NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

 

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers are a must if you want to prepare this chapter for your board exams. The Real Numbers chapter of Class 10 Maths includes some interesting topics like Euclid’s Division Lemma, Rational and Irrational Numbers, and the Fundamental Theorem of Arithmetic. Questions in this chapter are based on finding the HCF and LCM of given integers, proving that the given numbers are irrational, and identifying whether the given numbers ​​have a terminating decimal expansion or a non-terminating repeating decimal expansion without actually dividing the numbers. 

 

The NCERT Solutions for Class 10 Maths Real Numbers help you understand how to solve the questions of this chapter in a step by step way. These solutions are prepared to guide you on how to approach the questions in the exam and answer them correctly to secure full marks. The NCERT Solutions are a self-study guide for every Class 10 student who wants to ace their board examination. 

About NCERT Class 10 Maths Chapter 1 Real Numbers 

 

Here are some important points regarding the chapter that will help you in NCERT Class 10 Maths Solutions:

• Euclid’s division lemma: According to Euclid’s Division Lemma, a = bq + r, 0 ≤ r < b, where a, b, q, r are integers. 
• HCF of given numbers is the highest common factor among all which is also known as GCD i.e. greatest common divisor.
• LCM of given numbers is their least common multiple.
• If we have two positive integers  ‘m’ and ‘n’ then the property of their  HCF and LCM will be:
  HCF (m, n) × LCM (m, n) = m × n.
• Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
• Irrational numbers: a number ‘s’ is called irrational if it cannot be written in the form, p/q where p and q are integers and q ≠ 0. 
• Theorem: Let p be a prime number. If p divides a2, then p divides a, where a is a positive integer.
• Theorem: 2 is irrational.
• Theorem: Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form p/q, where p and q are coprime, and the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers.
• Theorem: Let x = p/q be a rational number, such that the prime factorization of q is of the form 2n5m, where n, m are non-negative integers. Then x has a decimal expansion that terminates.

Download Free NCERT Solutions for Class 10 Maths Real Numbers

 

There are 4 exercises included in this chapter with almost 18 unsolved

questions. All the NCERT exercises of this chapter are important as they help you understand the fundamental concepts of real numbers. Let us see what is included in each of the exercises:

 

NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.1 

The first exercise of this chapter is based on Euclid’s Division Lemma. You have to solve the questions of this exercise using Euclid’s division algorithm. There are 5 questions in this exercise. We have provided stepwise solutions to every question for your better practice. 

 

NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.2

The second exercise of this chapter is based on the fundamental theorem of arithmetic. You must know how to find the HCF and LCM of two or more numbers to solve this exercise. There are just 7 questions in this exercise including short answer and long answer type questions. 

 

NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.3 

The third exercise of this chapter is based on finding whether the given number is rational or irrational. The exercise includes just three questions. You must practice all of them very carefully to master the concepts of this exercise. 

 

NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.4

The fourth and the last exercise of this chapter is based on the decimal expansion of rational numbers. This exercise includes 3 questions whose stepwise solutions are prepared by askIITians experts for your better clarity. 

 

Important features of NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.4 

• The NCERT Solutions are prepared according to the latest CBSE Class 10 Maths syllabus and exam pattern. 
• You can download the NCERT Solutions for free and refer to them at any time while you study. 
• The solutions include stepwise explanations and clear reasoning so that you can understand how to approach questions in the exam. 
• We have mentioned where every theorem is used so that you can understand how to apply the theorems in the questions. 

NCERT Class 10 Maths Chapter 1 Real Numbers FAQs

 

1. Do I need to practice all the NCERT Exercises given in Chapter 1 Real Numbers? 

Yes, you must practice all the exercise questions of the chapter as the board exams are based on the NCERT textbook only. Moreover, NCERT exercises help clarify your fundamental concepts of the chapter so that you can tackle advanced-level questions easily. 

 

2. What are the important topics covered in NCERT Class 10 Maths Chapter 1 Real Numbers? 

Important topics included in Chapter 1 Real Numbers of Class 10 Maths are Euclid’s Division Lemma, Rational and Irrational Numbers, and the Fundamental Theorem of Arithmetic.

 

3. How many exercises are included in Chapter 1 Real Numbers of Class 10 Maths? 

Chapter 1 Real Numbers of Class 10 Maths includes 4 exercises. You can download revision notes, NCERT Solutions and extra questions based on this chapter easily from the askIITians website.