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HMH California GO Math Grade 8
8.NS.1
Know that numbers that are
not rational are called irrational.
Understand informally that
every number has a decimal
expansion; for rational numbers
show that the decimal expansion
repeats eventually, and convert a
decimal expansion which repeats
eventually into a rational number.
How can you describe relationships between sets of real numbers?
Classifying Real Numbers
Biologists classify animals based on shared
characteristics. A cardinal is an animal, a vertebrate,
a bird, and a passerine.
You already know that the set of rational numbers
consists of whole numbers, integers, and fractions.
The set of real numbers consists of the set of
rational numbers and the set of irrational numbers.
Animals
Vertebrates
Birds
Passerines
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Passerines, such
as the cardinal,
are also called
“perching birds.”
EXAMPLE 1
8.NS.1
Write all names that apply to each number.
A
5 is a whole number that is not a perfect square.
irrational, real
B –17.84
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Math
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–17.84 is a terminating decimal.
rational, real
Lesson 1.2
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Write all names that apply to each number.
2. The length of the side of a square that has an
area of 10 square yards.
Understanding Sets and Subsets
of Real Numbers
By understanding which sets are subsets of types of numbers, you can verify
whether statements about the relationships between sets are true or false.
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EXAMPLE 2
8.NS.1
Tell whether the given statement is true or false. Explain your choice.
A All irrational numbers are real numbers.
True. Every irrational number is included in the set of real numbers.
The irrational numbers are a subset of the real numbers.
B No rational numbers are whole numbers.
Give an example of a
rational number that is a
whole number. Show that
the number is both whole
and rational.
False. A whole number can be written as a fraction with a denominator
of 1, so every whole number is included in the set of rational numbers.
The whole numbers are a subset of the rational numbers.
Tell whether the given statement is true or false. Explain your choice.
3. All rational numbers are integers.
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Math Trainer
4. Some irrational numbers are integers.
Online Practice
and Help
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Unit 1
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Identifying Sets for Real-World
Situations
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EXAMPLLE 3
Identify the set of numbers that best describes each situation. Explain
your choice.
My Notes
A the number of people wearing glasses in a room
The set of whole numbers best describes the situation. The number of
people wearing glasses may be 0 or a counting number.
B the circumference of a flying disk has a diameter of 8, 9, 10, 11, or
14 inches
Identify the set of numbers that best describes the situation. Explain
your choice.
5. the amount of water in a glass as it evaporates
6. the weight of a person in pounds
Lesson 1.2
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Guided Practice
Write all names that apply to each number. (Example 1)
Tell whether the given statement is true or false. Explain your choice.
(Example 2)
9. All whole numbers are rational numbers.
10. No irrational numbers are whole numbers.
Identify the set of numbers that best describes each situation. Explain your
choice. (Example 3)
11. the change in the value of an account when given to the nearest dollar
1
12. the markings on a standard ruler
13. What are some ways to describe the relationships between sets of
numbers?
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Unit 1
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Name
Class
Date
8.NS.1
Write all names that apply to each number. Then place the numbers in the
correct location on the Venn diagram.
Identify the set of numbers that best describes each situation. Explain
your choice.
20. the height of an airplane as it descends to an airport runway
21. the score with respect to par of several golfers: 2, – 3, 5, 0, – 1
Lesson 1.2
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23. Critique Reasoning The circumference of a circular region is shown.
What type of number best describes the diameter of the circle? Explain
your answer.
24. Critical Thinking A number is not an integer. What type of number
can it be?
25. A grocery store has a shelf with half-gallon containers of milk. What type
of number best represents the total number of gallons?
FOCUS ON HIGHER ORDER THINKING
Work Area
26. Explain the Error Katie said, “Negative numbers are integers.” What was
her error?
27. Justify Reasoning Can you ever use a calculator to determine if a
number is rational or irrational? Explain.
29. Communicate Mathematical Ideas Irrational numbers can never be
precisely represented in decimal form. Why is this?
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