# NCERT solutions for Class 9 Maths chapter 1 - Number Systems [Latest edition]

## Chapter 1: Number Systems

Exercise 1.1Exercise 1.2Exercise 1.3Exercise 1.4Exercise 1.5Exercise 1.6
Exercise 1.1 [Page 5]

### NCERT solutions for Class 9 Maths Chapter 1 Number SystemsExercise 1.1 [Page 5]

Exercise 1.1 | Q 1 | Page 5

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

Exercise 1.1 | Q 2 | Page 5

Find six rational numbers between 3 and 4.

Exercise 1.1 | Q 3 | Page 5

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

Exercise 1.1 | Q 4.1 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every natural number is a whole number.

Exercise 1.1 | Q 4.2 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every integer is a whole number.

Exercise 1.1 | Q 4.3 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every rational number is a whole number.

Exercise 1.2 [Page 8]

### NCERT solutions for Class 9 Maths Chapter 1 Number SystemsExercise 1.2 [Page 8]

Exercise 1.2 | Q 1.1 | Page 8

State whether the following statement is true or false. Justify your answer.

Every irrational number is a real number.

• True

• False

Exercise 1.2 | Q 1.2 | Page 8

State whether the following statement is true or false. Justify your answer.

Every point on the number line is of the form sqrt m, where m is a natural number.

• True

• False

Exercise 1.2 | Q 1.3 | Page 8

State whether the following statement is true or false. Justify your answer.

Every real number is an irrational number.

• True

• False

Exercise 1.2 | Q 2 | Page 8

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.

Exercise 1.2 | Q 3 | Page 8

Show how sqrt5 can be represented on the number line.

Exercise 1.3 [Page 14]

### NCERT solutions for Class 9 Maths Chapter 1 Number SystemsExercise 1.3 [Page 14]

Exercise 1.3 | Q 1 | Page 14

Write the following in decimal form and say what kind of decimal expansion each has :-

(i) 36/100

(ii) 1/11

(iii) 4 1/8

(iv) 3/13

(v) 2/11

(vi) 329/400

Exercise 1.3 | Q 2 | Page 14

You know that 1/7=0.bar142857. 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.]

Exercise 1.3 | Q 3 | Page 14

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

(i) 0.bar6

(ii) 0.4bar7

(iii) 0.bar001

Exercise 1.3 | Q 4 | Page 14

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.

Exercise 1.3 | Q 5 | Page 14

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.

Exercise 1.3 | Q 6 | Page 14

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?

Exercise 1.3 | Q 7 | Page 14

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

Exercise 1.3 | Q 8 | Page 14

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

Exercise 1.3 | Q 9.1 | Page 14

Classify the following number as rational or irrational :-

sqrt23

Exercise 1.3 | Q 9.2 | Page 14

Classify the following number as rational or irrational :-

sqrt225

Exercise 1.3 | Q 9.3 | Page 14

Classify the following number as rational or irrational :-

0.3796

Exercise 1.3 | Q 9.4 | Page 14

Classify the following number as rational or irrational :-

7.478478...

Exercise 1.3 | Q 9.5 | Page 14

Classify the following number as rational or irrational :-

1.1010010001...

Exercise 1.4 [Page 18]

### NCERT solutions for Class 9 Maths Chapter 1 Number SystemsExercise 1.4 [Page 18]

Exercise 1.4 | Q 1 | Page 18

Visualise 3.765 on the number line, using successive magnification.

Exercise 1.4 | Q 2 | Page 18

Visualise 4.bar26  on the number line, up to 4 decimal places.

Exercise 1.5 [Page 24]

### NCERT solutions for Class 9 Maths Chapter 1 Number SystemsExercise 1.5 [Page 24]

Exercise 1.5 | Q 1.1 | Page 24

Classify the following numbers as rational or irrational :-

 2-sqrt5

Exercise 1.5 | Q 1.2 | Page 24

Classify the following numbers as rational or irrational :-

(3+sqrt23)-sqrt23

Exercise 1.5 | Q 1.3 | Page 24

Classify the following numbers as rational or irrational :-

(2sqrt7)/(7sqrt7)

Exercise 1.5 | Q 1.4 | Page 24

Classify the following numbers as rational or irrational :-

1/sqrt2

Exercise 1.5 | Q 1.5 | Page 24

Classify the following numbers as rational or irrational :-

2π

Exercise 1.5 | Q 2.1 | Page 24

Simplify of the following expression :-

(3+sqrt3)(2+sqrt2)

Exercise 1.5 | Q 2.2 | Page 24

Simplify of the following expression :-

(3+sqrt3)(3-sqrt3)

Exercise 1.5 | Q 2.3 | Page 24

Simplify of the following expression :-

(sqrt5+sqrt2)^2

Exercise 1.5 | Q 2.4 | Page 24

Simplify of the following expression :-

(sqrt5-sqrt2)(sqrt5+sqrt2)

Exercise 1.5 | Q 3 | Page 24

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 p is irrational. How will you resolve this contradiction?

Exercise 1.5 | Q 4 | Page 24

Represent sqrt9.3  on the number line.

Exercise 1.5 | Q 5.1 | Page 24

Rationalise the denominator of the following :-

1/sqrt7

Exercise 1.5 | Q 5.2 | Page 24

Rationalise the denominator of the following :-
1/(sqrt7-sqrt6)

Exercise 1.5 | Q 5.3 | Page 24

Rationalise the denominator of the following :-
1/(sqrt5+sqrt2)

Exercise 1.5 | Q 5.4 | Page 24

Rationalise the denominator of the following :-
1/(sqrt7-2)

Exercise 1.6 [Page 26]

### NCERT solutions for Class 9 Maths Chapter 1 Number SystemsExercise 1.6 [Page 26]

Exercise 1.6 | Q 1.1 | Page 26

Find :-

64^(1/2)

Exercise 1.6 | Q 1.2 | Page 26

Find :-

32^(1/5)

Exercise 1.6 | Q 1.3 | Page 26

Find :-

125^(1/3)

Exercise 1.6 | Q 2.1 | Page 26

Find :-

9^(3/2)

Exercise 1.6 | Q 2.2 | Page 26

Find :-
32^(2/5)

Exercise 1.6 | Q 2.3 | Page 26

Find :-

16^(3/4)

Exercise 1.6 | Q 2.4 | Page 26

Find :-

125^(-1/3)

Exercise 1.6 | Q 3.1 | Page 26

Simplify :-

2^(2/3).2^(1/5)

Exercise 1.6 | Q 3.2 | Page 26

Simplify :-

(1/3^3)^7

Exercise 1.6 | Q 3.3 | Page 26

Simplify :-

11^(1/2)/11^(1/4)

Exercise 1.6 | Q 3.4 | Page 26

Simplify :-

7^(1/2).8^(1/2)

## Chapter 1: Number Systems

Exercise 1.1Exercise 1.2Exercise 1.3Exercise 1.4Exercise 1.5Exercise 1.6

## NCERT solutions for Class 9 Maths chapter 1 - Number Systems

NCERT solutions for Class 9 Maths chapter 1 (Number Systems) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 9 Maths solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Maths chapter 1 Number Systems are Introduction of Real Number, Concept of 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.

Using NCERT Class 9 solutions Number Systems exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer NCERT Textbook Solutions to score more in exam.

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