NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions for Class 10 Maths Chapter 1 Real Number is prepared by home-tution expert teachers having years of teaching experience for the CBSE class 10 board. All the questions asked in Chapter 1, Real Numbers, in the NCERT textbook are solved with a proper explanation as per the CBSE guidelines.

What are you going to learn in Chapter 1 Real Numbers?

In Chapter 1, we will study Real Numbers in detail. As we all know, any number, excluding complex numbers, is a real number. Positive and negative integers, irrational numbers, and fractions are all examples of real numbers. To put it another way, any number found in the real world is a real number. Numbers can be found all around us. Natural numbers are used to count objects, integers are used to measure temperature, rational numbers are used to represent fractions, irrational numbers are used to calculate the square root of a number, etc. These various types of numbers form a collection of real numbers. Here, we are going to learn what a real number is. Euclid’s division algorithm, fundamental theorem of arithmetic, methods of finding LCM, HCF, and the complete explanation of rational and irrational numbers.

Chapter Overview:

Chapter 1, Real Numbers, introduces students to the fundamental concepts of number systems. Building upon previous classes, it explores properties of real numbers, Euclid's Division Lemma, the Fundamental Theorem of Arithmetic, and irrational numbers. These concepts are foundational for higher-level mathematics and competitive exams.

Topics Covered:

Euclid’s Division Lemma
- Statement and applications
- Finding the HCF of two numbers using Euclid’s algorithm
Fundamental Theorem of Arithmetic
- Prime factorization of integers
- Application to find LCM and HCF
Revisiting Irrational Numbers
- Proofs of irrationality (e.g., √2, √3, √5)
- Contradiction method
Revisiting Rational Numbers and Their Decimal Expansions
- Identifying terminating and non-terminating recurring decimals
- Application using prime factorization of the denominator

Key Formulas & Concepts covered in NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Euclid’s Division Lemma: For any two positive integers a and b There exist integers q and r such that:
a = bq + r, where 0 ≤ r < b
Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorized) as a product of primes in a unique way (except for the order of the primes).
Terminating Decimal: If the denominator (in lowest form) has no prime factors other than 2 or 5.