NCERT Solutions for Class 9 Maths Chapter 1 – Expert Guide on Number Systems

ncert solutions for class 9 maths chapter 1 provides detailed explanations and step-by-step solutions for Number Systems, simplifying concepts for better learning.

What is a rational number? A rational number is any number that can be expressed in the form of a fraction or ratio of two integers, where the denominator is not zero.

What is an irrational number? An irrational number cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating.

Give an example of an irrational number. An example is the square root of 2, as its decimal expansion is non-terminating and non-repeating.

Is 0 a rational number? Yes, 0 is a rational number as it can be expressed as 0 divided by any non-zero integer.

Explain what real numbers are. Real numbers consist of both rational and irrational numbers, encompassing all numbers along the number line.

What is the decimal representation of a rational number? The decimal representation of a rational number is either terminating or non-terminating but repeating.

How do you identify an irrational number from decimal expansion? If the decimal expansion neither terminates nor repeats, the number is irrational.

What are integers? Integers are the set of whole numbers and their negatives, including zero.

Can a whole number be negative? No, whole numbers are always zero or positive; they never include negative numbers.

What is the smallest whole number? The smallest whole number is 0.

Is every integer a rational number? Yes, every integer is a rational number because it can be expressed as itself divided by 1.

Explain terminating decimals with an example. Terminating decimals have a finite number of digits after the decimal point, e.g., 0.75.

What is a repeating decimal? A repeating decimal has one or more digits after the decimal point that repeat indefinitely, e.g., 0.3333…

Is √5 a rational number? No, √5 is irrational because its decimal expansion does not terminate or repeat.

Can the sum of two irrational numbers be rational? Yes, the sum of two irrational numbers can sometimes be rational, e.g., (√2) + (-√2) equals 0.

Is the product of two rational numbers always rational? Yes, multiplying two rational numbers always results in a rational number.

How do you represent √3 on a number line? Use a geometric method to represent √3 by constructing a right-angled triangle with sides 1 and √2, and extend it onto the number line.

What happens when you multiply a rational and irrational number? The product is typically irrational unless the rational number is zero.

Define natural numbers. Natural numbers are counting numbers starting from 1, without zero or negatives.

Is √9 rational or irrational? √9 is rational because it equals exactly 3.

Give an example of two irrational numbers whose product is rational. √2 multiplied by √8 equals 4, which is rational.

Is the decimal 0.1010010001… rational or irrational? This decimal is irrational as the digits are non-repeating and non-terminating.

Express 0.6 as a fraction. 0.6 as a fraction is 3/5.

Can a rational number have infinite decimals? Yes, rational numbers can have infinite decimals that repeat, such as 0.6666...

Explain why π (pi) is irrational. Pi (π) is irrational because its decimal form never terminates nor repeats.

What type of decimal is 1/3? 1/3 is a repeating decimal, written as 0.3333…

If √x is rational, what can you say about x? If √x is rational, then x must be a perfect square.

Is the sum of a rational and irrational number rational or irrational? The sum is always irrational.

Explain whole numbers. Whole numbers include 0 and all positive integers.

Why is 2/3 a rational number? Because 2/3 can be expressed as a fraction with integers, it is rational.

How do you show 3.47 on the number line? Locate 3, then mark the position between 3 and 4 closer to 3 at the 0.47 position.

What type of number is -7? -7 is an integer and a rational number.

Can irrational numbers be negative? Yes, irrational numbers can be negative, such as -√2.

What is the reciprocal of a rational number? The reciprocal is obtained by reversing the numerator and denominator.

Is 5.5 a rational number? Yes, because it can be expressed as 11/2.

Explain non-terminating decimals. Non-terminating decimals continue infinitely without stopping.

What is the difference between natural and whole numbers? Natural numbers start from 1, while whole numbers include 0.

Is every rational number an integer? No, rational numbers include fractions and decimals, not just integers.

Is √7 rational? No, √7 is irrational, as it cannot be expressed as a fraction.

How do you convert repeating decimals to fractions? Set the repeating decimal as x, multiply by a suitable power of 10, subtract equations to remove repeating digits, and solve for x.

Why is zero considered a rational number? Zero can be expressed as 0 divided by any non-zero integer.

Give one example of a terminating decimal. 0.25 is a terminating decimal.

Is 22/7 rational or irrational? 22/7 is rational, as it is expressed as a simple fraction.

Define a decimal number. A decimal number contains digits after the decimal point.

Are negative numbers included in natural numbers? No, natural numbers include only positive numbers starting from 1.

What makes numbers irrational? Numbers that cannot be expressed as simple fractions are irrational.

What is a non-repeating decimal? Decimals whose digits after the decimal point never repeat.

Explain the number line. The number line is a visual representation of numbers placed at equal intervals along a straight line.

Can irrational numbers be integers? No, irrational numbers can never be integers because integers are exact and irrational numbers have non-terminating decimals.

Is √16 irrational? No, √16 is rational, as it equals exactly 4.

Best Indian Books for NCERT Solutions for Class 9 Maths Chapter 1

Mathematics for Class 9 by R.D. Sharma
Publisher: Dhanpat Rai Publications
Content: Detailed explanations, solved examples, and extensive practice problems on Number Systems.

Secondary School Mathematics by R.S. Aggarwal
Publisher: Bharati Bhawan Publishers
Content: Step-by-step solutions, practice questions, multiple-choice questions, and higher-order thinking questions on Number Systems.

All in One Mathematics Class 9 by Arihant Experts
Publisher: Arihant Publications
Content: Comprehensive solutions, summaries, concept maps, practice tests, and HOTS questions on Number Systems.

NCERT Exemplar Problems Solutions Mathematics Class 9 by Oswaal Editorial Board
Publisher: Oswaal Books
Content: Concept-based exemplar problems, short and long-answer questions for Number Systems.

Together with Mathematics Class 9 by S.K. Batra
Publisher: Rachna Sagar Publications
Content: Extensive solved NCERT questions, MCQs, short-answer, and descriptive-type questions for thorough practice.

Xam Idea Mathematics Class 9 by Editorial Board
Publisher: VK Global Publications
Content: Chapter-wise solved NCERT questions, additional practice problems, and quick revision exercises for Number Systems.

Full Marks Mathematics Class 9 by Dr. Ram Kumar Sharma
Publisher: Full Marks Pvt. Ltd.
Content: Solutions to NCERT exercises, important questions, and chapter-wise summaries for effective understanding.

Mathematics Success Book Class 9 by Goyal Brothers
Publisher: Goyal Brothers Prakashan
Content: Chapter-wise solved exercises, HOTS questions, value-based problems, and practice tests.

CBSE Chapterwise Solutions Mathematics Class 9 by MTG Editorial Board
Publisher: MTG Learning Media Pvt. Ltd.
Content: Well-organized solutions, extensive numerical problems, MCQs, and exam-oriented questions on Number Systems.

Foundation Mathematics Class 9 by RS Agrawal
Publisher: Goyal Brothers Prakashan
Content: Detailed explanations, solved problems, skill-based exercises, and worksheets focusing on Number Systems.

Self-Help to NCERT Solutions Mathematics Class 9 by Munish Sethi
Publisher: Evergreen Publications
Content: Simple, clear solutions, supplementary questions, and summaries emphasizing concept clarity.

Cordova Learning Series Mathematics Class 9 by R.C. Yadav
Publisher: Cordova Publications
Content: Conceptual clarity, solved problems, mental math questions, and assessments for deep learning.

S Chand's Mathematics for Class 9 by H.K. Dass
Publisher: S Chand Publishing
Content: Conceptual explanations, solved examples, formative assessment questions, and practice exercises on Number Systems.

Learning Mathematics for Class 9 by M.L. Aggarwal
Publisher: Arya Publications
Content: Easy-to-follow solutions, skill-building problems, conceptual exercises, and revision tests.

Pearson IIT Foundation Mathematics Class 9 by Trishna Knowledge Systems
Publisher: Pearson Education
Content: Concept-focused solutions, competitive-level questions, practice tests, and foundation-building exercises.

NCERT Solutions for Class 9 Maths Chapter 1: Mastering Number Systems

NCERT solutions for Class 9 Maths Chapter 1, “Number Systems,” set the foundation for students' mathematical journey in secondary education. This chapter introduces students to essential concepts of number classifications, rational and irrational numbers, and their practical applications. A firm grasp of Number Systems helps students excel in algebra, geometry, and advanced mathematics in higher classes.

To effectively tackle Chapter 1, students should seek quality resources that offer clear explanations, systematic solutions, and practice problems that enhance analytical abilities. Expert-backed recommendations suggest opting for books by reputable authors such as R.D. Sharma and R.S. Aggarwal, whose detailed explanations simplify complex topics.

The best books present NCERT solutions clearly and methodically, beginning with conceptual basics and advancing toward challenging problems. They explain the properties of rational and irrational numbers, the number line, operations with decimals, and real numbers. R.D. Sharma's mathematics series, widely preferred by educators and students, breaks down each topic into simple steps, enabling students to master foundational concepts quickly.

For extensive practice, the Xam Idea series provides students with solved exercises, sample problems, and quick revision notes. It covers all types of questions—from short-answer and objective-type to HOTS (Higher Order Thinking Skills)—that encourage critical thinking. Similarly, Arihant's All-in-One Mathematics systematically organizes content, making revision straightforward.

Books like Oswaal NCERT Exemplar help students prepare rigorously for exams by providing exemplar problems, including questions that have appeared in previous years. These exemplars not only strengthen mathematical understanding but also boost students' confidence during exams.

To understand Number Systems deeply, practicing from books like Together with Mathematics by S.K. Batra and Mathematics Success Book by Goyal Brothers Prakashan is essential. These books contain extensive practice exercises, MCQs, and self-assessment questions designed to consolidate student knowledge effectively.

Additionally, books by MTG Editorial Board and Cordova Publications deliver visually appealing content with easy-to-follow diagrams, step-by-step explanations, and structured assessments. They encourage active learning by prompting students to engage directly with problem-solving techniques.

Many students face difficulty distinguishing rational from irrational numbers. Books like Foundation Mathematics by RS Agrawal and Self-Help to NCERT Mathematics by Munish Sethi address this issue head-on by providing clarity through numerous solved examples, enabling students to grasp the underlying concepts fully.

Pearson's IIT Foundation Mathematics goes a step further by integrating competitive exam-level questions. This approach helps students aiming for future exams like JEE and Olympiads, building foundational strength early on.

For beginners, Full Marks Mathematics by Dr. Ram Kumar Sharma and S Chand's Mathematics by H.K. Dass offer simplified explanations ideal for self-study. They use clear language and illustrative examples to make concepts more accessible to every learner.

Choosing the right book is crucial, as clarity in Number Systems directly impacts a student's capability to understand advanced mathematical concepts. Parents and educators alike emphasize selecting textbooks that offer practical exercises, clear examples, and structured solutions that align closely with NCERT guidelines.