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# NCERT Solutions for Maths Chapter 1 Exercise 1.2 Class 9 - Number Systems

Last updated date: 10th Aug 2024
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## NCERT Solutions for Class 9 Maths Chapter 1 - Number Systems Exercise 1.2 - FREE PDF Download

Class 9 Maths NCERT Solutions for Chapter 1 Number System  Exercise 1.2 focuses on the representation, and simplification of irrational numbers. This exercise helps students understand how to express irrational numbers on the number line and perform operations with them. Vedantu's solutions for exercise 1.2 class 9 maths provide clear, step-by-step explanations and methods to simplify irrational numbers, making it easier for students to grasp these concepts. The class 9 exercise 1.2 solutions are designed to build a strong foundation in number systems, which is crucial for more advanced topics in mathematics. This introduction ensures students are well-prepared to tackle problems involving irrational numbers with confidence.

Table of Content
1. NCERT Solutions for Class 9 Maths Chapter 1 - Number Systems Exercise 1.2 - FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 1 Exercise 1.2 Class 9| Vedantu
3. Access NCERT Solutions for Class 9 Maths Chapter 1 Number System
4. Class 9 Maths Chapter 1: Exercises Breakdown
5. CBSE Class 9 Maths Chapter 1 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 9 Maths
FAQs

## Glance on NCERT Solutions Maths Chapter 1 Exercise 1.2 Class 9| Vedantu

• Class 9 Maths Chapter 1 - Number Systems, Exercise 1.2 provides an in-depth look at irrational numbers and their properties.

• Any number that can be written in the form as a ratio of two natural numbers is a rational number.

• The irrational numbers are the numbers that cannot be represented in the form $\dfrac{p}{q},$ where $p$ and $q$ are integers and $q\ne 0.$

For example, $\sqrt{2},3\pi ,\text{ }.011011011...$ are all irrational numbers.

• Characteristics of Irrational Numbers.

• Non-Terminating and Non-Repeating Decimals:

• Irrational numbers have decimal expansions that neither terminate nor repeat.

• There are four exercises (27 fully solved questions) in class  9  maths chapter 1 Number System and There are 4 fully solved questions in exercise 1.2 class 9 maths.

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

### Exercise (1.2)

1. State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

Ans: Write the irrational numbers and the real numbers in a separate manner.

• The irrational numbers are the numbers that cannot be represented in the form $\dfrac{p}{q},$ where $p$ and $q$ are integers and $q\ne 0.$

For example, $\sqrt{2},3\pi ,\text{ }.011011011...$ are all irrational numbers.

• The real number is the collection of both rational numbers and irrational numbers.

For example, $0,\,\pm \dfrac{1}{2},\,\pm \sqrt{2}\,,\pm \pi ,...$ are all real numbers.

Thus, it is concluded that every irrational number is a real number.

Hence, the given statement is true.

(ii) Every point on the number line is of the form $\sqrt{m}$, where m is a natural number.

Ans: Consider points on a number line to represent negative as well as positive numbers.

Observe that, positive numbers on the number line can be expressed as $\sqrt{1,}\sqrt{1.1,}\sqrt{1.2},\sqrt{1.3},\,...$, but any negative number on the number line cannot be expressed as $\sqrt{-1},\sqrt{-1.1},\sqrt{-1.2},\sqrt{-1.3},...$, because these are not real numbers.

Therefore, it is concluded from here that every number point on the number line is not of the form $\sqrt{m}$, where $m$ is a natural number.

Hence, the given statement is false.

(iii) Every real number is an irrational number.

Ans: Write the irrational numbers and the real numbers in a separate manner.

• The irrational numbers are the numbers that cannot be represented in the form $\dfrac{p}{q},$ where $p$ and $q$ are integers and $q\ne 0.$

For example, $\sqrt{2},3\pi ,\text{ }.011011011...$ are all irrational numbers.

• Real numbers are the collection of rational numbers (Ex: $\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{5},\dfrac{5}{7},$……) and the irrational numbers (Ex: $\sqrt{2},3\pi ,\text{ }.011011011...$).

Therefore, it can be concluded that every irrational number is a real number, but every real number cannot be an irrational number.

Hence, the given statement is false.

2. Are the square roots of all positive integer numbers irrational? If not, provide an example of the square root of a number that is not an irrational number.

Ans: Square root of every positive integer does not give an integer.

For example: $\sqrt{2},\sqrt{3,}\sqrt{5},\sqrt{6},...$ are not integers, and hence these are irrational numbers. But $\sqrt{4}$ gives $\pm 2$ , these are integers and so, $\sqrt{4}$ is not an irrational number.

Therefore, it is concluded that the square root of every positive integer is not an irrational number.

3. Show how $\sqrt{5}$ can be represented on the number line.

Ans: Follow the procedures to get $\sqrt{5}$ on the number line.

• Firstly, Draw a line segment $AB$ of $2$ unit on the number line.

• Secondly, draw a perpendicular line segment $BC$ at $B$ of $1$ units.

• Thirdly, join the points $C$ and $A$, to form a line segment $AC$.

• Fourthly, apply the Pythagoras Theorem as

$A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}$

$A{{C}^{2}}={{2}^{2}}+{{1}^{2}}$

$A{{C}^{2}}=4+1=5$

$AC=\sqrt{5}$

• Finally, draw the arc $ACD$, to find the number $\sqrt{5}$ on the number line as given in the diagram below.

4. Classroom activity (Constructing the ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment $OP_{1}$ of unit length. Draw a line segment $P_{1}$ $P_{2}$ perpendicular to $OP_{1}$ of unit length (see Fig. 1.9). Now draw a line segment $P_{2}$ $P_{3}$ perpendicular to $OP_{2}$ . Then draw a line segment $P_{3}$ $P_{4}$ perpendicular to $OP_{3}$ . Continuing in this manner, you can get the line segment $P_{n–1}$Pn by drawing a line segment of unit length perpendicular to OPn–1. In this manner, you will have created the points $P_{2}$ ,$P_{3}$ ,...., $P_{n}$ ,... ., and joined them to create a beautiful spiral depicting $\sqrt{2}, \sqrt{ 3}, \sqrt{4}, …$

Ans:

Step 1: Mark a point O

Choose a point O on your paper. This will be the centre of your square root spiral.

Step 2: Draw line OA of 1 cm horizontally

From point O, draw a straight line OA horizontally to the right. The length should be 1 cm.

Step 3: Draw perpendicular line AB of 1 cm

From point A (the end of OA), draw a line AB vertically upwards. The length of AB should also be 1 cm.

Step 4: Join OB (length √2)

Join point O to point B (the end of AB). The length of OB should be √2 cm.

Step 5: Draw perpendicular line from B and mark C

From point B, draw another line perpendicular to OB (going upwards) of 1 cm. Mark the endpoint of this line as C.

Step 6: Join OC (length √3)

Join point O to point C. The length of OC should be √3 cm.

Step 7: Repeat the process

Repeat steps 5 and 6 to continue the spiral:

From point C, draw a perpendicular line of 1 cm upwards and mark the endpoint as D.

Join O to D. The length OD should be √4 cm.

Continue this process, each time increasing the length of the perpendicular line by 1 cm and joining the new point to O to form the next segment of the spiral, where the length of each segment from O increases by 1 each time (resulting in √2, √3, √4, etc.).

## Conclusion

In NCERT Solutions for Class 9 Chapter 1 Exercise 1.2 on the Number System by Vedantu, students delve into the basics of numbers. Key points include understanding the classification of numbers into natural, whole, integers, rational, and irrational. Focus on mastering operations like addition, subtraction, multiplication, and division with these numbers. Previous year question papers typically feature 5–7 questions, testing the application of these concepts. It's crucial to grasp the properties of different number types and how they interact in mathematical operations. By mastering these fundamentals, students build a solid foundation for more advanced mathematical concepts.

## Class 9 Maths Chapter 1: Exercises Breakdown

 Exercise Number of Questions Exercise 1.1 4 questions and solutions Exercise 1.3 9 questions and solutions

## Chapter-Specific NCERT Solutions for Class 9 Maths

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

## FAQs on NCERT Solutions for Maths Chapter 1 Exercise 1.2 Class 9 - Number Systems

1. Why should I opt for Vedantu’s NCERT solutions for class 9 maths Chapter 1 Exercise 1.2?

NCERT solutions for class 9 maths chapter 1 – Number Systems Exercise 1.2 is the second exercise of Chapter 1 of class 9 Maths. This exercise deals with Irrational numbers especially. Below are the advantages of opting for Vedantu’s NCERT Solutions.

• These NCERT Solutions help you solve and revise all the questions from exercise 1.2.in a very less time.

• After going through the stepwise solutions given by our subject expert teachers, you will be able to get more marks.

• First and foremost, these solutions will help the students score the highest possible marks.

• These are designed as per the NCERT guidelines which help in preparing the Class 9 students accordingly.

• The solutions consist of answers to all the important questions from the final examination point of view.

2. What is Class 9 maths Chapter 1 Exercise 1.2 all about?

NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.2 offered by Vedantu are prepared by our subject matter experts which makes it easy for the CBSE board students to learn efficiently. The students refer to these while solving the exercise problems. Exercise 1.2 or the second exercise in Number Systems deals with the irrational numbers. These provide an in-depth and stepwise explanation of each of the questions given in the exercises in the NCERT textbook for class 9 chapter 2. The solutions are prepared as per the latest NCERT curriculum and guidelines so that it should cover the whole syllabus accordingly. These are very helpful in scoring the best possible marks in the examinations.

3. How many questions are there in Class 9 maths Chapter 1 Exercise 1.2?

Class 9 Maths Chapter 1 Exercise 1.2 of the NCERT textbook consists of four questions in total. Among which, three are long type questions and one short question. Our Vedantu solutions consist of answers to all these questions crafted by our excellent experts.

You can download the NCERT solutions Class 9 maths Chapter 1 Exercise 1.2 from Vedantu website and mobile application. These solutions which are provided in PDF format are prepared by our subject matter experts. The students can always use these for reference while solving the exercise problems.

5. What are the topics covered in Exercise 1.2 of Chapter 1 of Class 9 Maths?

There are seven topics covered in Chapter 1 Number System of Class 9 Maths. But the topic on which Exercise 1.2 is based is:

• Exercise 1.1- Introduction to Number System

• Exercise 1.2 deals with the Introduction to irrational numbers

• Exercise 1.3-Real numbers and their decimal expansion

• Exercise 1.4- Representing real numbers on the number line

• Exercise 1.5- Operations on the real number

• Exercise 1.6- Laws of exponents of real numbers

• Summary of the chapter

Students can refer to the NCERT book of Class 9 Maths to understand these topics thoroughly.

6. How can I understand the Class 9 Maths Chapter 1 Number System Exercise 1.2?

If you want to understand Class 9 Maths Chapter 1 Number System easily, then check out Vedantu. Here, you will find a detailed explanation of the chapter in an understandable format. Moreover, you'll also get answers to the NCERT Maths questions for Class 9 Maths Chapter 1 Exercise 1.2 and numerous mock test papers to help you to understand the important concepts. These are available for free both on Vedantu’s website and on Vedantu’s mobile app.

7. How can I make a study plan for preparing Chapter 1 of Class 9 Maths?

To make a successful study plan for preparing the Chapter 1 Number System given in the Class 9 Maths book, you should follow the given steps:

• Build a schedule balanced with all your daily activities.

• Set a timetable and have a designated study area.

• Limit your study time to two hours on this chapter to ensure you don’t lose your focus. You can increase or decrease the time limit according to your preference. During this time, read all the important concepts, solve questions, etc.

8. State whether the statement is true or false. Every point on the number line is in the form of √m where m is a natural number.

The given statement is false. It is wrong according to the norm ‘ a negative can’t be expressed as square roots.

For example- √16= 4 where 4 is a natural number. On the other hand, √3= 1.73 which is not a natural number. Similarly, negative numbers can also be represented on the number line but we know that a negative number changes into a complex number if we take the root of a negative number. For instance- √-8= 8i where i = √-1. Hence, the statement- every point on the number line is in the form of √m where m is a natural number is wrong.

9. How can I score full marks in Exercise 1.2 of Chapter 1 of Class 9 Maths?

Here are the useful tips to score good marks in Exercise 1.2 of Chapter 1 Number System in Class 9 Maths:

• Keep a notebook for theories, formulas and methods to solve important questions for last moment revision.

• Solve tough mathematical problems by yourself.

• Understand Chapter 1 along with its weightage to filter important exercises.

• Pick out the concepts of the chapter that require extra revision. You can do this by solving different question papers.

10. What is the importance of Exercise 1.2 in Class 9 Maths?

Exercise 1.2 is essential for building a strong foundation in the Number System, which is fundamental for understanding more advanced mathematical concepts in higher classes.

11. How do you perform operations with different types of numbers in maths class 9 chapter 1 exercise 1.2?

Operations such as addition, subtraction, multiplication, and division are performed according to the properties of each type of number, such as closure, commutativity, associativity, and distributivity.

12. What are the properties of rational and irrational numbers discussed in class 9 maths chapter 1.2?

Properties such as closure under addition, subtraction, multiplication, and division for rational numbers, and non-repeatability and non-termination for irrational numbers are discussed.

13. How do you classify numbers in Class 9 Maths Exercise 1.2?

Numbers are classified into different categories such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers based on their properties and characteristics.

14. What is the significance of understanding rational and irrational numbers in class 9th maths exercise 1.2?

Understanding rational and irrational numbers is crucial as they form the basis for solving various mathematical problems and are used in real-life applications such as measurements, calculations, and scientific analysis.

15. What are the properties of whole numbers discussed in Exercise 1.2?

Properties such as closure under addition and multiplication, commutativity, associativity, and distributivity are discussed for whole numbers in class 9 math ex 1.2.