NCERT Solutions for Class 9 Maths Chapter 1- Number Systems

NCERT Solutions For Class 9 Maths Chapter 1 PDF Free Download

NCERT Solutions for Class 9 Maths chapter 1 – Number Systems are provided here. These NCERT solutions are created by the expert faculties at BYJU’S to help students in the preparation of their board exams. These expert faculties solve and provide the NCERT Maths solution so that it would help students to solve the problems comfortably. They also concentrate on making the solutions in such a way that it is easy for the students to understand. They give detailed and step-wise explanation of each answer to the questions given in the exercises in the NCERT textbook for class 9.

In CBSE class 9 chapter 1, Number Systems, students are introduced to a lot of important topics which will be helpful for those who wish to pursue Mathematics as a subject in further classes. Based on these NCERT solutions, students can prepare for their upcoming Board Exams. These solutions are helpful as the syllabus covered here follows NCERT guidelines.

Download PDF of NCERT Solutions for Class 9 Maths Chapter 1- Number Systems

 

NCERT Solutions for class 9 Maths Chapter 1 Number System Part 1
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 2
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 3
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 4
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 5
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 6
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 7
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 8
NCERT Solutions for class 9 Maths Chapter 1 Number System Part 9
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NCERT Solutions for class 9 Maths Chapter 1 Number System Part 11
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NCERT Solutions for class 9 Maths Chapter 1 Number System Part 21
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NCERT Solutions for class 9 Maths Chapter 1 Number System Part 31

 

Access Answers to Maths NCERT Problems class 9 Chapter 1 – Number Systems

 

Exercise 1.1 Page: 5

Q1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

ncert solutions class 9 maths chapter 1 fig 1

Q2. Find six rational numbers between 3 and 4.

ncert solutions class 9 maths chapter 1 fig 2

Q3. Find five rational numbers between 3/5 and 4/5 .

ncert solutions class 9 maths chapter 1 fig 3

Q4. State whether the following statements are true or false. Give reasons for your answers.

ncert solutions class 9 maths chapter 1 fig 4

 

Exercise 1.2 Page: 8

Q1. State whether the following statements are true or false. Justify your answers.

(i)Every irrational number is a real number.

ncert solutions class 9 maths chapter 1 fig 5

Q2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

ncert solutions class 9 maths chapter 1 fig 6

Q3. Show how 5 can be represented on the number line.

ncert solutions class 9 maths chapter 1 fig 7

Q4. 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 OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in Fig. 1.9 :

ncert solutions class 9 maths chapter 1 fig 8

Constructing this manner, you can get the line segment Pn–1Pn by square root spiral drawing a line segment of unit length perpendicular to OPn–1. In this manner, you will have created the points P2, P3,…., Pn,… ., and joined them to create a beautiful spiral depicting 2, 3, 4, …

Solution:

ncert solutions class 9 maths chapter 1 fig 9

 

Exercise 1.3 Page: 14

Q1. Write the following in decimal form and say what kind of decimal expansion each has :
(i) 36/100

ncert solutions class 9 maths chapter 1 fig 10

(ii) 1/11

ncert solutions class 9 maths chapter 1 fig 11

(iii) 4 1/8

ncert solutions class 9 maths chapter 1 fig 12

(iv) 3/13

ncert solutions class 9 maths chapter 1 fig 13

(v) 2/11

ncert solutions class 9 maths chapter 1 fig 14

(vi) 329/400

ncert solutions class 9 maths chapter 1 fig 15

You know that = \($\overline{0.142857}$\). Can you predict what the decimal expansions of 2/7,3/7,4/7,5/7,6/7 are, without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of 1/7 carefully.]

ncert solutions class 9 maths chapter 1 fig 16

Q3. Express the following in the form p/q, where p and q are integers and q ≠ 0.

ncert solutions class 9 maths chapter 1 fig 17

Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

ncert solutions class 9 maths chapter 1 fig 18

Q5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

Solution:

ncert solutions class 9 maths chapter 1 fig 19

Q6. Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Solution:

We observe that when q is 2, 4, 5, 8, 10… Then the decimal expansion is terminating. For example:

1/2= 0. 5, denominator q = 21

7/8= 0. 875, denominator q = 23

4/5= 0. 8, denominator q = 51

We can observe that the terminating decimal may be obtained in the situation where prime factorization of the denominator of the given fractions has the power of only 2 or only 5 or both.

Q7. Write three numbers whose decimal expansions are non-terminating non-recurring.

Solution:

We know that all irrational numbers are non-terminating non-recurring. three numbers with decimal expansions that are non-terminating non-recurring are:

a) √3 = 1.732050807568..
b) √26 = 5.099019513592..
c) √101 = 10.04987562112..

Q8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Solution:

5/7 = 0. 714285…

9/11 = 0.81….

Three different irrational numbers are:

a) 0.73073007300073000073…
b) 0.75075007300075000075…
c) 0.76076007600076000076…

Q9. Classify the following numbers as rational or irrational according to their type:
(i) √23

Sol:

√23 = 4.79583152331…

Since the number is non-terminating non-recurring therefore, it is an irrational number.

(ii) √225

Sol:

√225= 15 = 15/1

Since the number can be represented in p/q form, it is a rational number.

(iii) 0.3796

Sol:

Since the number, 0.3796, is terminating, it is a rational number.

(iv)7.478478

Sol:

The number, 7.478478, is non-terminating but recurring, it is a rational number.

(v)1.101001000100001…

Since the number, 1.101001000100001…, is non-terminating non-repeating (non-recurring), it is an irrational number.

Exercise 1.4 Page: 18

Q1. Visualise 3.765 on the number line, using successive magnification.

Solution:

ncert solutions class 9 maths chapter 1 fig 20

Q2. Visualise \($\overline{4.26}$\) on the number line, up to 4 decimal places.

Solution:

\(\overline{4.26}\)=4.26262626…..

\(\overline{4.26}\) up to 4 decimal places= 4.2626

ncert solutions class 9 maths chapter 1 fig 21

 

Exercise 1.5 Page: 24

Q1. Classify the following numbers as rational or irrational:

(i) 2 – √5 

ncert solutions class 9 maths chapter 1 fig 22

(iv) 1/√2

ncert solutions class 9 maths chapter 1 fig 23

(v) 2Π

ncert solutions class 9 maths chapter 1 fig 24

Q2. Simplify each of the following expressions:

(i) (3 +√3 ) (2 +√2 )

ncert solutions class 9 maths chapter 1 fig 25

Q3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter, (say d). That is, π = c/d This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Solution:

There is no contradiction. When we measure a value with a scale, we only obtain an approximate value. We never obtain an exact value. Therefore, we may not realize whether c or d is irrational. The value of π is almost equal to 22/7or 3.142857…

Q4. Represent (√9.3) on the number line.

ncert solutions class 9 maths chapter 1 fig 26

Q5. Rationalize the denominators of the following

ncert solutions class 9 maths chapter 1 fig 27

(iv) 1 / √7 – 2

ncert solutions class 9 maths chapter 1 fig 28

 

Exercise 1.6 Page: 26

Q1. Find:
(i) 64 1/2

ncert solutions class 9 maths chapter 1 fig 29

Q2. Find:
(i) 9 3/2

ncert solutions class 9 maths chapter 1 fig 30

Q3. Simplify:

(i) 22/3. 21/5

ncert sol class 9 maths chapter 1 fig 31

NCERT Solutions for class 9 Maths Chapter 1- Number Systems

As Number System is one of the important topics in Maths, it has a weightage of 6 marks in class 9 Maths exams. On an average three questions are asked from this unit.

  1. One out of three questions in part A (1 marks).
  2. One out of three questions in part B (2 marks).
  3. One out of three questions in part C (3 marks).

This chapter talks about

  • Introduction of Number Systems
  • Irrational Numbers
  • Real Numbers and their Decimal Expansions
  • Representing Real Numbers on the Number Line.
  • Operations on Real Numbers
  • Laws of Exponents for Real Numbers
  • Summary

List of Exercises

Exercise 1.1 Solutions 4 Questions ( 2 long, 2 short)

Exercise 1.2 Solutions 4 Questions ( 3 long, 1 short)

Exercise 1.3 Solutions 9 Questions ( 9 long)

Exercise 1.4 Solutions 2 Questions ( 2 long)

Exercise 1.5 Solutions 5 Questions ( 4 long 1 short)

Exercise 1.6 Solutions 3 Questions ( 3 long)

NCERT Solutions for class 9 Maths Chapter 1- Number Systems

NCERT Solutions for Class 9 Maths chapter 1 – Number System is the first chapter of class 9 Maths. Number System is discussed in detail in this chapter. The chapter discusses the Number Systems and their applications. The introduction of the chapter includes whole numbers, integers and rational numbers.

The chapter starts with the introduction of Number Systems in section 1.1 followed by two very important topics in section 1.2 and 1.3

  • Irrational Numbers – The numbers which can’t be written in the form of p/q.
  • Real Numbers and their Decimal Expansions – Here you study the decimal expansions of real numbers and see whether it can help in distinguishing between rational and irrationals.

Next, it discusses the following topics.

  • Representing Real Numbers on the Number Line – In this the solutions for 2 problems in Exercise 1.4.
  • Operations on Real Numbers – Here you explore some of the operations like addition, subtraction, multiplication and division on the irrational numbers.
  • Laws of Exponents for Real Numbers – Use these laws of exponents to solve the questions.

Key advantages of NCERT Solutions for Class 9 Maths Chapter 1- Number Systems

  • These NCERT Solutions for class 9 Maths helps you solve and revise the whole syllabus of class 9.
  • After going through the step-wise solutions given by our subject expert teachers, you will be able to score more marks.
  • It follows NCERT guidelines.
  • It contains all the important questions from the examination point of view.
  • It helps in scoring well in Maths in board exams.

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