Questions and Answers
What type of number is -54/9?
What type of number is √15?
What type of number is 32.343434343...?
What type of number is √81?
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What type of number is -30?
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What type of number is π?
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What type of number is 42/6?
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What type of number is -2/3?
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What type of number is 0?
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What type of number is 5?
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What type of number is 12.569843681549...?
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What type of number is 23.9?
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What type of number is -2345?
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What type of number is √9?
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What type of number is -43.76?
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What type of number is √7?
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What type of number is 0.333...?
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What type of number is 17?
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What type of number is -93/3?
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Natural numbers are represented as {______}
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Whole numbers are represented as {______}
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Integers are represented as {______}
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What are properties of rational numbers?
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What are properties of irrational numbers?
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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
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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.
