# NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems

NCERT Solutions for Class 9 Maths Chapter 1 will help you prepare all the concepts of Number Systems. In Chapter 1 of NCERT Solutions for Class 9 Maths, you will learn different concepts such as Rational Numbers, Irrational Numbers, Number Line, Operations on Real numbers, and of Exponents of Real Numbers. The NCERT exercise problems and their solutions will help you identify all the difficult topics of the Chapter easily.

NCERT Class 9 Maths Chapter 1 has a total of 27 questions in 6 exercises. All these questions are of diverse nature and provide comprehensive coverage of all the topics of the Chapter. The questions are of all kinds from beginners to advanced level to help you learn the application of these topics. With the help of these NCERT textbook questions for Chapter 1, you will also get an idea of the pattern of questions asked in the CBSE Class 9 exam.

NCERT Solutions for Class 9 Maths Chapter 1 are prepared by the Maths experts at Instasolv in a step by step manner to help you grasp the methodology easily. These solutions are prepared with the goal to make the topics of Number Systems an easy topic to retain for exams. These Solutions offer the answers for each and every question in a detailed and simple manner. Going through these NCERT solutions is an essential prerequisite for you to score good marks in CBSE exams.

## Important Points Covered in NCERT Solutions for Class 9 Maths Chapter 1: Number Systems

**Introduction**

- Natural numbers: a set of numbers beginning from 1, 2, 3 and so on.
- Whole numbers: a set of numbers beginning from 0, 1, 2, 3 and so on.
- Integers: The collection of all positive numbers, negative numbers and 0 are known as Integers.
- Rational numbers: A number ‘r’ is called a rational number if it can be expressed in the form of pq, where p and q are integers and q ≠ 0.

There can be infinite rational numbers between any two given rational numbers.

**Irrational Numbers**

A number ‘s’ is called irrational, if it cannot be written in the form of pq, where p and q are integers and q ≠ 0.

**Real Numbers**

The collection of the sets of all rational numbers and all irrational numbers is known as Real numbers.

**Real Number Line**

All real numbers can be represented by a unique point on the number line and in the same line of thought, all points on the number line represent a unique real number. Such a number line is known as the Real Number Line.

**Decimal Expansion of Real numbers**

In certain cases, the remainder becomes zero in a rational number after a finite number of steps. This implies that these decimals terminate after a few steps. Such a decimal expansion is known as terminating.

In certain cases, the remainder never becomes zero and repeats after a few numbers of steps, to make the decimal expansion go on forever and there is a repeating block that appears in the quotient. Such a decimal expansion is known as non-terminating recurring.

A rational number can either have a terminating or a non-terminating recurring decimal expansion or a terminating/ non-terminating recurring decimal is a rational number.

Similarly, an irrational number always has a non-terminating non-recurring decimal expansion. Moreover, a non-terminating, non-recurring decimal number is the example of an irrational number.

Process of Successive Magnification can be used to employ the process of visualisation of representation of numbers on the number line.

**Operations**

The sum or difference of a rational number and an irrational number is irrational.

The product or quotient of a non-zero rational number with an irrational number is irrational. If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational.

**Rationalisation and Law of Exponents**

Several formulae and rules can be followed to rationalise a given number and solve the maths problems of rational numbers with exponents.

**Exercise Wise Discussion of NCERT Solutions for Class 9 Maths Chapter 1**

- The NCERT Solutions for Class 9 Maths Chapter 1 cover all the major concepts of the chapter such as irrational numbers, square roots of irrational numbers, representing irrational numbers on a number line, the decimal expansion of rational numbers.
- The exercise questions deal with the questions of a difficulty level in increasing order, therefore helping you to grow along with the chapter.
- All the formulae and methods in the syllabus are covered in-depth for a robust revision of the topic.
- The Exercises have a diverse set of questions including interactive activities to make the topic interesting according to the curriculum guidelines.

**NCERT Solutions Class 9 Maths Chapter 1 by Instasolv**

- The NCERT Solutions for Class 9 Maths Chapter 1 by Instasolv are a one-stop destination for all your doubts and queries.
- The NCERT Maths Solutions for Class 9 prepared by the expert team of Instasolv are not only detailed but are also written in simple language to help you grasp the topics quickly.
- The NCERT Solutions provided by Instasolv are professional and on-point.
- These NCERT Solutions for Class 9 is an essential source from the exam point of view.
- These step by step and detailed set of solutions prepared by Instasolv Mathematics experts are compliant with the latest CBSE exam pattern and CBSE syllabus.
- We have covered all the questions and activities of the chapter to provide you with a comprehensive and free of cost assistance to do well in your exam.