Questions and Answers
What is the definition of rational numbers?
Numbers that can be written as a fraction. Includes decimals that end or repeat with a pattern.
What is the definition of integers?
Positive and negative numbers (including 0) that do not have fractions or decimals.
What is the definition of whole numbers?
Any positive number (including zero) that does not have a fraction or decimal.
What is the definition of natural numbers?
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Classify the following number: 36
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Classify the following number: -29
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Classify the following number: -2.6
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Classify the following number: 0
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All rational numbers are whole numbers.
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All whole numbers are rational numbers.
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Some integers are also whole numbers.
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All integers are whole numbers.
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All natural numbers are rational numbers.
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All rational numbers are natural numbers.
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Some integers are natural numbers.
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All natural numbers are integers.
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All rational numbers are whole numbers.
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Some whole numbers are rational numbers.
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All integers are rational numbers.
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Some rational numbers are integers.
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All whole numbers are natural numbers.
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All natural numbers are whole numbers.
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Study Notes
Rational Numbers
- Defined as numbers that can be expressed as a fraction.
- Includes decimals that either terminate or repeat with a pattern.
Integers
- Comprise positive and negative whole numbers, including zero.
- Do not include fractions or decimals.
Whole Numbers
- Any positive number, including zero.
- Excludes fractions and decimals.
Natural Numbers
- Positive numbers that don't have fractions or decimals, starting from one.
- Also referred to as counting numbers.
Classification of Numbers
- 36: Classifies as rational, integer, whole, and natural.
- -29: Classifies as rational and integer only.
- -2.6: A rational number.
- 0: Classifies as rational, integer, and whole.
True/False Statements Analysis
- Not all rational numbers are whole numbers (e.g., rational numbers can include fractions).
- All whole numbers are rational numbers, as they can be expressed as fractions (e.g., 5/1).
- Some integers are also whole numbers (e.g., 5).
- Not all integers are whole numbers (e.g., -5).
- All natural numbers are rational numbers, being subsets of them.
- Not all rational numbers are natural numbers (e.g., 2.5).
- Some integers are natural numbers (e.g., 3).
- All natural numbers are integers, consisting solely of non-negative whole numbers.
- Not all whole numbers are natural numbers due to the inclusion of zero.
- All natural numbers fit within the whole numbers classification.
Summary of Relationships
- Whole numbers are a subset of rational numbers.
- Rational numbers encompass integers, while integers consist of both whole numbers and negative numbers.
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Test your understanding of rational numbers through flashcards. This quick quiz covers definitions of rational numbers, integers, and whole numbers. Perfect for reinforcing key math concepts in your studies.
