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MATHEMATICS ASSIGNMENT CLASS IX  NUMBER SYSTEM

 (a) 1⁸ × 3⁰ × 5³ × 2²           Ans; 500,                

(b)  4 -3 × 4⁸ ÷ 4²                Ans; 64

(d) 3 -4 × 3 -5 ÷ 3¹⁰             Ans; 3 -19

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Chapter 1 Class 9 Number Systems

Click on any of the links below to start learning from Teachoo ...

Get solutions of all NCERT Questions of Chapter 1 Class 9 Number System free at teachoo. Answers to all NCERT Exercises and Examples are solved for your reference. Theory of concepts is also made for your easy understanding

In this chapter, we will learn

• Different Types of numbers like Natural Numbers, Whole numbers, Integers, Rational numbers
• How to find rational numbers between two rational numbers
• What is an irrational number
• Checking if number is irrational or not
• And how to draw an irrational number on the number line
• Then, we will study What a real number is
• And find Decimal expansions - Terminating, Non terminating - repeating, Non terminating Non repeating
• Converting non-terminating repeating numbers into p/q form
• Finding irrational numbers between two numbers
• Representing real numbers on the number line (we use magnification)
• We will learn how to add , subtract and multiply numbers with square root (like 5√2 + 3√3 - 8√2)
• We will learn some identities of numbers with square root (like (√a + √b) 2 )
• How to rationalize numbers
• We will also do questions on Law of Exponents (here, the exponents can also be in fractions)

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NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

Class 9 Maths Chapter 1 Solution for CBSE Board Class 9 Maths Exercise 1.1 in English Class 9 Maths Exercise 1.2 in English Class 9 Maths Exercise 1.3 in English Class 9 Maths Exercise 1.4 in English Class 9 Maths Exercise 1.5 in English

Class 9 Maths Chapter 1 Solution for State Boards Class 9 Maths Chapter 1 Exercise 1.1 Class 9 Maths Chapter 1 Exercise 1.2 Class 9 Maths Chapter 1 Exercise 1.3 Class 9 Maths Chapter 1 Exercise 1.4 Class 9 Maths Chapter 1 Exercise 1.5 Class 9 Maths Chapter 1 Exercise 1.6

Class 9 Maths Chapter 1 Solution in Hindi Class 9 Maths Exercise 1.1 in Hindi Class 9 Maths Exercise 1.2 in Hindi Class 9 Maths Exercise 1.3 in Hindi Class 9 Maths Exercise 1.4 in Hindi Class 9 Maths Exercise 1.5 in Hindi

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems in Hindi Medium and English medium has been updated for academic session 2024-25. Tiwari Academy is a popular online platform that provides educational resources and solutions for students. As we continue to offer Class 9 Maths NCERT Solutions, here are some potential benefits of using Tiwari Academy for learning Class 9 Maths. Question-answers and solutions are modified as per revised NCERT book published for 2024-25 syllabus. We typically provides simple yet complete solutions to NCERT textbooks, including step-by-step explanations for each problem. This can be especially helpful for students who may find difficulty in understanding certain concepts.

All the Solutions for Class 9th Maths Chapter 1 have been updated according to latest CBSE Curriculum and NCERT Books for 2024-25. Since UP Board Students are using same NCERT Textbooks , they can also download UP Board Solutions for Class 9 Maths Chapter 1 in Hindi Medium or English Medium. Class 9 Maths NCERT Solutions have been provided by explaining the formulae and giving step by step explanation.

The content is according to the latest CBSE syllabus 2024-25 for the students of CBSE Board as well as UP Board and MP Board following the updated NCERT (https://ncert.nic.in/) Books for their final exams. Solutions for chapter 1 9th Maths are available in PDF format on our website Tiwari Academy and also through videos on Apps and website.

Study Materials on 9th Maths Chapter 1

• Study Material 9th Maths Chapter 1 for 2024-25 – English Medium
• Study Material 9th Maths Chapter 1 for 2024-25 – Hindi Medium
• Class 9 Mathematics Solutions Main Page

The topic Number Systems is the basis of Arithmetic. It is like learning the alphabets of any mathematics. We can say that 9th Maths chapter 1 is the foundation of Maths for secondary classes. CBSE NCERT Solutions for Class 9 mathematics Chapter 1 Number Systems in PDF format. These solutions are available for free download for session 2024-25. These are updated as per latest curriculum. Kindly visit the Discussion Forum and become a partner in knowledge sharing in mathematics. NCERT Solutions Offline Apps 2024-25, work without internet connection. Everything on Tiwari Academy website and Apps are available free of cost. No login or registration is required.

Important Questions on 9th Maths Chapter 1

Is zero a rational number can you write it in the form p/q, where p and q are integers and q≠0.

Yes, zero is a rational number. It can be written in the form of p/q. For example: 0/1, 0/2, 0/5 are rational numbers, where p and q are integers and q≠0.

Simplify each of the following expression: (3 + √3)(2 + √2)

(3 + √3)(2 + √2) = 6 + 3√2 + 2√3 + √6

Find six rational numbers between 3 and 4.

Six rational numbers between 3 and 4 are 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6.

Express 0.99999… in the form of p/q . Are you surprised by your answer?

0.99999… Let x = 0.99999… … (i) Multiplying equation (i) by 10 both sides 10x = 9.99999… ⇒ 10x = 9 + 0.99999…… ⇒ 10x = 9 + x [From equation (i)] ⇒ 10x – x = 9 ⇒ 9x = 9 ⇒ x = 9/9 = 1 The answer makes sense as 0.99999… is very close to 1, that is why we can say that 0.99999=1.

Write three numbers whose decimal expansions are non-terminating non-recurring.

Three non-terminating non-recurring decimals: 0.414114111411114… 2.01001000100001… π=3.1416…

1. Natural numbers are those numbers which are used for counting. 2. Whole numbers are the collection of all natural numbers together with zero. 3. Integers are the collection of all whole numbers and negative of natural numbers. 4. Rational numbers are those numbers which can be expressed in the form of p/q, where p, q are integers and q is not equal to 0. 5. Irrational numbers are those numbers which cannot be expressed in the form of p/q, where p, q are integers and q is not = 0. 6. Real numbers are the collection of all rational and irrational numbers.

Two numbers are said to be equivalent, if numerators and denominators of both are in proportion or they are reducible to be equal. The decimal expansion of real numbers can be terminating or non-terminating repeating or non-terminating non-repeating. The decimal expansion of rational numbers can either be terminating or non-terminating and vice-versa. The decimal expansion of irrational numbers can either be non-recurring and vice-versa.

If a is a rational and b is an irrational, then a + b and a – b are irrational, and ab and a/b are irrational numbers, where b is not equal to 0. If a and b both are irrational, then a+b, a-b, ab and a/b may be rational or irrational. If a be any real number and n be any positive integer such that a^1/n = n√a is a real number, then ‘n’ is called exponent, a is called radical and √ is called radical sign.

How many questions in each exercise are given in chapter 1 of class 9 Maths?

There are 6 exercises in chapter 1 (Number systems) of class 9 Maths. In the first exercise (Ex 1.1), there are four questions. In the second exercise (Ex 1.2), there are four questions. In the third exercise (Ex 1.3), there are nine questions. In the fifth exercise (Ex 1.4), there are five questions. In the sixth exercise (Ex 1.5), there are three questions. So, there are in all 25 questions in chapter 1 (Number systems) of class 9 Maths. There are in all 20 examples in chapter 1 (Number systems) of class 9 Maths.

What are the core topics to study in chapter 1 Number systems of class 9 Mathematics?

In chapter 1, Number systems of class 9 Maths, students will study: 1. Natural Numbers, Whole Numbers, Integers, Rational Numbers. 2. Irrational Numbers. 3. Real Numbers and their Decimal Expansions. 4. Representing Real Numbers on the Number Line. 5. Operations on Real Numbers. 6. Laws of Exponents for Real Numbers.

Is chapter 1 of class 9th Maths difficult to solve?

Chapter 1 of class 9th Maths is not easy and not difficult. It lies in the middle of easy and difficult because some examples and questions of this chapter are easy, and some are difficult. However, the difficulty level of anything varies from student to student. So, Chapter 1 of class 9th Maths is easy or not depends on students also. Some students find it difficult, some find it easy, and some find it in the middle of easy and difficult.

How long it takes to study chapter 1 of class 9th Maths?

Students need a maximum of eight days to do chapter 1 of class 9th Maths if they give at least 2 hours per day to this chapter. This time also depends on student’s speed, efficiency, capability, and many other factors.

Chapter 2. Polynomials »

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NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 1 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 1 Number Systems NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.3

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.4

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.6

NCERT Solutions for Class 9 Maths Chapter 1 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter. As Number System is one of the important topics in Maths, it has a weightage of 6 marks in class 9 Maths exams. 

• Introduction of Number Systems
• Irrational Numbers
• Real Numbers and Their Decimal Expansions
• Representing Real Numbers on the Number Line.
• Operations on Real Numbers
• Laws of Exponents for Real Numbers

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• NCERT Solutions for Class 9 Maths Chapter 1 Free PDF Download

NCERT Solutions for Class 9 Maths Chapter 1 Number System

Learning of fundamentals in maths is always essential. NCERT Solutions for Class 9 Maths Chapter 1 will strengthen the student’s fundamental concept regarding numbers and number systems. It will help students to score better marks in exams. Our expert teachers of maths are constantly working hard for the subject to give the best NCERT Solutions for Class 9 Maths Chapter 1 Number System.

NCERT Solutions give a self-explanatory solution for every question of the chapter and will also help students to complete their homework without any external help.

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Download  NCERT Solutions for all subjects here

Download  NCERT Solutions for Class 9 here

Download  NCERT Solutions for Class 9 Maths Chapter-wise here

CBSE Class 9 Maths Chapter 1 Number System

NCERT Solutions for Class 9 Maths Chapter 1 Number System help students to understand numbers and integers with their various operations in a self-explanatory format. Information collected in our day to day life contains numbers. The different types of problems and examples will help to get strong concepts of the number system.

Sub-topics covered under NCERT Solutions for Class 9 Maths Chapter 1

1.1: Introduction

1.2: Irrational Numbers

1.3: Real Numbers and their Decimal Expansions

1.4: Representing Real Numbers on the Number Line

1.5: Operations on Real Numbers

• 1.6: Laws of Exponents for Real Numbers and

1.7: Summary

NCERT Solutions for Class 9 Maths Chapter 1

NCERT Solutions for Class 9 Maths Chapter 1 Number System help students to understand this fundamental chapter of Mathematics. This will create a strong basic understanding of numbers and their properties. Number System is useful in our day to day life also for performing various operations related to numbers. The different types of numbers like real numbers, rational numbers, and irrational numbers will give a strong understanding to the students.

Let us discuss the sub-topics in detail.

This chapter is about the numbers and their world. It discusses the properties of numbers and various types of numbers existing in maths. Rational numbers are the numbers in the form fractions are repeated decimal.

These are the numbers that are not expressible in the form of a fraction. Also, it covers the numbers with unpredictable digits after decimals. Many values containing pie are also irrational numbers. The student will learn the methods to represent these numbers on the number line using a compass.

This section explains about the representation of real numbers in decimal expansions format. It covers the numbers giving zero as well as non-zero remainders. Such expansions may be either termination or non-terminating.

The student will know that each and every real number is expressible on the number line. It shows their existence is real.

The student will about various operations on the numbers. They will also come to know about possible and not possible operations over rational numbers.

1.6: Laws of Exponents for Real Numbers

This is an interesting topic. It explains about exponents operated over real numbers. Also, the various formula will help students to perform the operations.

It is very clear that knowing about numbers and their properties is very essential. This chapter is doing that important task effectively. The student will get a lot from this chapter.

Download NCERT Solutions for Class 9 Maths Chapter 1 by clicking on the download button below

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We provide NCERT Solutions that give step by step solution for all numerical and conceptual problems. These solutions will help students to frame a better understanding of all the topics. We also provide free pdf downloads, free online classes, free video lectures, and free doubt clearing sessions. Our Maths teachers are highly capable and experienced. We are just a click away. Download Toppr for  Android  and  iOS  or  signup  for free.

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NCERT Solutions for Class 9

• NCERT Solutions for Class 9 History Chapter 3 Free PDF Download
• NCERT Solutions for Class 9 History Chapter 6 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 15 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 7 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 14 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 12 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 9 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 4 Free PDF Download
• NCERT Solutions for Class 9 Maths Chapter 11 Free PDF Download

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NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems: NCERT Solutions for Class 9 maths chapter 1 number systems begin with an introduction to the number system and the various types of numbers within it. Embibe’s expert professors have created Class 9 Maths chapter 1 NCERT solutions. These NCERT Class 9 Maths chapter 1 solutions assist students in dealing with challenges in their final exam preparation. These solutions also simplify problems so that students can understand them.

Number Systems discusses the Origin and History of Numbers, Integers, Rational Numbers, Non-Terminating, Non-Recurring Decimals, Irrational Number Properties, and many other topics. Embibe provides over 470+ practice questions for all of the subtopics covered in Chapter 1. Students must practice all of Embibe’s practice questions without fail. They can also attempt unlimited mock tests and go through the explainer videos for better understanding. Scroll down to learn more.

NCERT Solutions for Class 9 Maths Chapter 1: Important Topics

This exercise is easy to understand, and students can build fundamentals that will benefit them in the long run for entrance exams. Students will get exposed to a wide variety of problems that will help them in developing problem-solving skills. Students are advised to go through the chapter’s video lessons before moving on to problem-solving.

At Embibe, students can find the solutions to every question of this exercise. All the solutions are offered for, and students can also access NCERT 3D Videos, NCERT Exemplars , Embibe Explainers, practice questions , mock tests and so on for.

We have provided the list of topics included in this exercise below:

NCERT Solutions for Class 9 Maths Chapter 1: Points To Remember

Some of the important points related to Number Systems have been mentioned below for quick reference of students.

• Natural Numbers: These are the counting numbers (1, 2, 3,1, 2, 3, etc.).
• Whole Numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers.
• Prime Numbers: A natural number larger than 11 is a prime number if it does not have other divisors except for itself and 11. (The lowest prime number is 22. 22 is also the only even prime number. The lowest odd prime number is 33.)
• Composite Numbers: It is a natural number that has at least one divisor different from unity and itself.
• Odd Numbers: An integer that is not an even number is an odd number.
• Divisibility Tests: (i) Divisibility by 22 or 55: A number is divisible by 22 or 55 if the last digit is divisible by 22 or 55. (ii) Divisibility by 33 (or 99): All such numbers, the sum of whose digits are divisible by 33 (or 99), are divisible by 33 (or 99). (iii) Divisibility by 44: A number is divisible by 44 if the last 22 digits are divisible by 44. (iv) Divisibility by 66: A number is divisible by 66 if it is simultaneously divisible by 22 and 33. (v) Divisibility by 88: A number is divisible by 88 if the last 33 digits of the number are divisible by 88.

NCERT Solutions for Class 9 Maths: All Chapters

The detailed NCERT Class 9 Maths solutions are provided below for:

• 1st Chapter: Number Systems
• 2nd Chapter :  Polynomials
• 3rd Chapter: Coordinate Geometry
• 4th Chapter :  Linear Equations in Two Variables
• 5th Chapter :  Introduction to Euclid’s Geometry
• 6th Chapter: Lines and Angles
• 7th Chapter :  Triangles
• 8th Chapter: Quadrilaterals
• 9th Chapter: Areas of Parallelograms and Triangles
• 10th Chapter: Circles
• 11th Chapter: Constructions
• 12th Chapter: Heron’s Formula
• 13th Chapter: Surface Areas and Volumes
• 14th Chapter: Statistics
• 15th Chapter: Probability

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Students should take mock tests for NCERT Class 9 Maths subjects. It will help them prepare for the exam better. Click on the links below to access NCERT Class 9 Maths mock tests on Embibe:

FAQs on NCERT Solutions for Class 9 Maths Chapter 1

Some of the frequently asked questions on the NCERT Solutions for 9th Maths Chapter 1 are as follows:

Ans:  The concepts are explained in simple language in the NCERT solutions for Class 9 chapter 1 Maths by Embibe. The NCERT solutions are prepared by a team of experts at Embibe to help students enhance their exam preparation.

Ans:   Students will learn that a number system is called a rational number if it can be written as p/q, the decimal expansion of a rational and irrational number, and what is a real number and so on.

Ans:  The exercises covered in NCERT chapter 1 of Class 9 Maths are as follows:  1) Exercise 1.1: 4 Questions (4 short answers)  2) Exercise 1.2: 4 Questions (4 short answers)  3) Exercise 1.3: 9 Questions (8 short answers, 1 long answer)  4) Exercise 1.4: 2 Questions (2 long answers)  5) Exercise 1.5: 5 Questions (4 short answers, 1 long answer)  6) Exercise 1.6: 3 Questions (3 short answers).

Ans:  The NCERT solutions by Embibe will help students understand the chapter better. The NCERT solutions for chapter 1 of Class 9 Maths have been explained in a step-by-step and detailed manner through videos so that any student can understand them.

Ans:  Students can get the NCERT Solutions for Class 9 Maths Chapter 1 for from Embibe, and in return, they get tricks, tips, and notes that they can revise at the last minute before the exam. This will help the students to score well.

We hope you liked this detailed article on NCERT Solutions for 9th Maths Chapter 1. For more, stay tuned to Embibe.

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NCERT Solutions For Maths Chapter 1 Exercise 1.1 Class 9 - Number System

• NCERT Solutions
• Chapter 1 Number Systems Exercise 1.1

NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.1- FREE PDF Download

Chapter 1 of Class 9 Maths, "Number System," introduces students to the fundamental concepts of numbers, their classifications, and properties. Exercise 1.1 focuses on understanding different types of numbers, including natural, whole, integers, rational, and irrational numbers. Vedantu's NCERT Solutions for Class 9 Maths Chapter 1 - Number System are essential for exam success.

Solutions of class 9 ex 1.1 prepared by maths experts help students understand important concepts, boost confidence, and improve exam scores. These comprehensive solutions are available for free on Vedantu, making subjects like Science, Maths, and English easier to study.

Glance on NCERT Solutions Maths Chapter 1 Exercise 1.1 Class 9 | Vedantu

This exercise lays the groundwork for understanding the various number systems we use in mathematics.

Natural Numbers : These are the counting numbers, starting from 1 (1, 2, 3, ...).

Whole Numbers : These include natural numbers and zero (0, 1, 2, 3, ...).

Integers : This set comprises whole numbers and their negative counterparts (... -3, -2, -1, 0, 1, 2, 3, ...).

Rational Numbers : Numbers that can be expressed as a fraction (p/q), where p and q are integers and q ≠ 0 (e.g., 1/2, 3/4, -5/7).

Irrational Numbers : Numbers that cannot be expressed as a terminating or repeating decimal (e.g., √2, π).

By working through the problems in this exercise, students will gain practice in identifying different types of numbers and understanding their properties.

Exercise 1.1 Class 9th Class Math Solution Chapter 1 has over all 4 questions, all 4 are short answers.

Topics Covered in Class 9 Maths Chapter 1 Exercise 1.1

Different Types of Numbers.

Representation of Numbers.

Operations on Numbers.

Properties of Numbers.

Classifying Numbers.

Access PDF for Maths NCERT Chapter 1 Number System Exercise 1.1 Class 9

Exercise (1.1).

1.  Is zero a rational number? Can you write it in the form  $\dfrac{ {p}}{ {q}}$, where $ {p}$ and $ {q}$ are integers and $ {q}\ne  {0}$? Describe it.

Ans: Remember that, according to the definition of rational number,

a rational number is a number that can be expressed in the form of  $\dfrac{p}{q}$, where $p$ and $q$ are integers and  $q\ne \text{0}$. 

Now, notice that zero can be represented as $\dfrac{0}{1},\dfrac{0}{2},\dfrac{0}{3},\dfrac{0}{4},\dfrac{0}{5}.....$

Also, it can be expressed as $\dfrac{0}{-1},\dfrac{0}{-2},\dfrac{0}{-3},\dfrac{0}{-4}.....$

Therefore, it is concluded from here that $0$ can be expressed in the form of $\dfrac{p}{q}$, where $p$ and $q$ are integers.

Hence, zero must be a rational number.

2. Find any six rational numbers between $ {3}$ and $ {4}$. 

Ans: It is known that there are infinitely many rational numbers between any two numbers. Since we need to find $6$ rational numbers between $3$ and $4$, so multiply and divide the numbers by $7$ (or by any number greater than $6$)

Then it gives, 

$\begin{align} & 3=3\times \dfrac{7}{7}=\dfrac{21}{7} \\ & 4=4\times \dfrac{7}{7}=\dfrac{28}{7} \\ \end{align}$

Hence, $6$ rational numbers found between $3$ and $4$ are $\dfrac{22}{7},\dfrac{23}{7},\dfrac{24}{7},\dfrac{25}{7},\dfrac{26}{7},\dfrac{27}{7}$.

3. Find any five rational numbers between $\dfrac{ {3}}{ {5}}$ and $\dfrac{ {4}}{ {5}}$.

Ans: It is known that there are infinitely many rational numbers between any two numbers.

Since here we need to find five rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$,  so multiply and divide by $6$ (or by any number greater than $5$).

Then it gives,

$\dfrac{3}{5}=\dfrac{3}{5}\times \dfrac{6}{6}=\dfrac{18}{30}$,

$\dfrac{4}{5}=\dfrac{4}{5}\times \dfrac{6}{6}=\dfrac{24}{30}$.

Hence, $5$ rational numbers found between $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are  $\dfrac{19}{30},\dfrac{20}{30},\dfrac{21}{30},\dfrac{22}{30},\dfrac{23}{30}$.

4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number. 

Ans: Write the whole numbers and natural numbers in a separate manner.

It is known that the whole number series is $0,1,2,3,4,5.....$. and

the natural number series is $1,2,3,4,5.....$.

Therefore, it is concluded that all the natural numbers lie in the whole number series as represented in the diagram given below.

Thus, it is concluded that every natural number is a whole number.

Hence, the given statement is true.

(ii) Every integer is a whole number.

Ans: Write the integers and whole numbers in a separate manner.

 It is known that integers are those rational numbers that can be expressed in the form of $\dfrac{p}{q}$, where $q=1$.

Now, the series of integers is like $0,\,\pm 1,\,\pm 2,\,\pm 3,\,\pm 4,\,...$.

But the whole numbers are $0,1,2,3,4,...$. 

Therefore, it is seen that all the whole numbers lie within the integer numbers, but the negative integers are not included in the whole number series. 

Thus, it can be concluded from here that every integer is not a whole number.

Hence, the given statement is false.

(iii) Every rational number is a whole number.

Ans: Write the rational numbers and whole numbers in a separate manner. 

It is known that rational numbers are the numbers that can be expressed in the form  $\dfrac{p}{q}$, where $q\ne 0$ and the whole numbers are represented as $0,\,1,\,2,\,3,\,4,\,5,...$

Now, notice that every whole number can be expressed in the form of $\dfrac{p}{q}$

as  \[\dfrac{0}{1},\text{ }\dfrac{1}{1},\text{ }\dfrac{2}{1},\text{ }\dfrac{3}{1},\text{ }\dfrac{4}{1},\text{ }\dfrac{5}{1}\],…

Thus, every whole number is a rational number, but all the rational numbers are not whole numbers. For example,

$\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5},...$ are not whole numbers.

Therefore, it is concluded from here that every rational number is not a whole number.

Class 9th Maths Exercise 1.1 provides a foundational understanding of the Number System. It introduces natural numbers, whole numbers, integers, rational numbers, and irrational numbers. The exercise emphasizes representing these numbers on the number line, which enhances visual learning and comprehension. By completing this exercise, students build a critical base for more advanced mathematical concepts, fostering logical reasoning and problem-solving skills essential for future studies. Students that practise these kinds of questions will gain confidence and perform well on tests.

Class 9 Maths Chapter 1: Exercises Breakdown

CBSE Class 9 Maths Chapter 1 Other Study Materials

Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

FAQs on NCERT Solutions For Maths Chapter 1 Exercise 1.1 Class 9 - Number System

1.  What does this chapter mainly deals with?

Ans: The chapter mainly focuses on different types of numbers. They are: 

Complex Number

Imaginary Number

Real Number

Rational Number

Irrational Numbers

Whole Numbers

Natural Numbers

Natural Numbers - any of the given numbers that are used for counting purpose, starting from one, is considered a natural number.

Whole Numbers - the total union set of all the Natural numbers which includes zero are the set of whole numbers.

Integers - the set of all the whole numbers including their negative terms is called the set of integers.

Rational Numbers - any number which can be written as a ratio of two natural numbers is known as a rational number.

Irrational Numbers - any number which cannot be written in the form of a ratio of two natural numbers is known as an irrational number.

2.  Give a brief on decimal and decimal classification.

Ans: Decimal is very interesting and fun part of the Number System. Decimal fractions were first introduced and used by Chinese at the end of the 4 th century and then spread to the Middle East and from there to Europe. Decimals are used in our daily life without consciousness. For instance – counting of money, filling fuel into our vehicle or while measuring our weight. Decimals can never be whole numbers. Few example: 1.8, 000.23 etc.

Decimals classifications: Terminating decimal fractions are 17/4= 4.25, 21/5 = 4.2 and so on.

Non- terminating decimal fractions are 16/3 = 5.33333 , 15.35353535 etc.

Integer: All the numbers that does not have decimals in them are known as integers. Thus, -9, 4, 1476 etc. Do you know? All integers are whole numbers including the negative numbers.

3.  Give an overview of the chapter Number system.

Ans: In this Chapter, you will get to learn about the different types of numbers along with their varied characteristics. The chapter primarily deals with irrational numbers, real numbers and their decimal expansion. It is followed by representing real numbers on the numbers, operating on real numbers, and lastly laws of exponents for real numbers.

You will also be able to learn about rational numbers and irrational numbers with their properties. The chapter also introduces you to: 

Classification of expressions into rational or irrational numbers

Simplification of expressions

Number Line representation

Rationalization

4.  How Vedantu will help me in exam preparation?

Our NCERT solutions are prepared by our maths experts with various real-life examples. These examples will make you understand the concept quickly and memorise them for a longer time. Solutions provided to the questions are 100% accurate in the exercises which are crisp and concise to the point.

Our solutions are the best study guides, which help you in smart learning and efficient answering of questions. These solutions will also help you in improving a strong conceptual base with all the important concepts in a very easy and understandable language. You will also enjoy learning from our solutions which are really fun and interactive.

5. Is the Chapter Number System Exercise 1.1 important for Class 9 Maths?

Ans: The Number System is one of the most important aspects of the NCERT Solutions for Class 9 Maths. The mathematical notations produced using numbers and symbols are known as the Number System. Exercise 1.1 is a must-do to get a basic understanding of this chapter and also from the examination point of view. Vedantu will be there for you every step of the way, from comprehending rational and irrational numbers to solving problems with them.

6. Do I need to practice all the questions provided in Chapter 9 Maths Exercise 1.1 NCERT Solutions?

Ans: Yes, you must practise all of the questions in Chapter 9 Maths Exercise 1.1. Each question puts your knowledge to the test, emphasising the need for practising. Students may test themselves by answering all of the questions in this exercise, which will help them resolve their concerns and learn fundamental skills. NCERT answers provide in-depth knowledge in an easy-to-understand format.

7. Why should we refer to NCERT books for chapter 1 exercise 1.1 Maths for class 9?

Ans: The most compelling argument to utilise NCERT books is that they correspond to the CBSE curriculum to the letter. They are quite beneficial to CBSE kids. Books are factual and authored by subject matter specialists. All of the topics are described in simple terms. These answers have been created by professional lecturers to help you prepare for your exams. To boost your confidence and test result, visit the page NCERT Solutions for Class 9 Maths Chapter 1 exercise 1.1 by Vedantu at free of cost on the official website and on the Vedantu app.  

8. What are the different types of numbers in the number system of Class 9 Maths? 

Ans: There are eight types of numbers to study in class 9:

Rational number

Irrational number

Whole numbers

Natural numbers

9. What is the difference between a rational number and an irrational number?

Ans: A rational number is a ratio of two integers in which the denominator is not zero. Interestingly, a repeating decimal is also known as a rational number. A rational number is a kind of real number with a non-zero denominator. For eg: ½, 3.4 etc. A real number that cannot be expressed as a simple fraction is called an irrational number. For eg: 4/0

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Class 9 Mathematics Assignments

We have provided below free printable Class 9 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 9 Mathematics . These Assignments for Grade 9 Mathematics cover all important topics which can come in your standard 9 tests and examinations. Free printable Assignments for CBSE Class 9 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 9 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 9. Students can click on the links below and download all Pdf Assignments for Mathematics class 9 for free. All latest Kendriya Vidyalaya Class 9 Mathematics Assignments with Answers and test papers are given below.

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We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics and CBSE Assignments for Mathematics Class 9 will be really helpful for standard 9th students to prepare for the class tests and school examinations. Class 9th students can easily free download in Pdf all printable practice worksheets given below.

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Free Online Quiz for Class 9 Maths Chapter 2 Polynomials

Table of Contents

Welcome to our free online quiz for Class 9 Maths , focusing on Chapter 2 Polynomials ! This chapter is an important part of the CBSE Class 9 Maths Syllabus and helps you understand polynomials, including definitions, types, and how to solve polynomial expressions.

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Target Exam ---

To help you prepare, use NCERT Solutions and worksheets for practice. We also provide extra questions and a polynomials worksheet to test your knowledge. Completing these exercises will boost your confidence and get you ready for your exams. Start the quiz to strengthen your understanding!

What Are Polynomials?

In simple terms, a polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x 2 +3x+52×2+3x+5 is a polynomial. Understanding what is polynomial class 9 will help you grasp the concepts needed for solving various mathematical problems.

Class 9 Maths Chapter 2 Polynomials Quiz with Answer

This free online quiz is an excellent tool for students to practice and review Chapter 2 Polynomials from the CBSE Class 9 Maths Syllabus. It covers important concepts related to polynomials, giving you a great opportunity to test your understanding. The quiz works well with the exercises found in the NCERT Solutions for Class 9 Maths and can be used alongside worksheets for Class 9 Maths . It’s a fun and engaging way to improve your math skills and prepare effectively for your exams!

Overview of Class 9 Chapter 2 Polynomials

Chapter 2 in Class 9 Maths explains polynomials , which are algebraic expressions made up of numbers and variables. Here’s a breakdown of important topics in simple words:

• Introduction to Polynomials : Learning what polynomials are and how they work.
• Types of Polynomials : Understanding different types like linear (one degree), quadratic (two degrees), and cubic (three degrees).
• Degree of a Polynomial : The highest power of the variable in the polynomial.
• Zeroes of a Polynomial : Points where the polynomial equals zero.
• Factorization of Polynomials : Breaking polynomials into simpler factors.
• Algebraic Identities : Important formulas used to simplify and solve polynomial problems.

Quiz on Polynomial Class 9 Maths

To remember the concepts learned in this chapter, here are 5 quiz for class 9 Maths chapter 2 Polynomial with their answers:

Quiz 1 on Class 9 Maths Chapter 2 – Polynomials:

This quiz introduces you to the basic concepts of polynomials, including their definition and different types. It’s a great way to test your understanding of the fundamentals.

Polynomial Quiz 1

Quiz 2 on Class 9 Maths Chapter 2 – Polynomials:

In this quiz, you’ll focus on identifying the degree of polynomials and understanding their importance in algebra.

Polynomial Quiz 2

Quiz 3 on class 9 maths chapter 2 – polynomials:.

This quiz covers how to find the zeroes of a polynomial and explore their properties.

Polynomial Quiz 3

Quiz 4 on class 9 maths chapter 2 – polynomials:.

Learn how to factorize polynomials and simplify expressions in this practice quiz.

Polynomial Quiz 4

Quiz 5 on Class 9 Maths Chapter 2 – Polynomials:

The final quiz helps you master algebraic identities and how they apply to solving polynomial problems.

Polynomial Quiz 5

Important topics of class 9 maths chapter 2 – polynomials.

• Introduction to Polynomials : Learn what polynomials are and how they are formed using variables and coefficients.
• Types of Polynomials : Explore linear, quadratic, and cubic polynomials based on their degree (highest power of the variable).
• Degree of a Polynomial : Understand how to find the degree, which is key to solving polynomial equations.
• Zeroes of a Polynomial : Learn how to find the values of the variable where the polynomial equals zero.
• Factorization of Polynomials : Break polynomials into simpler factors to make solving easier.
• Algebraic Identities : Use important formulas to simplify polynomial expressions and solve problems faster.

Polynomials Quiz FAQs

What topics are covered in the polynomials quiz.

The quiz includes questions on the definition, types, degree, zeroes, and factorization of polynomials.

Is there a time limit for the Polynomials Quiz?

Yes, most quizzes have a time limit, typically between 10-20 minutes, depending on the platform.

How can I prepare for the Polynomials Quiz?

Review concepts from your textbook, use NCERT Solutions, and practice with worksheets.

Are there any difficult questions in the quiz?

The quiz includes a mix of basic and challenging questions to test your understanding.

Is this quiz helpful for Class 9 exams?

Yes, it covers important topics from the CBSE Class 9 Maths Syllabus and helps in exam preparation.

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• CBSE Notes For Class 9
• Class 9 Math Notes
• Chapter 1: Number System

Number System Class 9 Notes - Chapter 1

Cbse class 9 maths number system notes, introduction to number systems.

The number system is the process of representing numbers on the number line using certain rules and symbols. A number line is a depiction of numbers on a straight line with a specified interval between them. The number system is used to do mathematical computations ranging from complex scientific calculations to counting the number of chocolates left in the box. In this article, we are going to discuss the Class 9 Maths Chapter 1 Number System. To know more about Number System, visit here .

What Are Numbers?

Number: An arithmetical value representing a particular quantity. The various types of numbers are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, etc.

To know more about Numbers, visit here .

Natural Numbers

Natural numbers (N) are positive numbers i.e. 1, 2, 3 and so on. Natural numbers are positive integers.

To know more about Natural Numbers, visit here .

Whole Numbers

Whole numbers (W) are 0, 1, 2 and so on. Whole numbers are all natural numbers, including ‘0’. Whole numbers do not include any fractions, negative numbers or decimals. To know more about Whole Numbers, visit here .

Integers are numbers that include whole numbers along with negative numbers. An integer is a number from a set of negative and positive numbers, including zero, which has no decimal or fractional value. -3, 2, 0, 15, 900, etc., are examples of integers. Z is the symbol for a set of integers.

To know more about Integers, visit here .

Rational Numbers

A number ‘r’ is called a rational number if it can be written in the form p/q, where p and q are integers and q ≠ 0. Some examples of rational numbers include 3/5, 7/2, 11/13, and so on.

To know more about Rational Numbers, visit here .

Irrational Numbers

Any number that cannot be expressed in the form of p/q, where p and q are integers and q≠0, is an irrational number. Examples: √2, 1.010024563…, e, π To know more about Irrational Numbers, visit here . Properties of Irrational Numbers The following are the four properties of irrational numbers: (i) Negative of an irrational number is an irrational number. (ii) Sum and difference of a rational and an irrational number is always an irrational number. (iii) Sum, product and difference of two irrational numbers is either a rational or irrational number. (iv) Product of a rational number with an irrational number is either rational or irrational.

Real Numbers

Any number which can be represented on the number line is a real number (R). It includes both rational and irrational numbers. Every point on the number line represents a unique real number. Examples of real numbers include -15, 3.14, 25, 22/7 and so on. To know more about Real Numbers, visit here .

Also, read:

• Prime Numbers
• Composite Numbers
• Co Prime Numbers
• Even and Odd Numbers

For more information on Number Systems, watch the below video

Representation of Irrational Numbers on the Number Line

Let √x be an irrational number. To represent it on the number line we will follow the following steps:

• Take any point A. Draw a line AB = x units.
• Extend AB to point C such that BC = 1 unit.
• Find out the mid-point of AC and name it ‘O’. With ‘O’ as the centre draw a semi-circle with radius OC.
• Draw a straight line from B which is perpendicular to AC, such that it intersects the semi-circle at point D.

Length of BD=√x.

• With BD as the radius and origin as the centre, cut the positive side of the number line to get √x.

Identities for Irrational Numbers

Arithmetic operations between:

• Rational and irrational will give an irrational number. Example: 2 × √3 = 2√3 i.e. irrational.
• Irrational and irrational will give a rational or irrational number. Example: √3 × √3 = 3 which is rational

If a and b are real numbers,

• √(ab) = √a√b
• (√a+√b) (√a-√b) = a – b
• (a+√b)(a−√b) = a²−b
• (√a+√b)(√c+√d) = √ac+√ad+√bc+√bd
• (√a+√b)(√c−√d) = √ac−√ad+√bc−√bd
• (√a+√b) 2 = a+2√(ab)+b

Rationalisation

Rationalisation is the process of converting an irrational number into a rational number. For example, the rationalisation of 1/√2 is: 1/√2 × √2/√2 = √2/2 We know that √2 = 1.414. Hence, we can write it as = 1.414/2, which can be easily represented on the number line.

Laws of Exponents for Real Numbers

If a, b, m and n are real numbers then:

• a m  × a n = a m+n
• (a m ) n  = a mn
• a m /a n  = a m−n , where (m > n)
• a m b m =(ab) m

Here, a and b are the bases and m and n are exponents.

Decimal Representation of Rational Numbers

The decimal representation of a rational number is the process of converting a rational number into a decimal number. The converted decimal number should be equal to the given rational number. This process can be done with the help of the long division method. Once the rational numbers are converted into decimal values, we can easily represent them on the number line.

Decimal Expansion of Rational and Irrational Numbers

The decimal expansion of a rational number is either terminating or non-terminating and recurring.

Example: 1/2 = 0.5 , 1/3 = 3.33……. The decimal expansion of an irrational number is non terminating and non-recurring. Examples: √2 = 1.41421356.. To know more about decimal expansion of rational numbers, visit here .

Expressing Decimals as Rational Numbers

Case 1 – terminating decimals.

Example: 0.625

Let x = 0.625

Step 1: If the number of digits after the decimal point is y, then multiply and divide the number by 10 y .

So, x = 0.625 × (1000/1000) = 625/1000.

Step 2: Reduce the obtained fraction to its simplest form.

Hence, x = 5/8

Case 2: Recurring Decimals

If the number is non-terminating and recurring, then we will follow the following steps to convert it into a rational number:

Step 1: Let x be the given recurring decimal

Step 2: Multiply the first equation with 10 y , where y is the number of digits that are recurring.

Multiply both sides of (1) by 100.

Step 3. Subtract equation (1) from equation (2).

On subtracting equation (1) from (2), we get

⇒ 99x = 103.2

⇒ x = 103.2/99 = 1032/990

Which is the required rational number.

Step 4: Reduce the obtained rational number to its simplest form.

Thus, x = 172/165.

Frequently Asked Questions on CBSE Class 9 Maths Notes Chapter 1 Number System

What is the number system.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.

What is rationalisation?

Rationalization is the process of removing a radical or surd from the denominator and shifting it to the numerator.

What is a recurring decimal?

A recurring decimal exists when decimal numbers repeat forever.

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