Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Each square root is between two integers.
Name the two integers. Use a calculator to
find each value. Round to the
nearest tenth.
10 and 11
4 and 3
1.4
11.1
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Problem of the Day The circumference of a circle
is approximately 3.14 times its diameter. A
circular path 1 meter wide has an inner diameter
of 100 meters. How much farther is it around the
outer edge of the path than the inner edge?
6.28 m
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Learn to determine if a number is rational or
irrational.
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Vocabulary
irrational number real number Density Property
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Biologists classify animals based on shared
characteristics. The cardinal is an animal, a
vertebrate, a bird, and a passerine.
Animals
You already know that some numbers can be
classified as whole numbers, integers, or
rational numbers.
Vertebrates
Birds
Passerines
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Recall that rational numbers can be written as
fractions. Rational numbers can also be written
as decimals that either terminate or repeat.
4 5
23
3 3.8
0.6
1.44 1.2
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Irrational numbers can only be written as
decimals that do not terminate or repeat. If a
whole number is not a perfect square, then its
square root is an irrational number.
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The set of real numbers consists of the set of
rational numbers and the set of irrational
numbers.
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Additional Example 1 Classifying Real Numbers
Write all names 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
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C.
whole, integer, rational, real
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Check It Out Example 1
Write all names that apply to each number.
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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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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.
C.
4
not a real number
4 9
D.
rational
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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.
C.
7
not a real number
64 81
D.
rational
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The Density Property of real numbers states that
between any two real numbers is another real
number. This property is also true for rational
numbers, but not for whole numbers or integers.
For instance, there is no integer between 2 and
3.
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Additional Example 3 Applying the Density
Property of Real Numbers
There are many solutions. One solution is halfway
between the two numbers. To find it, add the
numbers and divide by 2.
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Check It Out Example 3
There are many solutions. One solution is halfway
between the two numbers. To find it, add the
numbers and divide by 2.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz
Write all names that apply to each number.
16 2
1.
2.
2
real, irrational
real, integer, rational
State if each number is rational, irrational, or
not a real number.
25 0
4.
3.
rational
not a real number
5.
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Lesson Quiz for Student Response Systems
1. Identify all names that apply to . A.
real, irrational B. real, rational C. not real,
irrational D. not real, rational
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Lesson Quiz for Student Response Systems
2. Identify the name that applies to .
A. irrational B. rational C. not a real
number D. none
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Lesson Quiz for Student Response Systems
3. Identify a real number between
. A. 4 B. C. D.