Rational and Irrational Numbers

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Rational and Irrational Numbers
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Rational and Irrational Numbers Essential Question
How do I distinguish between rational and
irrational numbers?
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Vocabulary
real number irrational number
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The set of real numbers is all numbers that can
be written on a number line. It consists of the
set of rational numbers and the set of irrational
numbers.
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Recall that rational numbers can be written as
the quotient of two integers (a fraction) or as
either terminating or repeating decimals.
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23
3 3.8
0.6
1.44 1.2
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(No Transcript)
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Make a Venn Diagram that displays the following
sets of numbers Reals, Rationals,
Irrationals, Integers, Wholes, and Naturals.
Reals
Rationals
-2.65
Integers
-3
-19
Wholes
0
Irrationals
Naturals
1, 2, 3...
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Additional Example 1 Classifying Real Numbers
Write all classifications that apply to each
number.
5 is a whole number that is not a perfect square.
5
A.
irrational, real
B.
12.75 is a terminating decimal.
12.75
rational, real
16 2
C.
whole, integer, rational, real
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Check It Out! Example 1
Write all classifications that apply to each
number.
9
A.
whole, integer, rational, real
35.9 is a terminating decimal.
35.9
B.
rational, real
81 3
C.
whole, integer, rational, real
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A fraction with a denominator of 0 is undefined
because you cannot divide by zero. So it is not a
number at all.
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Additional Example 2 Determining the
Classification of All Numbers
State if each number is rational, irrational, or
not a real number.
A.
21
irrational
0 3
B.
rational
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Additional Example 2 Determining the
Classification of All Numbers
State if each number is rational, irrational, or
not a real number.
4 0
C.
not a real number
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Check It Out! Example 2
State if each number is rational, irrational, or
not a real number.
A.
23 is a whole number that is not a perfect square.
23
irrational
9 0
B.
undefined, so not a real number
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Check It Out! Example 2
State if each number is rational, irrational, or
not a real number.
64 81
C.
rational