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Knowledge
The chapter explores different types of numbers in mathematics, including natural, whole, integers, rational, irrational, and real numbers, highlighting their unique characteristics. It details how real numbers can be represented on a number line and outlines the operations and laws of exponents applicable to these numbers. Finally, it emphasizes the significance of decimal expansions in distinguishing between rational and irrational numbers, laying a foundation for further studies in algebra.
Sections
References
1_Introduction_t.pdfClass Notes
Memorization
What we have learnt
- The number system consists ...
- Real numbers include both r...
- Decimal expansions can help...
Revision Tests
What we have learnt
- The number system consists of various types of numbers: natural, whole, integers, rational, irrational, and real numbers.
- Real numbers include both rational and irrational numbers.
- Decimal expansions can help distinguish between rational and irrational numbers.
- Exponent laws are essential for simplifying expressions.
- Real numbers can be placed on a number line.
Key Concepts
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Term: Natural Numbers
Definition: Counting numbers that start from 1 and go on infinitely (e.g., 1, 2, 3, ...).
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Term: Whole Numbers
Definition: Natural numbers including zero (e.g., 0, 1, 2, 3, ...).
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Term: Integers
Definition: All whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...).
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Term: Rational Numbers
Definition: Numbers that can be expressed as the quotient of two integers (e.g., 1/2, -3).
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Term: Irrational Numbers
Definition: Numbers that cannot be expressed as a fraction, with non-terminating and non-repeating decimals (e.g., √2, π).
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Term: Real Numbers
Definition: The set of all rational and irrational numbers, encompassing every point on the number line.
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Term: Laws of Exponents
Definition: Rules that help simplify expressions involving exponents, including properties for multiplication, powers, zero exponent, and negative exponents.
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Term: Decimal Expansions
Definition: Representations of numbers in decimal form, including terminating, non-terminating repeating, and non-terminating non-repeating decimals.