maths assignment class 9 chapter 1

Search This Blog

Cbse mathematics.

Basic concepts, definitions and formulas of mathematics, mathematics assignments for 9th standard to 10+2 standard, maths study material for 8th, 9th, 10th, 11th, 12th classes, Mathematics lesson plan for classes 8th,10th and 12th standard, Interesting maths riddles and maths magic, Class-wise mathematics study material for students from 8th to 12. A complete resource centre of mathematics for students and teachers

Featured Posts

Maths assignment class viii | quadrilateral, math assignment class ix ch -1| number system, maths assignment   class 9th chapter 1.

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

Download complete pdf file 

Plese send us solution today is our test

Need solutions toooo

Post a Comment

Breaking news, popular post on this blog, lesson plan maths class 10 | for mathematics teacher.

Lesson Plan Math Class 10 (Ch-1) | Real Numbers

Lesson Plan Math Class X (Ch-2) | Polynomials

• Assignment 10 15
• Assignment 11 12
• Assignment 12 14
• Assignment 8 8
• Assignment 9 5
• Lesson plan 10 15
• Lesson Plan 12 13
• Lesson Plan 8 10
• Maths 10 20
• Maths 11 21
• Maths 12 17

SUBSCRIBE FOR NEW POSTS

Get new posts by email:.

• 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.

Toppr provides free study materials, the last 10 years of question papers, 1000+ hours of video lectures for free. Download Toppr for  Android  and  iOS  or  signup  for free.

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

Download Toppr – Best Learning App for Class 5 to 12

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.

Customize your course in 30 seconds

Which class are you in.

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

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Download the App

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

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

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.

Mathematics Class 9 Assignments Pdf Download

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.

Topicwise Assignments for Class 9 Mathematics Download in Pdf

More assignments for class 9 mathematics.

Advantages of Class 9 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 9, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 9 .
• All Mathematics assignments for Class 9 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 9 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 9 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 9 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 9 which you can download in Pdf

We provide here Standard 9 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 9, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 9 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 9 for all subjects. You can download them all and use them offline without the internet.

Related Posts

Class 9 Mathematics Constructions Assignments

Class 9 Sanskrit Assignments

Class 9 Social Science Economics Assignments

NCERT Solutions Class 9 Maths Chapter 1 Number Systems

NCERT solutions for class 9 maths chapter 1 number systems consists of an introduction about the number system and the different kinds of numbers in it. The number system has been classified into different types of numbers like natural numbers, whole numbers , integers, rational numbers, irrational numbers , etc. The NCERT solutions class 9 maths chapter 1 covers all the basics of the number system which will be helpful in forming the basic foundation of mathematics.

Class 9 maths chapter 1 number systems will help the students in differentiating between rational and irrational numbers, wherein irrational numbers cannot be expressed in the form of a ratio, and also about real numbers. Class 9 maths NCERT solutions chapter 1 number systems sample exercises can be downloaded from the links below and also you can find some of these in the exercises given below.

• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.3
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.4
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.5
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.6

NCERT Solutions for Class 9 Maths Chapter 1 PDF

These NCERT solutions for class 9 maths involving the important concepts of real numbers , rational and irrational numbers, are available for free pdf download. The questions involving real numbers and their decimal form, the law of exponents are given below:

☛ Download Class 9 Maths NCERT Solutions Chapter 1 Number Systems

NCERT Class 9 Maths Chapter 1   Download PDF

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

It is advisable for the students to practice the questions in the above links as this will give them better clarity on the kind of numbers and their properties. An exercise-wise detailed analysis of NCERT Solutions Class 9 Maths Chapter 1 number systems is given below for reference.

• Class 9 Maths Chapter 1 Ex 1.1 - 4 Questions
• Class 9 Maths Chapter 1 Ex 1.2 - 4 Questions
• Class 9 Maths Chapter 1 Ex 1.3 - 9 Questions
• Class 9 Maths Chapter 1 Ex 1.4 - 2 Questions
• Class 9 Maths Chapter 1 Ex 1.5 - 5 Questions
• Class 9 Maths Chapter 1 Ex 1.6 - 11 Questions

☛ Download Class 9 Maths Chapter 1 NCERT Book

Topics Covered: The important topics focussed upon are irrational numbers, real numbers, and real numbers when expanded in the decimal form. The class 9 maths NCERT solutions chapter 1 covers the representation of real numbers on a number line, methods to perform operations on real numbers, and laws of exponents when dealing with real numbers.

Total Questions: Class 9 maths chapter 1 Number Systems consists of total 35 questions of which 30 are easy, 2 are moderate and 3 are long answer-type questions.

List of Formulas in NCERT Solutions Class 9 Maths Chapter 1

NCERT solutions class 9 maths chapter 1 covers important facts about the number systems which will help strengthen the math foundation. Like if a number ‘a’ is rational, and ‘b’ represents an irrational number, then ‘a+b’, and ‘a-b’ are irrational numbers, and ‘ab’ and ‘a/b’ are supposed to be irrational numbers, and ‘b’ is not equal to zero. For ‘a’ and ‘b’ positive real numbers the following formula or entities will be true:

• √ab = √a √b
• √(a/b) = √a / √b

Important Questions for Class 9 Maths NCERT Solutions Chapter 1

Video solutions for class 9 maths ncert chapter 1, faqs on ncert solutions class 9 maths chapter 1, do i need to practice all questions provided in ncert solutions class 9 maths number systems.

Practicing the NCERT solutions class 9 maths number systems and exercises on real numbers, rational numbers will help in exploring the number systems in a better way. The NCERT Solutions Class 9 Maths Number Systems will also provide a good insight into the solving of problems.

Why are Class 9 Maths NCERT Solutions Chapter 1 Important?

Since the number systems chapter deals with rational and irrational numbers, real numbers, and their expansion, their decimal form, also covering the law of exponents. Hence, this makes the NCERT solutions class 9 maths important for examinations.

What are the Important Formulas in NCERT Solutions Class 9 Maths Chapter 1?

There are several formulas or entities for positive real numbers which will be helpful in learning mathematics even for higher grades. Like if one wants to rationalize the denominator of 1/ ( √a + b ), then we can multiply and divide by its algebraic conjugate which is √a - b

How Many Questions are there in NCERT Solutions Class 9 Maths Chapter 1 Real Numbers?

The questions in the NCERT Solutions Class 9 Maths Chapter 1 are a great way for learning real numbers. There are around 35 questions dealing with number systems with 25 of them being simple and have straightforward logic, 6 of them are with medium complexity and 4 are elaborative questions.

What are the Important Topics Covered in NCERT Solutions Class 9 Maths Chapter 1?

The NCERT Solutions Class 9 Maths Chapter 1 deal with integers, real numbers, rational and irrational numbers. Apart from these the important topics covered are the real numbers, and what happens when they are expanded in decimal form, the law of exponents in the case of real numbers, how to differentiate between rational and irrational numbers etc.

How CBSE Students can utilize NCERT Solutions Class 9 Maths Chapter 1 effectively?

The students should first practice all the examples to understand the logic and problem solving technique and should try to solve all the exercise questions. The CBSE itself recommends the NCERT Solutions Class 9 Maths for the board exam studies.

• Bihar Board

SRM University

• NBSE Result 2024
• MP Board 10th Result 2024
• MP Board 12th Result 2024
• TS Board Results 2024
• NBSE Board Result 2024
• UK Board Result 2024
• Karnataka Board Result
• Shiv Khera Special
• Education News
• Web Stories
• Current Affairs
• नए भारत का नया उत्तर प्रदेश
• School & Boards
• College Admission
• Govt Jobs Alert & Prep
• GK & Aptitude
• Class 9 Maths NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 1 - Number System

Here you can find the ncert solutions for cbse class 9maths chapter 1- number system. it includes a detailed explanation of the answers and covers the easiest methods for solving the questions given in the chapter..

In this article, we are providing the NCERT solutions to Class 9 Maths Chapter 1 - Number System.  All these solutions are available in PDF format which you may access totally free of cost.  Our subject experts have reviewed these NCERT solutions to provide you the error-free content which will make it easy for you to make an effective preparation for the annual exams.

Why you should solve NCERT exercise questions?

Solving the NCERT exercise problems will help you

→ clear all the concepts and formulae you learned in a chapter

→ familiarise with different types of questions that can be asked in exams          

→ get enough practice which is the key to success in the Mathematics exam

→ improve your accuracy and speed

So, to get the desired result in exams, it’s very necessary for students to thoroughly solve the questions given at the end of each chapter of the Class 9 Maths NCERT book.

Some of the questions and solutions are as follows:

Get here latest School , CBSE and Govt Jobs notification in English and Hindi for Sarkari Naukari and Sarkari Result . Download the Jagran Josh Sarkari Naukri App . Check  Board Result 2024  for Class 10 and Class 12 like  CBSE Board Result ,  UP Board Result ,  Bihar Board Result ,  MP Board Result ,  Rajasthan Board Result  and Other States Boards.

• Nagaland Board Result 2024
• Nagaland Board HSLC Result 2024
• NBSE HSLC, HSSLC Result 2024
• Nagaland Board HSSLC Result 2024
• nbsenl.edu.in NBSE Result 2024
• NBSE Toppers List 2024
• एमपी बोर्ड 10 वीं टॉपर लिस्ट 2024
• AP SSC Results 2024 Manabadi by Jagran Josh
• AP SSC Topper List 2024
• CBSE Class 9 Subjects
• CBSE Class 9 Mathematics
• CBSE Class 9 Study Material
• NCERT Solutions for Class 9
• CBSE Class 9

Latest Education News

Today’s IPL Match (28 April) - CSK vs SRH: Team Squad, Match Time, Where to Watch Live and Stadium

Today’s IPL Match (28 April) - GT vs RCB: Team Squad, Match Time, Where to Watch Live and Stadium

Who Won Yesterday IPL Match: LSG vs RR, Match 44, Check All Details and Latest Points Table

[Today] IPL 2024 Points Table: Team Rankings and Net Run Rate

[Current] Orange Cap and Purple Cap Holders in IPL 2024

Purple Cap in IPL 2024: Top Players List with Most Wickets in TATA IPL

Orange Cap in IPL 2024: Top Players List with Most Runs in TATA IPL

Who Won Yesterday IPL Match: DC vs MI, Match 43, Check All Details and Latest Points Table

Uttarakhand Board Results 2024 Date and Time: Results Expected by April 30

Uttarakhand Board 10th, 12th Result 2024 Likely to Be Declared on April 30 , Check Steps To Download, Other Details Here

JNTUH Manabadi Result 2024 OUT at jntuh.ac.in; Direct Link to Download UG and PG Marksheet

TS Inter Supplementary Exam 2024: Check Time Table, Form Date, Eligibility and Fee

Picture Puzzle IQ Test: You Are Highly Observant If You Can Spot The Wallet In This Messy Room In 8 Seconds!

99.9% of People Failed To Find The Mouse Hidden In The Library. Try Your Luck!

[Official] West Bengal HS Result 2024 Date and Time Released, Check Notification Here

MP Board 10th, 12th Compartment 2024: MPBSE High School, Inter Supplementary Exam Date and Other Details

Optical Illusion Eye Test: Find the different coconut in the picture in 5 seconds!

IPL 2024 Full Schedule: आईपीएल 2024 का फुल शेड्यूल,आज किस टीम का है मैच जानें यहां    

IPL 2024 Stats: आईपीएल में किसने फेंकी थी पहली गेंद, किसने लिया था पहला विकेट और किसने जड़ा था पहला छक्का

IPL 2024 Live Streaming: मोबाइल या टीवी कहां और कैसे देखें आईपीएल का LIVE टेलीकास्ट?

Chapter 1 – Matrices and Determinants

Exercise 1.1, exercise 1.2, exercise 1.3, exercise 1.4, exercise 1.5, exercise 1.6, review exercise, multiple choice questions, this post has 15 comments.

Thank you so much I really appreciate you It really helped me I searched alot but I can’t find any answers Thank you again Good effort 👍

Bro literally everything thing is available here!very weldone bro! Excellent job ❤️❤️

Nice effort!

Please give extra MCQ’S of maths…

This is very good facility for students . We can study from here. I advice to free ilm owner to give math extra m.c.q.s

Thanks bro! this is very helpful for new students of class 9th….

Don’t know how to download offline

Simply, click on [open] link and download it.

where is chapter no 3 q no.3

Its help me alot in my test.

It helps much

Please ask me questions

Thats very nice site.

So i will give you give star

Leave a Reply Cancel reply

NCERT Solutions for Class 9 Maths Chapter 1 Number System

Here We have given NCERT Solutions for Class 9 Maths Chapter 1 Number System. These solutions are posted very carefully without any errors.

Your 9th standard is a major stepping point in your schooling because you are made aware of the looming 10th board exams at the end of two years. The foundation of all the relevant knowledge of mathematics during these two years is laid right here with Chapter 1 – Number Systems.

Table of Contents

Ncert solutions for class 9 maths chapter 1 number system exercise 1.1.

NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.2

NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.3

NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.4

NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.5

Check:- NCERT Solutions for Class 9 Maths

Types of Number Systems in Chapter 1

• Rational numbers (denoted by r): Numbers that can be written as p/q where q is a non-zero number. This category includes all integers, natural numbers and whole numbers within it. These can be represented as either a fraction or decimals. Examples include 1 /3, 0.25, 100. 10
• Irrational numbers (denoted by s): These numbers cannot be expressed in the form of p/q where q is a non-zero number. Examples include π,√2, √7 etc.
• Real numbers: The combination of all rational and irrational numbers gives the set of all real numbers. This term also implies the existence of imaginary numbers and that is a more complex topic that you will get into during your higher studies

Decimal expansion of rational numbers

While the definition of rational numbers given above uses the fraction form of the number, it is natural that we can express them as decimals as well. In this way, there are two types of expansions that you will encounter in the exercises of NCERT Class 9 Maths chapter 1.

• Terminating: The decimal values go to a  certain number of digits meaning that the remainder while dividing the fraction is 0. For example, ⅖ is 0.4, it terminates at this point
• Non-terminating: The values after the decimal keep on going without any limit for example ⅓ is 1.33333….., in such cases, the recurring portion of the decimal has a bar drawn over it to signify that it is recurring.
• Both terminating and non-terminating recurring decimal expansions are possible with rational numbers. However, for irrational numbers, the pattern will be non-terminating and non-recurring. For instance pi – which has a non-recurring pattern that goes on to infinity.

Operations on real numbers

By performing operations on irrational numbers you may get a rational number as a result – for example √7 x √7 = 7, a rational number that is the product of two irrational numbers. However, not every operation leads to a rational number coming from the result.

• The sum/difference between a rational and an irrational number is irrational
• The product/quotient of a rational number (except zero) and an irrational number are irrational
• Any operation on two irrational numbers may give an irrational number or a rational number.

FAQs (Frequently Asked Questions)

Why are class 9 maths ncert solutions chapter 1 important.

Understanding number systems is the basis of being able to effectively do algebra; if you cannot understand the terms and types of numbers you will encounter in practically every subsequent chapter then you will not be able to attempt any part of them. These various types include rational numbers, irrational numbers, integers, whole numbers, and natural numbers, among others. In order to get a brief overview of the chapter, including definitions for the types of natural numbers given in Class 9 Maths chapter 1 solutions keep reading on ahead.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 9 Maths Number Systems?

NCERT class 9 chapter 1 solutions contain the answers to 5 exercises (1.1 to 1.5) which contain several questions each. By going through these questions and their solutions you will become very thorough with the concepts such as giving the decimal expansions for fractions by long division, simplifying expressions containing irrational numbers, practising the laws of exponents and representing figures on a number line. You should also be familiar with the concepts of identities relating to square roots and exponents.

Class 9 maths NCERT solutions for Number Systems can be found on our site and recommend going through them carefully to make yourself more capable of handling every chapter in the NCERT maths curriculum.

Tagged with: 9 class maths chapter 1 | 9th class math chapter 1 question answer | cbse 9th class maths chapter 1 | cbse class 9 maths chapter 1 solutions | cbse class 9th maths chapter 1 | ch 1 class 9th maths | chapter 1 maths class 9 ncert solutions | class 9 ch 1 maths ncert solutions | class 9 maths chapter 1 ncert

Have any doubt Cancel Reply

Your email address will not be published. Required fields are marked *

Save my name and email in this browser for the next time I Submit.

Talk to our experts

1800-120-456-456

• Number Systems Class 9 Notes CBSE Maths Chapter 1(Free PDF Download)
• Revision Notes

Class 9 Maths Revision Notes for Number Systems of Chapter 1 - Free PDF Download

We have supplied review notes for Class 9 Mathematics Chapter 1 - Number System in printable pdf format to assist students in understanding the chapter's main ideas. Vedantu's subject matter specialists have presented each topic in simple words, including visuals when necessary.

With these revision notes, students can easily and speedily able to revise all the important concepts and formulae of the chapter. Hence, these revision notes act as a great reference tool and will help students have quick revisions of all the topics of the chapter before the exams. So, Waiting for What? Download Class 9 Maths revision notes for Chapter 1 free pdf through the link provided below.

Important Topics Covered in Class 9 Maths Chapter 1

Introduction to number system

Irrational Number

Real Number and Their Decimal Expansion

Representation of Real Number on Number Line

Operations on Real Number

Laws of Exponents for Real Number

Download CBSE Class 9 Maths Revision Notes 2024-25 PDF

Also, check CBSE Class 9 Maths revision notes for all chapters:

Access Class 9 Mathematics Chapter 1 – Number Systems Notes

Real numbers and imaginary numbers together form number systems.

We will discuss imaginary numbers in higher classes, let us restrict our discussion to real numbers

Real numbers are the set of natural numbers, whole numbers, integers, rational and irrational numbers. Denoted by R

Natural numbers:

These are counting numbers starting from $1$.

 The set $\left\{ 1,2,3,4,5,6,7.... \right\}$ is called natural numbers.

 Denoted by N

Whole numbers :

These are the set of natural numbers including $0$. 

The set $\left\{ 0,1,2,3,4,5,6.... \right\}$ is called whole numbers.

Denoted by W

Integers:  

These are the set of negative numbers, positive numbers and $0$ excluding fractions. 

The set $\left\{ ....-3,-2,-1,0,1,2,3.... \right\}$ is called integers.

Denoted by Z

Rational numbers:

These are those numbers which can be expressed in the form of fraction i.e., $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$. 

For example: $\dfrac{3}{5},\dfrac{-2}{9},\dfrac{-3}{4},$ etc. 

Denoted by Q

There are infinitely many rational numbers between any two rational numbers.

Irrational numbers:

These are those which are not rational i.e., which cannot be expressed in the form of  $\dfrac{p}{q}$ where $p$ and $q$ are integers and$q\ne 0$.

For example: $\sqrt{2},\sqrt{3},\sqrt{5},$ etc.

Real Numbers and Their Decimal Expansions

There are two cases of decimal expansions

Remainder becomes zero

Decimal expansion of numbers whose remainder becomes zero after some step is called terminating.

For example: $\dfrac{7}{8}=0.875$ , the remainder becomes zero after some steps

Remainder never become zero

Decimal expansion of numbers whose remainder never becomes zero after some step is called non-terminating.

It is further divided into non-terminating recurring and non-terminating non-recurring.

Non-terminating recurring means  numbers which keep on repeating the same value after decimal point.

For example: $\dfrac{9}{11}=0.818181....$ 

Non-terminating non-recurring means  numbers which do not keep on repeating the same value after decimal point but remainder never become zero.

For example: value of $\pi =3.141592653589793283....$ 

Decimal expansion of rational numbers is either terminating or non-terminating.

Decimal expansion of irrational numbers is non-terminating non-recurring.

Representing Real Number on Number Line

Representation of real numbers on the number line can be done by the process of successive magnification.

For example: If we want to locate $4.377$ on the number line we proceed by successive magnification i.e., $4.37$ lies between $4$ and $5$ then locate $4.37$ between $4.36$ and $4.38$further divide this portion into ten equal parts then $4.377$ will lie between $4.376$ and $4.378$. The number line is shown below

Operations on Real Numbers

Real numbers can be added, subtracted, multiplied and divided.

For example: 

Add $2+\sqrt{3}$ and $2-2\sqrt{3}$

$2+\sqrt{3}+2-2\sqrt{3}$ 

$=4-\sqrt{3}$ 

Subtract $2+\sqrt{3}$ and $2-2\sqrt{3}$ 

$\left( 2+\sqrt{3} \right)-\left( 2-2\sqrt{3} \right)$ 

$=2+\sqrt{3}-2+2\sqrt{3}$ 

$=3\sqrt{3}$ 

Multiply $2\sqrt{2}$ and $3\sqrt{3}$ 

$2\sqrt{2}\times 3\sqrt{3}$

$=2\times 3\times \sqrt{2}\times \sqrt{3}$ 

$=6\sqrt{6}$

Divide $10\sqrt{15}$ by $\sqrt{5}$ 

$\dfrac{10\sqrt{15}}{\sqrt{5}}=\dfrac{10\sqrt{3}\times \sqrt{5}}{\sqrt{5}}=10\sqrt{3}$

Some common facts of operation on real numbers are

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, then the result may be rational or irrational.

Rationalizing Denominator

When the denominator is irrational then the process of converting the denominator rational is called rationalizing the denominator.

It is obtained by multiplying numerator and denominator by the irrational term present in the denominator but with opposite sign.

For example: Rationalizing $\dfrac{1}{\sqrt{2}+3}$ 

$\dfrac{1}{\sqrt{2}+3}\times \dfrac{\sqrt{2}-3}{\sqrt{2}-3}$

$=\dfrac{\sqrt{2}-3}{{{\left( \sqrt{2} \right)}^{2}}-{{3}^{2}}}$ 

$=\dfrac{\sqrt{2}-3}{2-9}$ 

$=\dfrac{\sqrt{2}-3}{-7}$ 

Laws of Exponents for Real Numbers

There are some laws of exponent for real numbers such as

${{x}^{m}}.{{x}^{n}}={{x}^{m+n}}$ 

$\dfrac{{{x}^{m}}}{{{x}^{n}}}={{x}^{m-n}}$

${{\left( {{x}^{m}} \right)}^{n}}={{x}^{mn}}$ 

${{x}^{m}}{{y}^{m}}={{\left( xy \right)}^{m}}$ 

Number System Class 9 PDF – Free PDF Download

9 th class maths notes chapter 1 number systems free pdf.

The CBSE Class 9 Maths Notes Chapter 1 Number Systems are available on the official website of Vedantu in a PDF format for free. Students can avail benefits from the downloading of these PDFs in both soft copy and hard copy. The students can understand and practice it during their feasible time and need not bother about the interrupted internet connection. 

Class 9 Maths Chapter 1 Number Systems 

Introduction:- 

The Number Systems Class 9 Notes has recalled all the knowledge of numbers learned in the earlier classes. It has been explained by taking a funny scenario of having a bag and collecting different numbers. Let's say that the first natural numbers started from 1 and ask to collect the 0 also into the bag, which makes the set into whole numbers. It is denoted by W. Later on, moving back to the negative integers on the number line, which recalls the memory of integers Z. And the next important classification of numbers is rational numbers. It is in p/q form and denoted by Q.

Irrational Numbers:- 

After understanding certain solved examples, the PDF has directed to solve an exercise related to all the classifications of numbers studied so far. Class 9 Maths Notes Chapter 1 has taken the initiation to introduce irrational numbers to the students, which takes a form that doesn't equal the rational number. The point is that all the numbers can be represented on the number line at any point. Similarly, every point of the number line denotes a number irrespective of its classification. This principle is called a real number line because those numbers are called real numbers.

Real Numbers and their Decimal Expansion

To explore more about the real numbers, these Notes of Class 9 Maths Chapter 1 have explained both rational and irrational numbers in a new way that is nothing but the decimal point method.

So every fraction can be represented using decimals by dividing exactly where two cases will arise. 

The quotient will be zero

The quotient will not be zero

if the numerator is exactly divided by the denominator, then the quotient will be 0 and if the numerator is not divided by the denominator exactly then the quotient may not be 0.

Representing Real Numbers on The Number Line

In this section, Notes for Class 9 Maths Chapter 1 has experimented while explaining the representation of real numbers on the number line. As the real numbers are very nearby, including all the points of the number line, they can be seen using a magnifying glass. This visualization of representing real numbers using a magnifying glass is known as the process of successive magnification.

Class 9th Maths Chapter 1 Notes has explained all the properties like commutative, closure, identity, distributive, etc., concerning addition, subtraction, multiplication, and division of rational and irrational numbers. Few observations had been made from this. They are as follows:

The sum or difference between a rational number and the irrational number is irrational.

All four mathematical operations done by two irrational numbers might be either rational or irrational.

Laws of Exponents For Real Numbers

The Notes of Mathematics Class 9 Chapter 1 have focused more on this area and covered the idea of exponents in detail. The exponent is the number or variable that appears at the top of a digit. It is not also referred to as power. The original digit is known as the base. It can be written as mn. They have supplied some solid and unsolved examples to help you learn these exponentials in depth. The last of these exponents were wider apart than the next classes. The square roots and cube roots produced from these exponents are also described in the Chapter 1 Mathematics Class 9 notes.

Benefits of Class 9 Maths Chapter 1 Revision Notes

A great reference tool to strengthen the important concepts of the chapter.

Students become more confident to solve even the complex question of the chapter during the exam.

Exam stress and anxiety are reduced.

Help students minimise the chance of making silly mistakes.

Saves precious time during exams as these notes will help you to revise all the important topics of the chapter quickly.

The accuracy of answers attempted during the exams is higher.

CBSE Class 9 Mathematics Chapter 6 Revision Notes are one of the most useful resources you may utilize since each chapter's topic is given in an easy-to-read style. Viewing these notes helps students remember all of the ideas covered in the chapter. As a result, it will save time during tests. They will also receive all of the chapter's major formulae in one spot.

FAQs on Number Systems Class 9 Notes CBSE Maths Chapter 1(Free PDF Download)

1.  If (1, −2) is a solution of the equation 2x – y = p, then find the value of p.

It is given that, 2x − y = p

Putting x = 1, y = −2, in above equation, we get

= 2(1) - (-2 )

After substituting the values of X and y, we get the value of P is 4.

Hence the equation is 

2. Write any five rational numbers that lie between ⅗ and ⅘.

As we already learned that the rational numbers can also be represented as decimals, the given rational numbers are,

The decimal values that lie between 0.6 and 0.8 are many. So we can take any 5 among them.

0.61, 0.62, 0.63, …..0.7, 0.71, 0.72, 0.73 …...0.8.

Now convert these decimal values into rational numbers to answer the given question.

61/100, 62/100, 63/100, ….., 7/100, 71/100,72/100…….

These are some of the rational numbers that lie between ⅗  and ⅘.

Hence it is solved.

3. How many exercises are there in Chapter 1 Class 9?

Chapter 1 Class 9 Mathematics has a total of six tasks. It is critical for students to practise and complete all of the exercises in order to have a better understanding of the ideas, which will eventually assist them in obtaining suitable scores in the test. Students may get the NCERT Solution from Vedantu, where the exercises come with solved and explained answers, making understanding and learning easier. The activities are solved step by step so that there is no uncertainty or confusion among the pupils. Those who practise these solutions will undoubtedly do well in the exam.

4. What are rational numbers in Class 9?

Rational numbers are numbers that come in the form of p/q, in which case both p and q are integers and q is not equal to zero.

It is important for the student to be thorough with this chapter to get a better understanding of the concepts pertaining to rational and irrational numbers, which will not just help them in scoring desirable grades in the Class 9 examination but will also prove its worth in higher education. The students are advised to practice the exercises present in the NCERT solutions to get a better hold of the concepts.

5. What are number systems in Maths?

Number state is the method in Chapter 1 Class 9 Maths by which numbers are represented on the number line with the help of set symbols and rules that range from 0 to 9 called digits. In the Class 9 syllabus, the number systems are classified into natural numbers, whole numbers, rational numbers, irrational numbers, integers, etc and the first chapter covers all the relevant and basic concepts pertaining to these. The students need to be thorough in these concepts in order to easily comprehend the succeeding chapters.

6. Where can I get the NCERT Solutions for math chapter 1 class 9?

The NCERT Solutions for Chapter 1 Class 9 Maths can be easily availed from any online website. The student can visit the website of Vedantu or download the Vedantu app where they can easily download the solutions for free. These exercises are designed by experts to help the student in comprehending the concepts better. These exercises have elaborate answers making each step of the question easy to grasp. Moreover, the solutions with the previous year’s question papers will help the student to develop a better understanding of the question pattern and prepare them for the exam.

7. How to prepare for Class 9 Maths Chapter 1?

STUDY MATERIALS FOR CLASS 9

Find your desired course

Select your favourite category and start learning..

←  Class 9 Math

 Chapter 2  →

Chapter 1 Number Systems

Math ncert solutions class 9, chapter 1: number systems.

Social Science

Notes + Important Questions

NCERT Solutions

Helpbook Solutions

Sample Papers

Assignments

Number Systems

Polynomials

Coordinate Geometry

Linear Equations in Two Variables

Introduction to Euclid’s Geometry

Lines and Angles

Quadrilaterals

Heron’s Formula

Surface Areas and Volumes

As Featured In

• Privacy Policy
• Terms and Conditions
• Refunds or Cancellations
• Course Catalog

Hello there, haven’t we seen you before?

New here? Sign Up

Already have an account? Sign In

• NCERT Exemplar
• Maths Exemplar Class 9
• Number Systems

NCERT Exemplar Solutions for Class 9 Maths Chapter 1 - Number Systems

Ncert exemplar solutions class 9 maths chapter 1 – free pdf download.

NCERT Exemplar Class 9 Maths Chapter 1 Number System is provided here for students to prepare well for exams. These exemplar problems and solutions are designed by experts in accordance with the CBSE Syllabus for Class 9, which covers the following topics of the Number System:

• Rational numbers and irrational numbers
• Finding rational numbers between two given numbers
• Locating irrational numbers in a number line
• Real numbers and their decimal expansions are terminating or non-terminating, recurring or non-recurring.
• Finding irrational numbers between two given numbers
• Operations performed on real numbers
• Rationalising the denominator
• Laws of exponents for real numbers

To facilitate easy learning and help students understand the concepts discussed in Chapter 1, free NCERT Exemplars are provided here, which can be downloaded in the form of a PDF. Students can use these materials as a reference tool for studying as well as practising sums. The exemplars also contain solved questions relevant to the exercise problems present in the NCERT textbook .

Download the PDF of NCERT Exemplar Solutions for Class 9 Maths Chapter 1 – Number Systems

Access Answers to NCERT Exemplar Solutions for Class 9 Maths Chapter 1 Number Systems

Exercise 1.1 Page No: 2

Write the correct answer in each of the following:

1. Every rational number is

(A) a natural number

(B) an integer

(C) a real number

(D) a whole number

Explanation:

We know that rational and irrational numbers taken together are known as real numbers. Therefore, every real number is either a rational number or an irrational number. Hence, every rational number is a real number.

Hence, (C) is the correct option.

2. Between two rational numbers

(A) there is no rational number

(B) there is exactly one rational number

(C) there are infinitely many rational numbers

(D) there are only rational numbers and no irrational numbers

Between two rational numbers, there is infinitely many rational numbers.

3. Decimal representation of a rational number cannot be

(A) terminating

(B) non-terminating

(C) non-terminating repeating

(D) non-terminating non-repeating

The decimal representation of a rational number cannot be non-terminating and non-repeating.

Hence, (D) is the correct option.

4. The product of any two irrational numbers is

(A) always an irrational number

(B) always a rational number

(C) always an integer

(D) sometimes rational, sometimes irrational

The product of any two irrational numbers is sometimes rational and sometimes irrational.

5. The decimal expansion of the number √2 is

(A) a finite decimal

(B) 1.41421

(C) non-terminating recurring

(D) non-terminating non-recurring

The decimal expansion of the number √2 = 1.41421356237…

6. Which of the following is irrational?

(A) √4/√9 = 2/3

(B) √12/√3 = 2√3/√3 = 2

(C) √7 = 2.64575131106

(D) √81 = 9

Here, (C) √7 = 2.64575131106 is a non-terminating decimal expansion.

7. Which of the following is irrational?

(D) 0.4014001400014…

A number is irrational if and only if its decimal representation is non-terminating and non-recurring.

(A) is a terminating decimal and, therefore, cannot be an irrational number.

(B) is a non-terminating and recurring decimal and, therefore, cannot be irrational.

(C) is a non-terminating and recurring decimal and, therefore, cannot be irrational.

(D) is a non-terminating and non-recurring decimal and therefore is an irrational number.

8. A rational number between √2 and √3 is

(A) (√2+√3)/2

(B) (√2. √3)/2

√2 =1.4142135…. and √3 =1.732050807….

(A) (√2+√3)/2 = 1.57313218497… is a non-terminating and non-recurring decimal and, therefore, is an irrational number.

(B) (√2. √3)/2 = 1.22474487139… is a non-terminating and non-recurring decimal and, therefore, is an irrational number.

(C) 1.5 is a terminating decimal and, therefore, is a rational number.

(D) 1.8 is a terminating decimal and, therefore, is a rational number.

Here both 1.5 and 1.8 are rational numbers. But, 1.8 does not lie in between √2 =1.4142135…. and √3 =1.732050807…. Whereas 1.5 lies in between √2 =1.4142135…. and √3 =1.732050807….

9. The value of 1.999… in the form p/q , where p and q are integers and q ≠ 0, is

(B) 1999/1000

(A) 19/10 = 1.9

(B) 1999/1000= 1.999

(D) 1/9 = 0.111….

Let x = 1.9999….. — (1)

Multiply equation (1) with 10

10x = 19.9999….. — (2)

Subtract equation (1) from equation(2),

x = 1.9999… = 2

10. 2√3 + √3 is equal to

Taking √3 common,

√3(2+1) = √3(3) = 3√3

Exercise 1.2 Page No: 6

1. Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.

Yes, if x and y are rational and irrational numbers, respectively, then x+ y is an irrational number.

For example,

Let x = 5 and y = √2.

Then, x+y = 5 + √2 = 5 + 1.414… = 6.414…

Here, 6.414 is a non-terminating and non-recurring decimal and therefore is an irrational number.

Hence, x + y is an irrational number.

2. Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer with an example.

No, if x is a rational number and y is an irrational number, then xy is not necessarily an irrational number. It can be rational if x = 0, which is a rational number.

For example:

Let y = √2, which is irrational.

Consider x = 2, which is rational.

Then, x × y = 2 × √2 = 2√2, which is irrational.

Consider x = 0, which is rational.

Then xy = 0 × √2 = 0, which is rational.

Therefore, we can conclude that the product of a rational and an irrational number is always irrational, only if the rational number is not zero.

Exercise 1.3 Page No: 9

1. Find which of the variables x, y, z and u represent rational numbers and which irrational numbers:

(i) x 2  = 5

(ii) y 2  = 9 (iii) z 2  = .04

(iv) 𝑢 2  = 17/4

(i) x 2  = 5

On solving, we get

Hence, x is an irrational number.

(ii) y 2  = 9

Hence, y is a rational number.

(iii) z 2  = .04

⇒ z = ± 0.2

Hence, z is a rational number.

(iv) u 2 = 17/4

⇒ u = ± √17/2

√17 is irrational.

Hence, u is an irrational number

2. Find three rational numbers between

(i) –1 and –2

(ii) 0.1 and 0.11 (iii) 5/7 and 6/7

(iv) 1/4 and 1/5

Three rational numbers between –1 and –2 are –1.1, –1.2 and –1.3.

(ii) 0.1 and 0.11

Three rational numbers between 0.1 and 0.11 are 0.101, 0.102 and 0.103.

(iii) 5/7 and 6/7

5/7 can be written as (5 × 10)/(7 × 10) = 50/70

6/7 can be written as (6 × 10)/(7 × 10) = 60/70

Three rational numbers between 5/7 and 6/7 = three rational numbers between 50/70 and 60/70.

Three rational numbers between 5/7 and 6/7 are 51/70, 52/70, 53/70.

Here, according to the question,

LCM of 4 and 5 is 20.

Let us make the denominators common, 80.

(4 × 20) = 80 and (5 × 16) = 80

1/4 can be written as (1 × 20)/(4 × 20) = 20/80

1/5 can be written as (1 × 16)/(5 × 16) = 16/80

Three rational numbers between 1/4 and 1/5 = three rational numbers between 16/80 and 20/80.

Therefore, the three rational numbers are 17/80, 18/80 and 19/80.

3. Insert a rational number and an irrational number between the following:

(i) 2 and 3

(ii) 0 and 0.1 (iii) 1/3 and 1/2

(iv) –2/5 and 1/2 (v) 0.15 and 0.16

(vi) √2 and √3 (vii) 2.357 and 3.121 (viii) .0001 and .001 (ix) 3.623623 and 0.484848 (x) 6.375289 and 6.375738.

So, the rational number between 2 and 3 = 2.5

And, the irrational number between 2 and 3 = 2.040040004…

(ii) 0 and 0.1

So, the rational number between 0 and 0.1 = 0.05

And, irrational number between 0 and 0.1 = 0.007000700007…

(iii) 1/3 and 1/2

LCM of 3 and 2 is 6.

1/3 can be written as (1 × 20)/(3 × 20) = 20/60

1/2 can be written as (1 × 30)/(2 × 30) = 30/60

So, the rational number between 1/3 and 1/2 = 25/60

And, irrational number between 1/3 and 1/2 = irrational number between 0.33 and 0.5 = 0.414114111…

(iv) – 2/5 and 1/2

LCM of 5 and 2 is 10.

-2/5 = -0.4

-2/5 can be written as (-2 × 2)/(5 × 2) = -4/10

1/2 can be written as (1 × 5)/(2 × 5) = 5/10

So, rational number between -2/5 and 1/2 = rational number between -4/10 and 5/10 = 1/10

And, irrational number between -2/5 and 1/2 = irrational number between -0.4 and 0.5 = 0.414114111…

(v) 0.15 and 0.16

The rational number between 0.15 and 0.16 = 0.151

The irrational number between 0.15 and 0.16 = 0.151551555…

(vi) √2 and √3

√2 = 1.41 and √3 = 1.732

Rational number between √2 and √3 = rational number between 1.41 and 1.732 = 1.5

The irrational number between √2 and √3 = irrational number between 1.41 and 1.732 = 1.585585558…

(vii) 2.357 and 3.121

The rational number between 2.357 and 3.121 = 3

The irrational number between 2.357 and 3.121 = 3.101101110…

(viii) .0001 and .001

Rational number between .0001 and .001 = 0.00011

The irrational number between .0001 and .001 = 0.0001131331333…

(ix) 3.623623 and 0.484848

The rational number between 3.623623 and 0.484848 = 1

The irrational number between 3.623623 and 0.484848 = 1.909009000…

(x) 6.375289 and 6.375738.

The rational number between 6.375289 and 6.375738 = 6.3753

The irrational number between 6.375289 and 6.375738 = 6.375414114111…

4. Represent the following numbers on the number line:

7, 7.2, −3/2, −12/5

5. Locate √5, √10 and √17 on the number line.

√5 on the number line:

5 can be written as the sum of the square of two natural numbers:

i.e., 5 =1+ 4 =1 2 + 2 2

On the number line,

Take OA = 2 units.

Perpendicular to OA, draw BA = 1 unit.

Using the Pythagoras theorem,

We have, OB= √5

Draw an arc with centre O and radius OB using a compass such that it intersects the number line at point C.

Then, we get, C corresponds to √5. Or we can say that OC = √5

√10 on the number line:

10 can be written as the sum of the square of two natural numbers:

i.e., 10 =1+ 9 =1 2 + 3 2

Take OA = 3 units.

We have, OB= √10

Then, point C corresponds to √10. Or we can say that OC = √10

√17 on the number line:

17 can be written as the sum of the square of two natural numbers:

i.e., 17 =1+ 16 =1 2 + 4 2

Take OA = 4 units.

We have, OB= √17

Then, point C corresponds to √17. Or, we can say that OC = √17

6. Represent geometrically the following numbers on the number line:

Draw a line segment such that AB = 4.5 units.

Mark C at a distance of 1 unit from B.

Mark O is the mid-point of AC.

Draw a semicircle with centre O and radius OC.

Draw a line perpendicular to AC, passing through B and intersecting the semicircle at D.

Now, BD = √4.5.

Draw an arc with centre B and radius BD, meeting AC produced at E.

Then, BE = BD = √4.5 units.

Draw a line segment such that AB = 5.6 units.

Now, BD = √5.6

Then BE = BD = √5.6 units.

Draw a line segment such that AB = 8.1 units.

Mark O, is the mid-point of AC.

Now, BD = √8.1.

Then BE = BD = √8.1 units.

Draw a line segment such that AB = 2.3 units.

Now, BD = √2.3.

Then BE = BD = √2.3 units.

7. Express the following in the form p/q, where p and q are integers and q ≠ 0 :

(ii) 0.888…

(v) 0.2555…

(vii) .00323232…

(viii) .404040…

We know that,

0/2 can be written as,

0.2 = 2/10 = 1/5

Assume that 𝑥 = 0.888 …

⇒ 𝑥 = 0.8 ……………. Eq.(1)

Multiply L.H.S and R.H.S by 10,

10 𝑥 = 8.8 ……………. Eq.(2)

Subtracting equation (1) from (2),

10 𝑥 − 𝑥 = 8.8 − 0.8

Assume that 𝑥 = 5.2 ……………. Eq.(1)

10 𝑥 = 52.2 …………… Eq. (2)

10 𝑥 − 𝑥 = 52.2 − 5.2

Assume that 𝑥 = 0.001 ……………. Eq. (1)

Multiply L.H.S and R.H.S by 1000,

1000 𝑥 = 1.001 …………… Eq. (2)

1000𝑥 − 𝑥 = 1.001 − 0.001

⇒ 𝑥 = 1/999

Assume that 𝑥 = 0.2555 …

⇒ x = 0.25 ……………. Eq. (1)

10 x = 2.5 ……………. Eq. (2)

Multiply L.H.S and R.H.S by 100,

100 x = 25.5 …………. Eq. (3)

Subtracting equation (2) from (3),

100 x-10x = 25.5 – 2.5

⇒ 𝑥 = 23/90

Let 𝑥 = 0.134 ………….…. Eq. (1)

10 𝑥 = 1.34 ………………. Eq. (2)

1000 𝑥 = 134.34 …………. Eq. (3)

1000 𝑥 − 10𝑥 = 134.34 − 1.34

⇒ 990𝑥 = 133

⇒ 𝑥 = 133/990

Let 𝑥 = 0.00323232 …

⇒ x = 0.0032 ………….…. Eq. (1)

100x = 0.32 ……………. Eq. (2)

Multiply L.H.S and R.H.S by 10000,

10000 x = 32.32 …………. Eq. (3)

10000 x-100x = 32.32 – 0.32

⇒ 9900𝑥 = 32

⇒ 𝑥 = 32/9900 = 8/2475

Let 𝑥 = 0.404040 …

⇒ 𝑥 = 0. 40 ………..….…. (1)

100 𝑥 = 40.40 ……….…. (2)

100 𝑥 − 𝑥 = 40.40 − 0.40

⇒ 𝑥 = 40/99

Exercise 1.4 Page No: 12

Let x = 0.6

Multiply by 10 on L.H.S and R.H.S,

So, the p/q form of 0.6 = 3/5

Let y = 0.77777…

10y = 7.7777…

10y – y = 7.7777777……. – 0.7777777…………..

So the p/q form of 0.7777… = 7/9

Let z = 0.47777…

10z = 4.7777…

10z – z = 4.7777777… – 0.47777777…

9z = 4.2999

So the p/q form of  0.4777… = 43/90

x+y+z = 3/5 + 7/9 + 43/90

= (54 + 70 + 43)/90

2. Simplify:

Let us first make the denominators the same,

To make the denominators the same, cross-multiply the first and second terms of the equation.

Now, again make the denominators the same by cross-multiplying the obtained term and the third term of the given equation in the question.

3. If √2 =1.414, √3 =1.732, then find the value of

Let us first make the denominators the same by cross multiplication method

Observing the denominator, we can say that,

Denominators are of the form,

(a + b) × (a – b) = (a 2  – b 2 )

Here a = 3√3

a 2  = (3√3) 2 = 27

b 2  = (2√2) 2 = 8

BYJU’S also provides study resources, such as notes, exemplar books, NCERT Solutions and question papers for students to prepare well and score good marks in their exams. Also, it is recommended to solve sample papers and previous years’ question papers which gives an idea of question types asked in the annual exam from Chapter 1, Number System. Solving the NCERT Exemplar questions will help students to understand the chapter and to practise higher-level questions related to the Number System .

Download BYJU’S – The Learning App and get personalised videos, explaining different types of Maths topics, such as number systems and different types of numbers, etc., and experience a new way of learning to understand the concepts easily.

Frequently Asked Questions on NCERT Exemplar Solutions for Class 9 Maths Chapter 1

What are the topics covered in chapter 1 of ncert exemplar solutions for class 9 maths, what are rational numbers according to ncert exemplar solutions for class 9 maths chapter 1, how to rationalise the denominator discussed in chapter 1 of ncert exemplar solutions for class 9 maths, leave a comment cancel reply.

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Good work for byjus

very useful solutions

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.