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Questions and Answers
What type of number is -54/9?
What type of number is -54/9?
What type of number is √15?
What type of number is √15?
What type of number is 32.343434343...?
What type of number is 32.343434343...?
What type of number is √81?
What type of number is √81?
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What type of number is -30?
What type of number is -30?
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What type of number is π?
What type of number is π?
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What type of number is 42/6?
What type of number is 42/6?
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What type of number is -2/3?
What type of number is -2/3?
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What type of number is 0?
What type of number is 0?
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What type of number is 5?
What type of number is 5?
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What type of number is 12.569843681549...?
What type of number is 12.569843681549...?
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What type of number is 23.9?
What type of number is 23.9?
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What type of number is -2345?
What type of number is -2345?
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What type of number is √9?
What type of number is √9?
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What type of number is -43.76?
What type of number is -43.76?
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What type of number is √7?
What type of number is √7?
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What type of number is 0.333...?
What type of number is 0.333...?
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What type of number is 17?
What type of number is 17?
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What type of number is -93/3?
What type of number is -93/3?
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Natural numbers are represented as {______}
Natural numbers are represented as {______}
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Whole numbers are represented as {______}
Whole numbers are represented as {______}
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Integers are represented as {______}
Integers are represented as {______}
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What are properties of rational numbers?
What are properties of rational numbers?
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What are properties of irrational numbers?
What are properties of irrational numbers?
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What are the subsets of rational numbers?
What are the subsets of rational numbers?
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Study Notes
Classifying Real Numbers
- Real numbers are classified into different sets based on properties and characteristics.
- The sets include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
Key Definitions
- Natural Numbers: {1, 2, 3, 4, ...} - positive integers starting from 1.
- Whole Numbers: {0, 1, 2, 3, 4, ...} - all natural numbers including zero.
- Integers: {..., -3, -2, -1, 0, 1, 2, 3, ...} - whole numbers and their negative counterparts.
Rational Numbers
- Defined as numbers that can be expressed as fractions of integers (p/q where q ≠ 0).
- Include terminating decimals and repeating decimals.
- Examples:
- -54/9: Integer, Rational
- 32.343434343...: Rational
- 42/6: Natural, Whole, Integer, Rational
- 0: Whole, Integer, Rational
- 23.9: Rational
- -2/3: Rational
Irrational Numbers
- Cannot be expressed as fractions.
- These numbers have non-repeating, non-terminating decimal representations.
- Examples:
- √15: Irrational
- π: Irrational
- 12.569843681549...: Irrational
- √7: Irrational
- 0.333...: Rational but indicates the transition to repeating decimals.
Mixed Classifications
- Certain numbers can belong to multiple classifications:
- √81: Natural, Whole, Integer, Rational (equal to 9)
- 5: Natural, Whole, Integer, Rational
- -30: Integer, Rational
- -2345: Integer, Rational
- -93/3: Integer, Rational
- -43.76: Rational
Properties
- Rational Numbers: Can be written as a fraction; includes both terminating and repeating decimals.
- Irrational Numbers: Cannot be written as a fraction; characterized by non-repeating, non-terminating decimals.
Subsets of Rational Numbers
- Rational numbers include integers, whole numbers, and natural numbers as subsets.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of real numbers with these flashcards! Each card presents a number and its classification as either integer, rational, irrational, or natural. Perfect for students learning about number classification.
