Introduction to Number Systems
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
Navigate through the learning materials and practice exercises.
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
- -- Natural Numbers
- Counting numbers that start from 1 and go on infinitely (e.g., 1, 2, 3, ...).
- -- Whole Numbers
- Natural numbers including zero (e.g., 0, 1, 2, 3, ...).
- -- Integers
- All whole numbers and their negative counterparts (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...).
- -- Rational Numbers
- Numbers that can be expressed as the quotient of two integers (e.g., 1/2, -3).
- -- Irrational Numbers
- Numbers that cannot be expressed as a fraction, with non-terminating and non-repeating decimals (e.g., √2, π).
- -- Real Numbers
- The set of all rational and irrational numbers, encompassing every point on the number line.
- -- Laws of Exponents
- Rules that help simplify expressions involving exponents, including properties for multiplication, powers, zero exponent, and negative exponents.
- -- Decimal Expansions
- Representations of numbers in decimal form, including terminating, non-terminating repeating, and non-terminating non-repeating decimals.
Additional Learning Materials
Supplementary resources to enhance your learning experience.