NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.3

One of the most significant and well-respected educational organizations in the nation, the Central Board of Secondary Education (abbreviated as CBSE) answers to the Union Government of India. Numerous public and private schools that are part of the CBSE board use the NCERT curriculum.

Here, the Extramarks subject specialists have come up with the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 that make learning simple for students. As they go through the exercise difficulties, the students resort to it as a resource. The decimal expansion of real numbers is covered in the third exercise in Exercise 1.3 Class 9 Maths. They offer a thorough and step-by-step explanation for each response to the problems asked in the exercises in the Class 9 NCERT textbook. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 are always created in accordance with CBSE standards to ensure that the whole curriculum is covered. These are highly beneficial for getting high marks in CBSE exams.

The subject specialists at Extramarks have provided the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 on this page. The main goal of the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 is to make the Class 9 Mathematics problems presented in the textbooks recommended by the CBSE syllabus simpler. The logically organized Class 9 Mathematics, the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3, contains every exercise’s problems. As a result, the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 provide in-depth instruction and aid students in developing their arithmetic and logical thinking abilities. Learning has been made significantly more comfortable by the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 by greatly simplifying and clarifying challenging concepts. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 should be used as soon as feasible by students as a preparation tool. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 would be beneficial to incorporate into their curriculum.

To provide students with a competitive advantage during their preparation, Extramarks provides the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 (in accordance with the CBSE syllabus) for all courses. For students who desire to perform above expectations in the Class 10 Board Examinations, the NCERT Solutions For Class 9 Mathematics Chapter 1 may be the most helpful tool for enhancing board exam preparation.

CBSE Class 9 NCERT Solutions Maths Chapter 1 Exercise 1.3

Students can obtain the PDF version of the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 from the Extramarks. The website provides all the Mathematics and other board-approved NCERT solutions. The NCERT standards and norms that are crucial for students learning and examinations are correctly followed by these NCERT Solutions. There are answers to all the questions in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3. Some students might find it challenging to answer every question on their own. Use of the  NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 can therefore increase productivity and morale.

Access NCERT Solutions for Class 9 Maths Chapter 1 – Number System

To better their test preparation, they should immediately get the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3  from the Extramarks website. If someone already has the Extramarks app downloaded to their phone, they can also get the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 using that method. The Class 9 Maths Chapter 1 Exercise 1.3 Solutions’ best feature is that it can be used both offline and online.

Exercise 1.3 Class 9 Maths answers for their perusal online

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The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 are an excellent resource for practising Mathematics in preparation for the test, since practice makes perfect. The Extramarks provides the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 in a clear manner. These solutions have been created by subject-matter experts with years of expertise in the field. They are aware of the types of questions they will be asked during the examination. Given that the test will have a variety of mathematical problems and questions, they will naturally be able to prepare for it better. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 are consistently a great resource for students. There is a thorough examination of real numbers and their properties in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3. The detailed examination of real numbers and their decimal expansion is provided in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3. This is crucial for their future comprehension of the subject in general. All the answers to the questions that are featured in the exercises will be distributed step-by-step in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3. Everything is based on the NCERT standards and the CBSE curriculum. This covers everything on the course and raises their exam grade.

NCERT Solutions for Class 9 Maths Chapter 1 Other Exercises

The first chapter of Mathematics for Class 9 is titled Number System. In this chapter, the Number System is covered in great detail. The number systems and their uses are covered in this chapter. Whole, integer, and rational numbers are all included in the chapter’s introduction.

The chapter begins with an overview of number systems in section 1.1, followed by sections 1.2 and 1.3 on two crucial subjects.

Irrational numbers are those that cannot be expressed as p/q.

Real Numbers and their Decimal Expansions – In this section, students examine real number decimal expansions to determine if they may be used to discern between logical and irrational behaviour. All the definitions and simplified terms are provided in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3.

It then talks about the following subjects.

Real Numbers on the Number Line – These are the answers to the two problems in Exercise 1.4.

Operations on Real Numbers – In this section, students will learn about various irrational number operations, such as addition, subtraction, multiplication, and division.

Exponentiation Laws for Real Numbers – To answer the problems, use these exponentiation laws.

The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 can help students to learn more about Number Systems and how to resolve all types of issues. One of the greatest academic tools for studying for their CBSE exams is this one.

The solutions are presented in clear, easy-to-understand language. Students experience less stress when studying as a result of this. For the convenience of use by students, all the questions are answered in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 in a simple step-by-step manner.

The solutions are arranged comprehensively and logically, so students will not need to search through their NCERT textbooks or lecture notes to finish last-minute touch ups to their revision. All the problems in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 have been properly solved with key pointers.

The NCERT solutions include all the important questions as well as thorough justifications for each response that are crucial for understanding. The complicated pattern is repeated in the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3. As a result, students may prepare for any test with the help of the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3.

The NCERT Solutions for Class 9 Mathematics Chapters are as follows. There are 15 chapters in total

Chapter 1 Number System

Chapter 2 Polynomials

Chapter 3 Coordinate Geometry

Chapter 4 Linear Equations in Two Variables

Chapter 5 Introduction to Euclid’s Geometry

Chapter 6 Lines and Angles

Chapter 7 Triangles

Chapter 8 Quadrilaterals

Chapter 9 Areas of Parallelograms and Triangles

Chapter 10 Circles

Chapter 11 Constructions

Chapter 12 Heron’s Formula

Chapter 13 Surface Areas and Volumes

Chapter 14 Statistics

Chapter 15 Probability

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NCERT Solutions for Class 9

The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 is only one aspect of this. Students may obtain digital PDFs for every topic and chapter in their syllabus at the Extramarks. Students can always make use of the professionally crafted NCERT Solutions, which are designed to aid in understanding and problem-solving. One can anticipate doing better on their future test due to these solutions, which will also help one review and stay focused. Since the solutions are based on NCERT guidelines, there will not be any misunderstanding on their behalf.

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One of the most crucial topics in Class 9 in Mathematics is Class 9 Maths Ex 1.3, and with the appropriate direction and understanding, students can do well on the examination. Besides this, the fear of numbers that many students may easily overcome with consistent practice. In this sense, Extramarks provides a dependable NCERT Solution like the Class 9 Maths Chapter 1 Exercise 1.3 Solutions. Extramarks is a reliable source of NCERT Solutions, materials, tools, and helpful advice for all of their topics. Extramarks works to provide students with shrewd and creative study (NCERT) solutions that will hasten their learning and help them do better on tests.

CBSE Study Materials for Class 9

The foundation for Class 10 and beyond is laid by the CBSE Study Materials for Class 9. The mathematics, science, and social studies curricula for Class 9 are vast and difficult. It covers every foundational idea that’s crucial for competitive exams like the IIT JEE, Olympiads, NEET, and more. As a result, students must prepare for and pass their Class 9 exams. In order to help students with their studies, Extramarks has provided the CBSE Study Materials for Class 9.

A panel of topic experts created the CBSE Study Materials for Class 9, and the format is well-structured in compliance with NCERT standards. 

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CBSE Study Materials

NCERT, or the National Council of Educational Research and Training, is an autonomous organisation. The Societies Registration Act allowed for the establishment of this organisation in 1961. The Government of India controls it. Its goal is to advance the nation’s literary, artistic, and humanitarian growth. The NCERT textbooks and NCERT curriculum are published for students in classes 1 to 12. The NCERT textbooks and curricula are regarded as reliable resources for the CBSE Board Exam. These textbooks and curricula serve as the foundation for competitive exams like the National Eligibility Entrance Test (NEET), Union Public Service Commission (UPSC), Indian Institute of Technology (IIT), Provincial Civil Service (PCS), etc. in addition to being applicable for annual exams or CBSE Board Examinations.

Students may learn and get ready for the exams more rapidly thanks to the Extramarks’ fascinating, interesting, and user-friendly CBSE study tools. The study resources are produced by subject experts while keeping in mind the most recent CBSE syllabus. 

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Q.1

Write the following in decimal form and say what kind ofdecimal expansion each has:i 36100  ii 111  iii 418  iv 313  v 211  vi 329400

Ans

(i)36100=0.36 It is a terminating decimal because remainder is zero.(ii)111=0.0909090909… It is a non-terminating decimal because remainder is not zero.(iii)418=4.125 It is a terminating decimal because remainder is zero.(iv)313=0.230769230769…    =0.230769¯ It is a non terminating decimal because it is a repeating(v)211=0.181818181818…  =0.18¯ It is a terminating decimal because it is a repeating (vi)329400=0.8225 It is a terminating decimal because remainder is zero.

Q.2

You know that 17 = 0.142857¯. Can you predict what thedecimal expansions of 27 ,37 ,47, 57, 67 are, without actuallydoing the long division? If so, how?

Ans

Given: 17=0.142857¯∴        27=2×0.142857¯=0.285714¯        37=3×0.142857¯=0.428571¯        47=4×0.142857¯=0.571428¯        57=5×0.142857¯=0.714285¯        67=6×0.142857¯=0.857142¯

Q.3

Express the following in the form pq, where p and q areintegers and q¹0.i 0  ii 0.47 ¯  iii 0.001¯

Ans

(i)  Let x=0.6¯...(i)Multiplying both sides by 10, we get       10x=10×0.6¯       10x=6.6¯...(ii)Subtracting equation(i) from equation(ii), we get10x−x=6.6¯−0.6¯9x=6   x=69   x=23∴        0.6¯=23(ii) Let x=0.47¯...(i)Multiplying both sides of equation(i) by 10, we get       10x=10×0.47¯       10x=4.7¯...(ii)Multiplying both sides of equation(ii) by 10, we get    100x=10×4.7¯    100x=47.7¯...(iii)Subtracting equation(ii) from equation(iii), we get100x−10x=47.7¯−4.7¯    90x=43         x=4390∴           0.47¯=4390(iii)Let x=0.001¯...(i)Multiplying both sides of equation(i) by 1000, we get    1000x=1000×0.001¯        =1.001¯...(ii)Subtracting equation(i) from equation(ii), we get1000x −x=1.001¯−0.001¯          999x=1      x=1999∴     0.001¯=1999

Q.4

Express 0.99999, in the form pq. Are you surprised by your answer?With your teacher and classmates discussway the answer makes sense.

Ans

 Let x=0.99999…=0.9¯…(i)Multiplying both sides by 10, we get       10x=10×0.9¯       10x=9.9¯…(ii)Subtracting equation(i) from equation(ii), we get10x−x=9.9¯−0.9¯9x=9   x=99   x=1∴  0.99999…=1

Q.5

What can the maximum number of digits be in the repeatingblock of digits in the decimal expansion of 117? Perform thedivision to check your answer.

Ans

              0.0588235294117647        17 1.00                                           085 ¯                 150                  136 ¯                    140                     136 ¯                          40              34 ¯                 60                   51 ¯                     90                     85 ¯            50            34 ¯            160             153 ¯                                           70                  68 ¯                     20                      17 ¯            30            17 ¯             130              119 ¯                110               102 ¯          80          68 ¯         120         119 ¯               1 Thus,  1 17 =0. 0588235294117647 ¯ 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Q.6

Look at several examples of rational numbers in the formpq q≠0 , where p and q are integers with no commonfactors other than 1 and having terminating decimalrepresentations (expansions).Can you guess what propertyq must satisfy?

Ans

Since, the rational number pq will be terminating decimal if denominator qis either 2, 4, 5, 8, 10 and so on…92=4.5114=2.75178=2.125135=2.63210=3.2We see that rational number pq will be terminating if prime factors of qare either 2 only or multiple of 2 and 5 only or both.

Q.7  Write three numbers whose decimal expansions are non-terminating non-recurring.

Ans Three numbers whose decimal expansions are non- terminating non-recurring are as follows: 0.030030012003000050004123000… 0.01200012500003500050010008879000102003… 1.5200050040060080010030010040038001…

Q.8

Find three different irrational numbers between therational numbers 57 and 911.

Ans

Since, 57=0.714285¯ and 911=0.81¯Three irrational numbers between 57 and 911 are:0.72005006004000202005004…0.75005006004000202005004…0.80005006004000202005004…

Q.9

Classify the following numbers as rational or irrational:i 23  ii 225 iii 0.3796 iv 7.478478...   v 1.101001000100001...

Ans

(i)23=4.7983152331272…Since, this number is non-terminating and non-repeating, therefore it is irrational number.(ii)225=15, It is rational number.(iii)0.3796, It is rational number because this number is terminating.(iv)7.478478…=7.478¯, this is rational number as it is non-terminating and repeating. (v)1.101001000100001…,​ It is irrational number because it is non-terminating non repeating.

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FAQs (Frequently Asked Questions)

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

There are toilet 6 exercises in the Class 9 Mathematics Chapter 1 textbook. Listwise is given as follows

Exercise 1.1 4 Questions ( 2 long, 2 short)

Exercise 1.2 4 Questions ( 3 long, 1 short)

Exercise 1.3 9 Questions ( 9 long)

Exercise 1.4 2 Questions ( 2 long)

Exercise 1.5 5 Questions ( 4 long 1 short)

Exercise 1.6 3 Questions ( 3 long)

The Extramarks provide all exercise solutions. Students can check the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3.

2. How can the Extramarks the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 assist students?

The Mathematics specialists have prepared the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 to the questions in accordance with the most recent recommendations made by the CBSE and NCERT. To make their preparation quick and simple to grasp, they have broken down the solutions into steps. All the pertinent examinations and illustrations for the questions with real-world examples are provided.

Students can develop a strong foundation for all the topics by using these answers, which are organized in a methodical fashion. Extramarks makes sure that all the themes and subtopics from each chapter are addressed, and they have also created the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 so that studying will be more enjoyable, engaging, and effective for students.

3. What are the major features of the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3?

Students can use the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.3 to complete and review the Ch 1 Maths Class 9 Ex 1.3.

They will be able to earn higher scores after carefully practising the step-by-step answers provided by subject-matter experts.

It adheres to NCERT standards. From the standpoint, the test comprises all the crucial questions. It aids in achieving high Mathematics scores on standardized tests.