#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Coordinate Geometry

Chapter 4 - Linear Equations in two Variables

Chapter 5 - Introduction to Euclid's Geometry

Chapter 6 - Lines and Angles

Chapter 7 - Triangles

Chapter 8 - Quadrilaterals

Chapter 9 - Areas of Parallelograms and Triangles

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Heron's Formula

Chapter 13 - Surface Area and Volumes

Chapter 14 - Statistics

Chapter 15 - Probability

## Chapter 1 - Number Systems

#### Page 5

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

Find six rational numbers between 3 and 4.

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

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

Every natural number is a whole number.

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

Every integer is a whole number.

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

Every rational number is a whole number.

#### Page 8

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

(i) Every irrational number is a real number.

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

(iii) Every real number is an irrational number.

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.

Show how `sqrt5` can be represented on the number line.

#### 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`

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.]

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`

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.

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.

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?

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

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

Classify the following number as rational or irrational :-

`sqrt23`

Classify the following number as rational or irrational :-

`sqrt225`

Classify the following number as rational or irrational :-

0.3796

Classify the following number as rational or irrational :-

7.478478...

Classify the following number as rational or irrational :-

1.1010010001...

#### Page 18

Visualise 3.765 on the number line, using successive magnification.

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

#### Page 24

Classify the following numbers as rational or irrational :-

`(i) 2-sqrt5`

`(ii) (3+sqrt23)-sqrt23`

`(iii) (2sqrt7)/(7sqrt7)`

`(iv) 1/sqrt2`

`(v) 2π`

Simplify each of the following expressions :-

`(i) (3+sqrt3)(2+sqrt2)`

`(ii) (3+sqrt3)(3-sqrt3)`

`(iii) (sqrt5+sqrt2)^2`

`(iv) (sqrt5-sqrt2)(sqrt5+sqrt2)`

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?

Represent `sqrt9.3` on the number line.

Rationalise the denominators of the following :-

`(i) 1/sqrt7`

`(ii) 1/(sqrt7-sqrt6)`

`(iii) 1/(sqrt5+sqrt2)`

`(iv) 1/(sqrt7-2)`

#### Page 26

Find :-

`(i) 64^(1/2)`

`(ii) 32^(1/5)`

`(iii) 125^(1/3)`

Find :-

`(i) 9^(3/2)`

`(ii) 32^(2/5)`

`(iii) 16^(3/4)`

`(iv) 125^(-1/3)`

Simplify :-

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

`(ii) (1/3^3)^7`

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

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

#### Textbook solutions for Class 9

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

NCERT solutions for Class 9 Mathematics chapter 1 (Number Systems) include all questions with solution and detail explanation from Mathematics Textbook for Class 9. 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 created the CBSE Mathematics Textbook for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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

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