NCERT Class 10 Maths: Chapter 1 – Real Numbers Short Notes

Class 10 Maths NCERT Syllabus

The Class 10 Maths NCERT syllabus covers various essential topics, including Real Numbers, Algebra, Trigonometry, Coordinate Geometry, Geometry, Mensuration, and Statistics and Probability. Each chapter is designed to provide students with a strong foundation in mathematical concepts and their applications.

Chapter 1: Real Numbers

Abstract: The first chapter, Real Numbers, introduces students to the fundamental concepts of real numbers, including the properties of real numbers, decimal expansions of rational and irrational numbers, and the process of finding the highest common factor (HCF) and the least common multiple (LCM) using Euclid’s division algorithm. The chapter also covers the Fundamental Theorem of Arithmetic and the process of rationalizing the denominator.

Multiple Choice Questions and Answers

1. What is the decimal expansion of a rational number?

• A) Terminating
• B) Non-terminating
• C) Recurring
• D) Both A and C
• Answer: D) Both A and C

1. What is the process of finding the HCF of two numbers using Euclid’s division algorithm?

• A) Repeated addition
• B) Repeated subtraction
• C) Repeated multiplication
• D) Repeated division
• Answer: D) Repeated division

Very Short Questions and Answers

1. Question: What are real numbers?
   Answer: Real numbers include all rational and irrational numbers, such as whole numbers, integers, fractions, and square roots of positive numbers.
2. Question: What is Euclid’s division lemma?
   Answer: Euclid’s division lemma states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.

Short Questions and Answers

1. Question: What are the properties of real numbers?
   Answer: The properties of real numbers include closure, commutativity, associativity, distributivity, the existence of an additive identity, the existence of an additive inverse, the existence of a multiplicative identity, and the existence of a multiplicative inverse.
2. Question: What is the decimal expansion of an irrational number?
   Answer: The decimal expansion of an irrational number is non-terminating and non-recurring.

Long Question and Answer

Question: How do you find the highest common factor (HCF) of two numbers using Euclid’s division algorithm?
Answer: The HCF of two numbers can be found using Euclid’s division algorithm by repeatedly applying the algorithm until the remainder is 0, and then the divisor at this step is the required HCF.