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10th Class Mathematics Chapter – 1: REAL NUMBERS – PDF Free Download
At Ramsetu, we aim to provide educational resources that make learning engaging and comprehensive. Chapter 1, “REAL NUMBERS,” from the 10th Class Mathematics textbook, covers fundamental concepts that form the basis for various topics in mathematics. This chapter provides students with a clear understanding of real numbers, their properties, and their applications.
Practical applications and relevance of real numbers in everyday life.
Key Concepts and Definitions:
Real Numbers: The set of numbers that includes both rational and irrational numbers.
Rational Numbers: Numbers that can be expressed as the quotient of two integers (e.g., 1/2, 3.75).
Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π).
Euclidean Algorithm: A method for finding the greatest common divisor (GCD) of two numbers.
Decimal Expansion: Representation of real numbers in decimal form.
Chapter Content:
Summary of “REAL NUMBERS”:
Introduction to real numbers and their classification.
Properties of real numbers and their subsets.
Fundamental Theorem of Arithmetic.
Euclidean Algorithm for finding GCD.
Decimal expansions of rational and irrational numbers.
Key Concepts:
Fundamental Theorem of Arithmetic: Every integer greater than 1 is either a prime number or can be uniquely factorized as a product of prime numbers.
Euclidean Algorithm: A technique to find the GCD of two integers.
Decimal Expansions:
Terminating Decimal: A decimal that ends (e.g., 0.75).
Non-Terminating Repeating Decimal: A decimal that repeats a pattern infinitely (e.g., 0.666…).
Non-Terminating Non-Repeating Decimal: A decimal that does not repeat and goes on infinitely (e.g., π).
Formulas and Properties:
Prime Factorization: Expressing a number as a product of prime numbers.
LCM and GCD: Methods to find the least common multiple and greatest common divisor.
Applications:
Real-life applications of real numbers in various fields such as engineering, physics, and economics.
Use of the Euclidean Algorithm in computer science and cryptography.
Importance of decimal representation in financial calculations and measurements.
Frequently Asked Questions (FAQs):
What are real numbers?
Real numbers include all the rational and irrational numbers. They can be represented on a number line.
How do you find the GCD of two numbers using the Euclidean Algorithm?
To find the GCD using the Euclidean Algorithm, divide the larger number by the smaller number, then divide the divisor by the remainder, and repeat this process until the remainder is zero. The last non-zero remainder is the GCD.
What is the difference between rational and irrational numbers?
Rational numbers can be expressed as the quotient of two integers, while irrational numbers cannot be expressed as a simple fraction.
