NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 Number Systems

Q: How are numbers classified?

Numbers are classified into many sets namely rational numbers, irrational numbers, natural numbers, whole numbers, integers and real numbers.

Q: Whole numbers are also known as ________ numbers

Whole numbers are also known as counting numbers.

Q: _____ is the smallest whole number.

0 is the smallest whole number.

Q: ______ is the smallest natural number.

1 is the smallest natural number.

Q: What is the reciprocal of the reciprocal of rational numbers?

The reciprocal of the reciprocal of the rational numbers is the number itself.

Q: What is the irrational number according ?

A number that cannot be written in the form of a fraction with an integer in the numerator and in the denominator is known as an irrational number.

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 Number Systems

Edited By Vishal kumar | Updated on Apr 21, 2025 06:49 PM IST

To master mathematics understanding numbers along with their multiple categories represents your first essential step. Real numbers consist of rational along with irrational numbers so studying them enables problem-solving in various situations. The positioning and motion of numbers on the number line reveals important concepts about mathematical operation. The content explores essential rules with properties which make equation solving and expression simplification straightforward.

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NCERT Solutions Class 9 Maths Chapter 1: Exercise 1.1
Topics covered in Chapter 1 Number System: Exercise 1.1
NCERT Solutions of Class 9 Subject Wise
NCERT Exemplar Solutions of Class 9 Subject Wise

Rational and irrational numbers represent a vital section of NCERT curriculum where students often refer to NCERT Solutions. The exercise functions as an essential tool for solidifying number type knowledge described in NCERT Books which leads to complete understanding of real numbers and their practical applications. The defined resources help students in particular to comprehend real numbers more effectively and understand their properties.

NCERT Solutions Class 9 Maths Chapter 1: Exercise 1.1

Q1 Is zero a rational number? Can you write it in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0?

Answer:

Yes, zero is a rational number.

We know that any number of the form $\frac{p}{q}$ , where p and q are integers and q $\neq$ 0, is a rational number.

Zero can be written as $\frac{0}{1}, \frac{0}{2}, \frac{0}{3}, \dots,$ etc.

Hence, 0 is rational because it satisfies the condition of being in $\frac{p}{q}$ form.

Q2 Find six rational numbers between 3 and 4.

Answer:

There are an infinite number of rational numbers between 3 and 4.
We can find rational numbers between two numbers using the formula:
If $a < b$ , then a rational number between them is $\frac{a + b}{2}$

Let us find six rational numbers between 3 and 4:

Let $a$ = 3, $b$ = 4

$x_{1} = \frac{3 + 4}{2} = \frac{7}{2}$ = 3.5

$x_{2} = \frac{3 + 3.5}{2} = \frac{6.5}{2}$ = 3.25

$x_{3} = \frac{3 + 3.25}{2} = \frac{6.25}{2}$ = 3.125

$x_{4} = \frac{3.5 + 4}{2} = \frac{7.5}{2}$ = 3.75

$x_{5} = \frac{3.75 + 4}{2} = \frac{7.75}{2}$ = 3.875

$x_{6} = \frac{3.5 + 3.75}{2} = \frac{7.25}{2}$ = 3.625

Therefore, six rational numbers between 3 and 4 are:
3.125, 3.25, 3.5, 3.625, 3.75, 3.875

Q3 Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ .

Answer:

First, convert to same denominator:
$\frac{3}{5} = \frac{18}{30}, \frac{4}{5} = \frac{24}{30}$

Thus, five rational numbers between them can be:
$\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}$

Q4 (i) State whether the following statements are true or false. Give reasons for your answers. (i)Every natural number is a whole number.

Answer:

True,

The number that is starting from 1, i.e 1, 2, 3, 4, 5, 6, .................. are natural numbers

The number that is starting from 0. i.e, 0, 1, 2, 3, 4, 5.............are whole numbers

Therefore, we can clearly see that the collection of whole numbers contains all natural numbers.

Q4 (ii) State whether the following statements are true or false. Give reasons for your answers. (ii) Every integer is a whole number.

Answer:

False,

Integers may be negative or positive but whole numbers are always positive. For eg. -1 is an integer but not a whole number.

Q4 (iii) State whether the following statements are true or false. Give reasons for your answers.(iii) Every rational number is a whole number.

Answer:

False,

We know that any number of the form $\frac{p}{q}$ , where p and q are integers and q $\neq$ 0, is a rational number.

And numbers that are starting from 0 i.e. 0,1,2,3,4,......... are whole numbers

Therefore, we can clearly see that every rational number is not a whole number for eg. $\frac{3}{4}$ is a rational number but not a whole number.

Also Read:

Topics covered in Chapter 1 Number System: Exercise 1.1

Introduction to number systems and their types: A number system functions as a symbolic system for number representation. The number system brings various mathematical numbers into view helping students study them effectively.
Classification of numbers: Groups of numbers follow different criteria: natural numbers begin with 1 while whole numbers contain 0 as well and integers encompass negatives and rational and irrational numbers address fractional and non-repeating decimal values.
Understanding rational numbers and the representation in the form $\frac{p}{q}$ : Rational numbers are numbers that can be written in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0. These include fractions and integers.
Identify and finding rational numbers between two given numbers: Any two numbers have rational numbers between them which we can locate through averaging or turning denominators identical.
Evaluating the truth value of statements: Verification consists of determining truth or falsity of mathematical statements with available definitions and known rules and properties.

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NCERT Solutions of Class 9 Subject Wise

Students must check the NCERT solutions for class 9 of Mathematics and Science Subjects.

NCERT Exemplar Solutions of Class 9 Subject Wise

Students must check the NCERT Exemplar solutions for class 9 of Mathematics and Science Subjects.

Frequently Asked Questions (FAQs)

1. How are numbers classified?

Numbers are classified into many sets namely rational numbers, irrational numbers, natural numbers, whole numbers, integers and real numbers.

2. Whole numbers are also known as ________ numbers

Whole numbers are also known as counting numbers.

3. _____ is the smallest whole number.

0 is the smallest whole number.

4. ______ is the smallest natural number.

1 is the smallest natural number.

5. What is the reciprocal of the reciprocal of rational numbers?

The reciprocal of the reciprocal of the rational numbers is the number itself.

6. What is the irrational number according ?

A number that cannot be written in the form of a fraction with an integer in the numerator and in the denominator is known as an irrational number.

Also Read

NCERT Solutions for Class 9 Science Chapter 8 - Force and Laws of Motion

NCERT Solutions for Class 9 Science Chapter 10 - Work and Energy

NCERT Solutions for Exercise 12.1 Class 9 Maths Chapter 12 - Heron's Formula

NCERT Solutions for Exercise 7.2 Class 9 Maths Chapter 7 - Triangles

NCERT Solutions for Exercise 5.1 Class 9 Maths Chapter 5 - Introduction To Euclid's Geometry

NCERT Solutions for Exercise 4.2 Class 9 Maths Chapter 4 - Linear Equations in Two Variables

NCERT Class 9 Maths Chapter 5 Notes Introduction To Euclid’s Geometry - Download PDF

NCERT Class 9 Maths Chapter 1 Notes Number System - Download Free PDF

NCERT Class 9 Maths Chapter 6 Notes Lines and Angles - Download PDF

Triangles Class 9th Notes - Free NCERT Class 9th Maths Chapter 7 Notes - Download PDF

NCERT Class 9 Maths Chapter 8 Notes Quadrilaterals - Download PDF

Heron's Formula Class 9th Notes - Free NCERT Class 9 Maths Chapter 12 Notes - Download PDF

NCERT Exemplar Class 9 Maths Solutions Chapter 2 Polynomials

NCERT Exemplar Class 9 Maths Solutions Chapter 6 Lines and Angles

NCERT Exemplar Class 9 Maths Solutions Chapter 5 Introduction to Euclids Geometry

NCERT Exemplar Class 9 Science Solutions Chapter 15 Improvement in Food Resources

NCERT Exemplar Class 9 Science Solutions Chapter 14 Natural Resources

NCERT Exemplar Class 9 Science Solutions Chapter 5 The Fundamental Unit of Life

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