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# NCERT Solutions For Maths Chapter 1 Exercise 1.1 Class 9 - Number System

Last updated date: 10th Aug 2024
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## NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.1- FREE PDF Download

Chapter 1 of Class 9 Maths, "Number System," introduces students to the fundamental concepts of numbers, their classifications, and properties. Exercise 1.1 focuses on understanding different types of numbers, including natural, whole, integers, rational, and irrational numbers. Vedantu's NCERT Solutions for Class 9 Maths Chapter 1 - Number System are essential for exam success.

Table of Content
1. NCERT Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.1- FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 1 Exercise 1.1 Class 9 | Vedantu
3. Topics Covered in Class 9 Maths Chapter 1 Exercise 1.1
4. Access PDF for Maths NCERT Chapter 1 Number System Exercise 1.1 Class 9
4.1Exercise (1.1)
5. Class 9 Maths Chapter 1: Exercises Breakdown
6. CBSE Class 9 Maths Chapter 1 Other Study Materials
7. Chapter-Specific NCERT Solutions for Class 9 Maths
FAQs

Solutions of class 9 ex 1.1 prepared by maths experts help students understand important concepts, boost confidence, and improve exam scores. These comprehensive solutions are available for free on Vedantu, making subjects like Science, Maths, and English easier to study.

## Glance on NCERT Solutions Maths Chapter 1 Exercise 1.1 Class 9 | Vedantu

• This exercise lays the groundwork for understanding the various number systems we use in mathematics.

• Natural Numbers: These are the counting numbers, starting from 1 (1, 2, 3, ...).

• Whole Numbers: These include natural numbers and zero (0, 1, 2, 3, ...).

• Integers: This set comprises whole numbers and their negative counterparts (... -3, -2, -1, 0, 1, 2, 3, ...).

• Rational Numbers: Numbers that can be expressed as a fraction (p/q), where p and q are integers and q ≠ 0 (e.g., 1/2, 3/4, -5/7).

• Irrational Numbers: Numbers that cannot be expressed as a terminating or repeating decimal (e.g., √2, π).

• By working through the problems in this exercise, students will gain practice in identifying different types of numbers and understanding their properties.

• Exercise 1.1 Class 9th Class Math Solution Chapter 1 has over all 4 questions, all 4 are short answers.

## Topics Covered in Class 9 Maths Chapter 1 Exercise 1.1

• Different Types of Numbers.

• Representation of Numbers.

• Operations on Numbers.

• Properties of Numbers.

• Classifying Numbers.

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## Access PDF for Maths NCERT Chapter 1 Number System Exercise 1.1 Class 9

### Exercise (1.1)

1.  Is zero a rational number? Can you write it in the form  $\dfrac{ {p}}{ {q}}$, where ${p}$ and ${q}$ are integers and ${q}\ne {0}$? Describe it.

Ans: Remember that, according to the definition of rational number,

a rational number is a number that can be expressed in the form of  $\dfrac{p}{q}$, where $p$ and $q$ are integers and  $q\ne \text{0}$.

Now, notice that zero can be represented as $\dfrac{0}{1},\dfrac{0}{2},\dfrac{0}{3},\dfrac{0}{4},\dfrac{0}{5}.....$

Also, it can be expressed as $\dfrac{0}{-1},\dfrac{0}{-2},\dfrac{0}{-3},\dfrac{0}{-4}.....$

Therefore, it is concluded from here that $0$ can be expressed in the form of $\dfrac{p}{q}$, where $p$ and $q$ are integers.

Hence, zero must be a rational number.

2. Find any six rational numbers between ${3}$ and ${4}$.

Ans: It is known that there are infinitely many rational numbers between any two numbers. Since we need to find $6$ rational numbers between $3$ and $4$, so multiply and divide the numbers by $7$ (or by any number greater than $6$)

Then it gives,

\begin{align} & 3=3\times \dfrac{7}{7}=\dfrac{21}{7} \\ & 4=4\times \dfrac{7}{7}=\dfrac{28}{7} \\ \end{align}

Hence, $6$ rational numbers found between $3$ and $4$ are $\dfrac{22}{7},\dfrac{23}{7},\dfrac{24}{7},\dfrac{25}{7},\dfrac{26}{7},\dfrac{27}{7}$.

3. Find any five rational numbers between $\dfrac{ {3}}{ {5}}$ and $\dfrac{ {4}}{ {5}}$.

Ans: It is known that there are infinitely many rational numbers between any two numbers.

Since here we need to find five rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$,  so multiply and divide by $6$ (or by any number greater than $5$).

Then it gives,

$\dfrac{3}{5}=\dfrac{3}{5}\times \dfrac{6}{6}=\dfrac{18}{30}$,

$\dfrac{4}{5}=\dfrac{4}{5}\times \dfrac{6}{6}=\dfrac{24}{30}$.

Hence, $5$ rational numbers found between $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are  $\dfrac{19}{30},\dfrac{20}{30},\dfrac{21}{30},\dfrac{22}{30},\dfrac{23}{30}$.

4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Ans: Write the whole numbers and natural numbers in a separate manner.

It is known that the whole number series is $0,1,2,3,4,5.....$. and

the natural number series is $1,2,3,4,5.....$.

Therefore, it is concluded that all the natural numbers lie in the whole number series as represented in the diagram given below.

Thus, it is concluded that every natural number is a whole number.

Hence, the given statement is true.

(ii) Every integer is a whole number.

Ans: Write the integers and whole numbers in a separate manner.

It is known that integers are those rational numbers that can be expressed in the form of $\dfrac{p}{q}$, where $q=1$.

Now, the series of integers is like $0,\,\pm 1,\,\pm 2,\,\pm 3,\,\pm 4,\,...$.

But the whole numbers are $0,1,2,3,4,...$.

Therefore, it is seen that all the whole numbers lie within the integer numbers, but the negative integers are not included in the whole number series.

Thus, it can be concluded from here that every integer is not a whole number.

Hence, the given statement is false.

(iii) Every rational number is a whole number.

Ans: Write the rational numbers and whole numbers in a separate manner.

It is known that rational numbers are the numbers that can be expressed in the form  $\dfrac{p}{q}$, where $q\ne 0$ and the whole numbers are represented as $0,\,1,\,2,\,3,\,4,\,5,...$

Now, notice that every whole number can be expressed in the form of $\dfrac{p}{q}$

as  $\dfrac{0}{1},\text{ }\dfrac{1}{1},\text{ }\dfrac{2}{1},\text{ }\dfrac{3}{1},\text{ }\dfrac{4}{1},\text{ }\dfrac{5}{1}$,…

Thus, every whole number is a rational number, but all the rational numbers are not whole numbers. For example,

$\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{5},...$ are not whole numbers.

Therefore, it is concluded from here that every rational number is not a whole number.

Hence, the given statement is false.

## Conclusion

Class 9th Maths Exercise 1.1 provides a foundational understanding of the Number System. It introduces natural numbers, whole numbers, integers, rational numbers, and irrational numbers. The exercise emphasizes representing these numbers on the number line, which enhances visual learning and comprehension. By completing this exercise, students build a critical base for more advanced mathematical concepts, fostering logical reasoning and problem-solving skills essential for future studies. Students that practise these kinds of questions will gain confidence and perform well on tests.

## Class 9 Maths Chapter 1: Exercises Breakdown

 Exercises Number of Questions Exercise 1.2 4 Questions & Solutions (4 short Answers) Exercise 1.3 9 Questions & Solutions (8 short Answers, 1 long Answer) Exercise 1.4 5 Questions & Solutions (4 short Answers, 1 long Answer) Exercise 1.5 3 Questions & Solutions (3 short Answers)

## 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 1.1 Class 9 - Number System

1. What does this chapter mainly deals with?

Ans: The chapter mainly focuses on different types of numbers. They are:

• Complex Number

• Imaginary Number

• Real Number

• Rational Number

• Irrational Numbers

• Integers

• Whole Numbers

• Natural Numbers

• Natural Numbers - any of the given numbers that are used for counting purpose, starting from one, is considered a natural number.

• Whole Numbers - the total union set of all the Natural numbers which includes zero are the set of whole numbers.

• Integers - the set of all the whole numbers including their negative terms is called the set of integers.

• Rational Numbers - any number which can be written as a ratio of two natural numbers is known as a rational number.

• Irrational Numbers - any number which cannot be written in the form of a ratio of two natural numbers is known as an irrational number.

2. Give a brief on decimal and decimal classification.

Ans: Decimal is very interesting and fun part of the Number System. Decimal fractions were first introduced and used by Chinese at the end of the 4th century and then spread to the Middle East and from there to Europe. Decimals are used in our daily life without consciousness. For instance – counting of money, filling fuel into our vehicle or while measuring our weight. Decimals can never be whole numbers. Few example: 1.8, 000.23 etc.

Decimals classifications: Terminating decimal fractions are 17/4= 4.25, 21/5 = 4.2 and so on.

Non- terminating decimal fractions are 16/3 = 5.33333 , 15.35353535 etc.

Integer: All the numbers that does not have decimals in them are known as integers. Thus, -9, 4, 1476 etc. Do you know? All integers are whole numbers including the negative numbers.

3. Give an overview of the chapter Number system.

Ans: In this Chapter, you will get to learn about the different types of numbers along with their varied characteristics. The chapter primarily deals with irrational numbers, real numbers and their decimal expansion. It is followed by representing real numbers on the numbers, operating on real numbers, and lastly laws of exponents for real numbers.

You will also be able to learn about rational numbers and irrational numbers with their properties. The chapter also introduces you to:

• Classification of expressions into rational or irrational numbers

• Simplification of expressions

• Number Line representation

• Rationalization

4. How Vedantu will help me in exam preparation?

Our NCERT solutions are prepared by our maths experts with various real-life examples. These examples will make you understand the concept quickly and memorise them for a longer time. Solutions provided to the questions are 100% accurate in the exercises which are crisp and concise to the point.

Our solutions are the best study guides, which help you in smart learning and efficient answering of questions. These solutions will also help you in improving a strong conceptual base with all the important concepts in a very easy and understandable language. You will also enjoy learning from our solutions which are really fun and interactive.

5. Is the Chapter Number System Exercise 1.1 important for Class 9 Maths?

Ans: The Number System is one of the most important aspects of the NCERT Solutions for Class 9 Maths. The mathematical notations produced using numbers and symbols are known as the Number System. Exercise 1.1 is a must-do to get a basic understanding of this chapter and also from the examination point of view. Vedantu will be there for you every step of the way, from comprehending rational and irrational numbers to solving problems with them.

6. Do I need to practice all the questions provided in Chapter 9 Maths Exercise 1.1 NCERT Solutions?

Ans: Yes, you must practise all of the questions in Chapter 9 Maths Exercise 1.1. Each question puts your knowledge to the test, emphasising the need for practising. Students may test themselves by answering all of the questions in this exercise, which will help them resolve their concerns and learn fundamental skills. NCERT answers provide in-depth knowledge in an easy-to-understand format.

7. Why should we refer to NCERT books for chapter 1 exercise 1.1 Maths for class 9?

Ans: The most compelling argument to utilise NCERT books is that they correspond to the CBSE curriculum to the letter. They are quite beneficial to CBSE kids. Books are factual and authored by subject matter specialists. All of the topics are described in simple terms. These answers have been created by professional lecturers to help you prepare for your exams. To boost your confidence and test result, visit the page NCERT Solutions for Class 9 Maths Chapter 1 exercise 1.1 by Vedantu at free of cost on the official website and on the Vedantu app.

8. What are the different types of numbers in the number system of Class 9 Maths?

Ans: There are eight types of numbers to study in class 9:

• Complex Number

• Imaginary Number

• Real Number

• Rational number

• Irrational number

• Integers

• Whole numbers

• Natural numbers

9. What is the difference between a rational number and an irrational number?

Ans: A rational number is a ratio of two integers in which the denominator is not zero. Interestingly, a repeating decimal is also known as a rational number. A rational number is a kind of real number with a non-zero denominator. For eg: ½, 3.4 etc. A real number that cannot be expressed as a simple fraction is called an irrational number. For eg: 4/0