# NCERT Exemplar Class 10 Maths Chapter 1 Solutions: Real Numbers

NCERT Exemplar Class 10 Maths Solutions for Chapter 1 ‘Real Numbers’ are discussed here to provide you with complete information about the chapter. The solutions of NCERT Class 10 Maths Exemplar are prepared by expert Maths teachers to help you grasp the topics properly before appearing in the exams. It will also help you in the proper concept building of the topics.

Chapter 1 ‘Real Numbers’ of NCERT Class 10 Maths Exemplar contains 39 questions which are divided into 4 exercises. The chapter discusses important topics like Euclid’s division algorithm, the fundamental theorem of arithmetic, revisiting rational and irrational numbers and decimal expansions. The chapter discusses all real numbers and also its applications. All these topics are going to develop a strong base for understanding further chapters in mathematics.

Instasolv provides you with a strong foundation of the chapter based on CBSE guidelines. Our solutions discuss all the important questions from the examination point of view. As you go through the step-by-step solutions provided by our elite teachers who have gained proficiency in mathematics, it is definitely going to provide you with an edge in the subject with good scores.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 1

The chapter is fully based on real numbers and its applications. Euclid’s division algorithm, tells about the divisibility of integers. It states that any positive integer can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b. It has many applications in connection to the divisibility properties of integers. It is used in computing HCF of natural numbers whereas fundamental theorem of arithmetic says that every composite natural number can be expressed as a product of primes that works on multiplication of positive integers.

**Euclid’s Division Lemma:**

Given positive integers a and b, there exist whole number q and r satisfying a=bq+r, 0r<b.

**Euclid’s Division Algorithm:**

The HCF of two positive integers a and b with the condition a>b can be obtained by:

Step 1.Firstly apply Euclid’s division lemma on a and b, a=bq+r, 0r<b for whole numbers q and r.

Step 2.If r=0, HCF(a,b)=b

If r0, apply euclid’s division on b and r.

b=r+rq_{1}+r_{1}, 0≤r_{1}<b for some whole number q_{1} and r_{1}.

Step 3.If r_{1}=0, then HCF of (b,r)=r

HCF(a,b)=HCF(b,r)=HCF(a,b)=r.

Continue the above process until the remainder is zero. Last non-zero remainder=HCF(a,b).

**Fundamental Theorem of Arithmetic:**

Every composite number can get factorized as a product of primes.

The relation between HCF and LCM of two natural numbers

HCF x LCM= product of two natural numbers.

LCM of two natural numbers is always divisible by their HCF.

**Rational and Irrational Numbers:**

A number that we can express in the form of p/q, with condition that p and q both are integers and q≠0 is called a rational number. A number that cannot be expressed in this form is called an irrational number.

### Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 1

- The chapter initially begins with the discussion of the real numbers in exercise 1.1 It contains 10 multiple-choice questions.
- The other exercises 1.2 and 1.3 deal with the very important concept of the chapter Euclid’s division algorithm, Euclid’s division lemma and the Fundamental theorem of arithmetic.
- Further, the exercises are going to help you in revising the concepts that were discussed in class 9 like rational and irrational numbers in exercise 1.2 and 1.3.
- The topics of decimal expansion including recurring and terminating rational numbers are discussed in exercise 1.4.
- Exercise 1.2 includes 10 very short answer questions. Exercise 1.3 includes 14 short answer questions and Exercise 1.4 comprises 5 long answer questions.

### Why Use NCERT Exemplar Class 10 Maths Solutions Chapter 1 by Instasolv?

- Our solutions to the NCERT Class 10 Exemplar problems for Maths Chapter 1 strictly follow the guidelines provided by the CBSE board which will help you prepare for the exam in a systematic way.
- It will save time which you can utilize in the revision of the chapter.
- It will help you stay regular in studies and score good marks in the examination.
- You will get a complete understanding of the concepts related to real numbers as our NCERT Exemplar problems and solutions will provide you with a clear vision of the topics.