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

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

Edited By Vishal kumar | Updated on Oct 20, 2023 10:25 AM IST

NCERT Solutions for class 9 Maths Chapter 1 Exercise 1.1 Number Systems - Download Free PDF

NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.1- Welcome to the Updated class 9 Maths ex 1.1 solution. On this Careers360 page, you will find comprehensive and well-explained exercise 1.1 class 9 maths solutions Written by subject matter experts. These NCERT Solutions are freely available for download.

The initial exercise in Number Systems, class 9 ex 1.1, serves as an introduction. It offers a detailed, step-by-step explanation of each answer to the questions found in the NCERT textbook for Class 9. The class 9 Maths Chapter 1 Exercise 1.1 consistently adheres to NCERT guidelines, ensuring comprehensive coverage of the entire syllabus. These resources prove to be highly beneficial for achieving excellent scores in CBSE examinations.

Access Number Systems Class 9 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:

Any number that can represent in the form of \frac{p}{q} (where \ q \neq 0) is a rational number

Now, we can write 0 in the form of \frac{p}{q} for eg. \frac{0}{1},\frac{0}{2},\frac{0}{-1} etc.

Therefore, 0 is a rational number.

Q2 Find six rational numbers between 3 and 4.

Answer:

There are an infinite number of rational numbers between 3 and 4. one way to take them is
\Rightarrow 3 = \frac{21}{7} \ and \ 4 = \frac{28}{7}
Therefore, six rational numbers between 3 and 4 are \frac{22}{7}, \frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}

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

Answer:

We can write
\Rightarrow \frac{3}{5}= \frac{3\times 6}{5\times 6} = \frac{18}{30}
And
\Rightarrow \frac{4}{5}= \frac{4\times 6}{5\times 6} = \frac{24}{30}
Therefore, five rational numbers between \frac{3}{5} and \frac{4}{5} . are \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:

(i) 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:

(ii) FALSE
Because 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:

(iii) FALSE
Numbers that can be represented in the form of \frac{p}{q} \ ( where \ q \neq 0) are rational numbers.
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

More About NCERT Solutions for Class 9 Maths Exercise 1.1: Number System

The notion of numbers and the number system is covered in NCERT Solutions for Class 9 Maths exercise 1.1. Numbers are mathematical values used for counting, measuring items, and completing arithmetic calculations. Mathematically, numbers are classified into numerous sets including rational numbers, irrational numbers, natural numbers, whole numbers, integers, and real numbers. Natural numbers are counting numbers that have values ranging from 1 to but do not include fractions. Whole numbers, often known as counting numbers, have values ranging from 0 to but do not include fractions. Integers are a collection of whole numbers and their opposites.

There is another large set known as real numbers, which includes all numbers from -∞ to including zero and fractions. The combination of both rational and irrational numbers are real numbers, and they can be either positive or negative. NCERT solutions for Class 9 Maths Chapter 1 exercise 1.1 include six questions, five of which are short and one of which is a long answer, all of which are simple to solve. In NCERT book Class 9 Maths chapter 1, the ideas connected to the number system are thoroughly discussed. The following exercises are included along with Class 9 Maths Chapter 1 exercise 1.1.

The concept of real numbers was the main subject of the NCERT syllabus Class 9 Maths exercise 1.1. Based on rational numbers and irrational numbers there are 6 questions in exercise 1.1 Class 9 Maths. The union of rational and irrational numbers is known as real numbers. A number that can be expressed as a fraction and can be written as pq where p and q are integers and q≠0 are rational numbers. Irrational numbers are numbers that cannot be represented in the form of a fraction with an integer in the numerator and denominator and do not include zero. In addition, natural numbers are a subset of integers, but integers are a subset of Rational Numbers and Rational Numbers are a subset of Real numbers.

Also Read| Number Systems Class 9 Notes

Benefits of NCERT Solutions for Class 9 Maths Exercise 1.1:

• NCERT solutions for Class 9 Maths exercise 1.1 help students to understand the difference between natural, integer, whole numbers, etc. The questions present in NCERT solutions for Class 9 Maths exercise 1.1 are very simple and easy to solve.

• Exercise 1.1 Class 9 Maths, also helps the students to understand the notation of different numbers, like N for natural numbers, and Z for integers.

• NCERT solution for Class 9 Maths chapter 1 exercise 1.1 exercises, also aids us in our higher studies and allows us to understand the concepts related to NUMBER SYSTEM and its types.

key Features of 9th Class Maths Exercise 1.1 Answers

  1. Stepwise Solutions: The Solutions for ex 1.1 class 9 class are presented in a clear and stepwise manner, making it easy for students to follow along.

  2. Detailed Explanations: Each class 9 maths ex 1.1 answers is accompanied by a detailed explanation, helping students understand the concepts and techniques used to solve the problems.

  3. NCERT Guidelines: The exercise 1.1 class 9 maths answers adhere to the guidelines provided by the National Council of Educational Research and Training (NCERT), ensuring that they cover the entire syllabus accurately.

  4. Comprehensive Coverage: The class 9 maths chapter 1 exercise 1.1 solutions cover all the questions given in Exercise 1.1 of the textbook, leaving no questions unanswered.

  5. Free Access: 9th class maths exercise 1.1 answers are accessible for free of charge, making them easily accessible to students.

  6. Clarity and Accuracy: The class 9 ex 1.1 answers are presented in a clear and accurate manner, eliminating any ambiguity.

Also see-

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Question (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. 

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

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Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

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In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

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Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

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less than 3

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more than 3 but less than 6

Option 3)

more than 6 but less than 9

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A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
QA Manager
4 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
ITSM Manager
3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
Big Data Analytics Engineer

Big Data Analytics Engineer Job Description: A Big Data Analytics Engineer is responsible for collecting data from various sources. He or she has to sort the organised and chaotic data to find out patterns. The role of Big Data Engineer involves converting messy information into useful data that is clean, accurate and actionable. 

2 Jobs Available
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