2023 NCERT Math Class 9 Number System

2023 NCERT Math Class 9 Number System Ex. 1.1 | 9th Math NCERT Solution Number System

The study of numbers forms 2023 NCERT Math Class 9 Number System, and a solid understanding of the number system is crucial for students’ mathematical development. In this comprehensive blog post, we will delve into the intriguing world of the number system as taught in Class 9 Mathematics. From the basic building blocks of natural numbers to the vast realm of real numbers, we will explore concepts such as number lines, rational numbers, irrational numbers, whole numbers, integers, and more. So, let’s embark on this mathematical journey together!

2023 NCERT Math Class 9 Number System

2023 NCERT Math Class 9 Number System : Natural Numbers:

The number system begins with the set of natural numbers. Natural numbers, denoted as N, comprise the counting numbers: 1, 2, 3, 4, and so on. These numbers represent quantities used for counting, such as the number of objects or people.

Download 2023 NCERT Class 9 Math Book full PDF

More Book related details visit NCERT Website

2023 NCERT Math Class 9 Number System : Whole Numbers:

Expanding upon the natural numbers, the set of whole numbers, denoted as W, includes zero (0) along with the counting numbers. Whole numbers allow us to represent the absence of objects or null quantities. In essence, whole numbers form a more comprehensive representation of quantities.

2023 NCERT Math Class 9 Number System : Integers:

Integers, denoted as Z, encompass both positive and negative numbers along with zero. Integers allow us to represent values in the opposite direction on a number line. For every positive number, there exists a corresponding negative number, forming a symmetrical representation.

2023 NCERT Math Class 9 Number System : Rational Numbers:

Rational numbers, denoted as Q, encompass numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Rational numbers include both terminating and repeating decimals. They can be positive, negative, or zero. For example, 1/2, -3/5, 2/7 are all rational numbers.

2023 NCERT Math Class 9 Number System : Irrational Numbers:

Irrational numbers, denoted as I, are numbers that cannot be expressed as fractions and do not terminate or repeat as decimals. They possess an infinite and non-repeating decimal representation. Examples of irrational numbers include √2, π (pi), and e (Euler’s number). The decimal expansion of irrational numbers is non-terminating and non-repeating.

2023 NCERT Math Class 9 Number System : Real Numbers:

The set of real numbers, denoted as R, encompasses both rational and irrational numbers. It includes all possible numbers on the number line, from negative infinity to positive infinity. Real numbers consist of integers, fractions, terminating decimals, and infinite non-repeating decimals.

2023 NCERT Math Class 9 Number System : Number Line:

A number line is a visual representation of the entire number system. It helps us visualize the relative positions and relationships between different types of numbers. On a number line, natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers are placed at appropriate positions.

NCERT Class 9 Math Number System Exercise 1.1 :

Q1. Is zero a rational number? Can you write it in the form p/q , where p and q are integers and q≠0?

A1. Yes, zero is indeed a rational number. It can be expressed in the form of p/q, where both p and q are integers, and q is not equal to zero.

To represent zero in this form, we can choose any value of p as zero and any non-zero value of q. For example, we can write 0 as 0/1 or 0/2 or 0/1000, and so on. In each case, p is zero, and q is a non-zero integer, satisfying the condition for a number to be rational.

The fact that any integer divided by non-zero integer results in a rational number, including the division of zero by a non-zero integer, reinforces the classification of zero as a rational number.

Q2. Find six rational numbers between 3 and 4

A2. There are infinite rational numbers between 3 and 4. (6+2=8) We need to find 6 rational numbers so we will multiply numerator and denominator with 8. This can be represented as 24/8 and 32/8(multiplying both 3/1 and 4/1 by 8/8) respectively, therefore 6 rational numbers between 3 and 4 are 25/8 ,26/8 ,27/8 ,28/8 ,29/8 ,30/8.

Q3. Find five rational numbers between 3/5 and 4/5

A3.There are infinite rational numbers between 3/5 and 4/5. (5+1=6) We need to find 5 rational numbers so we will multiply numerator and denominator with 6. This can be represented as 18/30 and 24/30(multiplying both 3/5 and 4/5 by 6/6)respectively,therefore 5 rational numbers between 3/5 and 4/5 are 19/30 ,20/30 ,21/30 ,22/30 ,23/30

State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

A3.(i) True,since the collection of whole numbers contain all the natural numbers.

(ii) False,as integers maybe negative but whole numbers are always positive for example -5 is a integer but not a whole number.

(iii)False,as rational can be fractional but whole number cannot be fractional for example,2/3 is a rational number but not a whole number.


The study of the number system in Class 9 Mathematics is a foundational step towards understanding and utilizing numbers in various mathematical contexts. From the basic concept of natural numbers to the intricate properties of irrational numbers and real numbers, each component plays a vital role in our mathematical journey.

By grasping the concepts of number lines, rational numbers, irrational numbers, whole numbers, integers, and real numbers, students can develop a deeper understanding of mathematical operations, equations, and problem-solving strategies.

Embrace the beauty and intricacy of the number system, as it provides a framework for exploring and understanding the mathematical universe. So, let’s continue to explore, discover, and apply the concepts of the number system to expand our mathematical horizons!

2023 NCERT Class 9 Math Book PDF Download

2023 NCERT Class 9 Math Book PDF Download | Best way to download NCERT PDF books

Now fresh copy is available of 2023 NCERT Class 9 Math Book PDF Download. In today’s digital era, the accessibility of educational resources has become easier than ever before. With the advent of technology, students can now access textbooks and study materials in digital formats, such as PDFs. Here you can download 2023 NCERT Class 9 Math book in PDF format, empowering students to enhance their learning experience and excel in their academic pursuits.

2023 NCERT Class 9 Math Book PDF Download

2023 NCERT Class 9 Math Book PDF Download : Importance of NCERT Class 9 Math Book:

The NCERT (National Council of Educational Research and Training) Class 9 Math book serves as a fundamental resource for students studying mathematics. This book is designed to develop a strong foundation in mathematical concepts, foster problem-solving skills, and promote logical thinking. It covers a wide range of topics that form the basis for advanced math education.

2023 NCERT Class 9 Math Book PDF Download : Benefits of Using PDF Format:

The PDF format offers numerous advantages for students and educators alike. Here are a few benefits of using the PDF version of the NCERT Class 9 Math book:

a. Portability: PDF files can be easily accessed and viewed on various devices like smartphones, tablets, laptops, or e-readers. Students can carry their entire textbook collection without the burden of physical books.

b. Searchability: PDFs allow users to search for specific keywords or topics within the book, enabling quick and efficient navigation. This feature proves invaluable during revision or when trying to locate specific concepts.

c. Annotation and highlighting: PDF readers often come with built-in tools that allow users to annotate, highlight, and bookmark important sections. These features aid in note-taking and revisiting essential points during exam preparation.

Steps to Download the 2023 NCERT Class 9 Math Book PDF:

You can download 2023 NCERT Class 9 Math Book PDF format from below download Button or you can follow following steps :

Download NCERT Class 9 Math Book PDF

Here is a step-by-step guide to help you download the NCERT Class 9 Math book in PDF format:

Step 1: Visit the official NCERT website.

Go to the official website of NCERT (www.ncert.nic.in) using any web browser.

Step 2: Navigate to the “Textbooks” section.

Locate the “Textbooks” section on the website’s homepage and click on it.

Step 3: Select the subject and class.

In the textbooks section, select the subject as “Mathematics” and choose the class as “Class 9.”

Step 4: Choose the book and download.

From the list of available textbooks, find and click on the link for the “Mathematics Class 9” book. This will take you to the book’s download page. Click on the PDF download link to start the download process.

Step 5: Access the downloaded PDF.

Once the download is complete, locate the downloaded PDF file on your device. You can now open it using a PDF reader or viewer application.


Access to educational resources in digital formats, such as the 2023 NCERT Class 9 Math book in PDF, has revolutionized the way students learn and study. The convenience, portability, and searchability of PDFs make them an excellent tool for enhancing the learning experience. By following the steps outlined in this comprehensive guide, students can easily download the NCERT Class 9 Math book and utilize it to strengthen their mathematical foundation.

Remember, the PDF version of the textbook is just a tool. To truly benefit from it, students must actively engage with the material. By creating a study plan, taking organized notes, and practicing regularly, students can unlock the full potential of the NCERT Class 9 Math book. Additionally, exploring supplementary resources and seeking guidance from teachers or online forums can further enrich the learning process.

As we move forward in the digital age, the availability of educational resources in digital formats will continue to grow. Embracing these advancements and leveraging the benefits of PDF textbooks can significantly contribute to academic success. So, empower yourself with the 2023 NCERT Class 9 Math book PDF and embark on a journey of mathematical exploration and achievement. Happy learning!


Is the 2023 NCERT Class 9 Math book available for free download on shastrarth.com?

Yes, shastrarth.com offer downloads of NCERT textbooks. However, we provide valuable educational content, study guides, and resources to help students excel in their academic pursuits.

Are there any other websites where I can download the 2023 NCERT Class 9 Math book in PDF format?

Yes, besides the official NCERT website, there are several reputable platforms that offer free downloads of NCERT textbooks in PDF format. It’s important to verify the authenticity and accuracy of the downloaded material before utilizing it for your studies.

Can I access the 2023 NCERT Class 9 Math book in PDF format on my mobile device?

Absolutely! Once you have downloaded the PDF file, you can easily access it on your mobile device using a PDF reader application. This allows you to study mathematics on the go, making learning more convenient and accessible.

Are there any additional resources available on shastrarth.com to supplement the NCERT Class 9 Math book?

Yes, shastrarth.com offers a wide range of additional resources to complement your study of the NCERT Class 9 Math book. You can find practice questions, solved examples, concept explanations, and study tips to further enhance your understanding and performance in mathematics.

Can I use the 2023 NCERT Class 9 Math book in PDF format for exam preparation?

Absolutely! The NCERT Class 9 Math book is a valuable resource for exam preparation. By downloading the PDF version, you can easily navigate through the book, highlight important sections, and take notes. Regular practice with exercises from the book will strengthen your problem-solving skills and help you perform well in exams.


Adhyatm and Gurukul: The Harmonious Blend of Spirituality and Science in Ancient Indian Education

In ancient India, the education system was deeply rooted in the principles of spirituality and the pursuit of knowledge. The concepts of Adhyatma (spirituality) and Gurukul (traditional school) formed the bedrock of this holistic approach to education. Let us embark on a journey back in time to explore the seamless integration of spirituality and science in the old Indian Gurukul teaching method.


Section 1: The Essence of Adhyatma

Adhyatma, meaning “spirituality” in Sanskrit, refers to the exploration of the inner self and the profound connection between the individual and the universal consciousness. This section delves into the spiritual foundation of ancient Indian education, emphasizing the development of character, moral values, and the understanding of one’s purpose in life. Adhyatma nurtured the students’ spiritual growth, fostering a sense of harmony, compassion, and reverence for all aspects of existence.

Section 2: The Gurukul Teaching Method

Gurukul, a traditional residential school, epitomized the holistic education system of ancient India. Under the guidance of a revered Guru (teacher), students received comprehensive instruction encompassing a wide range of subjects. This section explores the unique characteristics of the Gurukul system, emphasizing its personalized approach, experiential learning, and the close bond between the Guru and the students.

Section 3: Integration of Spirituality and Science

In the ancient Gurukuls, spirituality and science were not seen as separate realms but as intertwined paths to understanding the universe. This section highlights how spiritual teachings and scientific knowledge were seamlessly interwoven. Students learned about the laws of nature, astronomy, mathematics, and medicine, while also exploring profound philosophical concepts, meditation techniques, and the interconnectedness of all living beings.

Section 4: The Relevance Today

The principles of Adhyatma and the Gurukul teaching method continue to hold relevance in the modern world. This section discusses how the integration of spirituality and science can enhance contemporary education. By nurturing values, promoting critical thinking, and instilling a sense of interconnectedness, we can cultivate well-rounded individuals who can tackle complex challenges and contribute to the betterment of society.


The ancient Indian Gurukul system, deeply rooted in spirituality and the pursuit of knowledge, exemplifies the harmonious blend of science and spirituality. It highlights the interconnectedness of all disciplines and the importance of nurturing the mind, body, and spirit. By embracing the timeless wisdom of Adhyatma and the Gurukul teaching method, we can create an education system that not only imparts knowledge but also instills moral values, fosters holistic development, and inspires a sense of wonder and reverence for the mysteries of existence. Let us draw inspiration from this ancient tradition as we navigate the challenges of the modern world, forging a future where spirituality and science converge for the betterment of humanity.


Welcome to the Marvels of Science: A Journey of Discovery

Welcome to our first post on the captivating world of science! Science is a voyage of exploration, uncovering the mysteries of the universe and shedding light on the incredible phenomena that surround us. Join us on this exhilarating journey as we delve into the vast realm of scientific knowledge, from the infinitesimally small building blocks of matter to the awe-inspiring expanse of the cosmos.


Section 1: The Quest for Understanding

In this section, we delve into the innate curiosity that drives scientific inquiry. Humans have always sought to understand the world around them, and science provides us with the tools to embark on this quest for knowledge. From the ancient philosophers pondering the nature of reality to the modern scientific method, we explore the evolution of scientific thinking and its impact on shaping our understanding of the natural world.

Section 2: Branches of Science: Illuminating the Web of Knowledge

\Science encompasses a rich tapestry of disciplines, each offering a unique perspective and contributing to our collective understanding. In this section, we explore the major branches of science, such as physics, chemistry, biology, astronomy, geology, and more. Discover the intricate interconnections between these fields and witness how they collaborate to unravel the mysteries of our existence.

Section 3: Scientific Wonders and Breakthroughs

Science continually pushes the boundaries of human knowledge, unveiling astonishing discoveries and groundbreaking breakthroughs. In this section, we embark on a tour of some of the most remarkable scientific achievements throughout history and the present day. From the theory of relativity to the mapping of the human genome, we celebrate the ingenuity and perseverance of scientists who have forever transformed our understanding of the world.

Section 4: Science in Everyday Life

Science is not confined to laboratories and academic institutions; it permeates every aspect of our daily lives. In this section, we explore the practical applications of scientific knowledge in our modern world. From medical advancements and technological innovations to environmental conservation and space exploration, science touches our lives in countless ways. Discover how scientific principles shape our society, drive innovation, and address the challenges we face.


As we embark on this journey of scientific exploration, we invite you to join us in celebrating the wonders of science. From the tiniest atoms to the vastness of the cosmos, science offers us a lens through which we can comprehend the complexities and marvels of the natural world. Stay tuned for future posts, where we’ll dive deeper into fascinating scientific topics, unravel perplexing mysteries, and ignite the spark of curiosity within us all. Together, let’s embrace the quest for knowledge and embark on a lifelong adventure of discovery.


The Beauty of Mathematics: Unveiling the Patterns that Shape our World

Welcome to our inaugural blog post, where we embark on a journey to unravel the captivating world of mathematics. Mathematics is not merely a subject confined to textbooks and classrooms; it is a language that reveals the hidden patterns and structures that underpin our universe. Join us as we explore the elegance and power of mathematics, delving into its historical significance, real-world applications, and the sheer beauty it holds.


Section 1: A Glimpse into Mathematical History

In this section, we delve into the rich history of mathematics, tracing its origins to ancient civilizations and highlighting the remarkable contributions of renowned mathematicians. From the groundbreaking discoveries of ancient Greece to the revolutionary advancements of modern mathematicians, we uncover the evolution of mathematical concepts and theories that have shaped the way we perceive the world.

Section 2: Mathematics in Everyday Life

Here, we explore the practical applications of mathematics in our daily lives. From the algorithms that power our smartphones and the encryption techniques that secure our online transactions to the mathematical models used in predicting weather patterns and analyzing stock market trends, mathematics plays a vital role in countless aspects of our modern world. Discover how mathematics enables us to make sense of complex phenomena and solve real-world problems.

Section 3: The Intricate World of Mathematical Patterns

One of the most awe-inspiring aspects of mathematics is the presence of intricate patterns and symmetries that exist across various disciplines. In this section, we delve into the mesmerizing world of patterns, from the Fibonacci sequence found in nature to the fractal structures that emerge from mathematical equations. We explore the beauty of geometric patterns, numerical sequences, and the harmony they bring to the world around us.

Section 4: Mathematics as a Powerful Problem-Solving Tool

Mathematics equips us with invaluable problem-solving skills that transcend the realm of numbers. In this section, we discuss how mathematical thinking fosters logical reasoning, critical analysis, and creative problem-solving abilities. We explore how mathematical principles and techniques are employed in various fields, such as engineering, computer science, economics, and even art, to tackle complex challenges and drive innovation.


As we conclude our first foray into the realm of mathematics, we invite you to join us on this exhilarating exploration of numerical wonders. Mathematics serves as a gateway to understanding the underlying order in the chaos, unveiling the symphonies of patterns and unlocking new realms of knowledge. Stay tuned for future posts, where we’ll delve deeper into intriguing mathematical concepts, demystify complex theories, and continue to celebrate the beauty that lies within the fascinating world of mathematics.