. 13
Classifying Real Numbers.notebook
September 02, 2014
Keep your notes and complete the "Sets of Real Numbers" paper for homework. You may need to look at your notes to label the number with the correct set. Remember, many numbers are part of more than one number set.
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Classifying Real Numbers.notebook
September 02, 2014
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