#### 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

## Solutions for Chapter 1: Number Systems

Below listed, you can find solutions for Chapter 1 of CBSE NCERT for Class 9 Maths.

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

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

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.

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

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

Every irrational number is a real number.

True

False

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

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

Every real number is an irrational number.

True

False

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.

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

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

`36/100`

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

`1/11`

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

`4 1/8`

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

`3/13`

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

`2/11`

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

`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.**

`0.bar6`

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

`0.4bar7`

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

`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...

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

Visualise 3.765 on the number line, using successive magnification.

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

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

Classify the following numbers as rational or irrational :-

` 2-sqrt5`

Classify the following numbers as rational or irrational :-

`(3+sqrt23)-sqrt23`

Classify the following numbers as rational or irrational :-

`(2sqrt7)/(7sqrt7)`

Classify the following numbers as rational or irrational :-

`1/sqrt2`

Classify the following numbers as rational or irrational :-

`2π`

Simplify of the following expression :-

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

Simplify of the following expression :-

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

Simplify of the following expression :-

`(sqrt5+sqrt2)^2`

Simplify of the following expression :-

`(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 denominator of the following :-

`1/sqrt7`

Rationalise the denominator of the following :-

`1/(sqrt7-sqrt6)`

Rationalise the denominator of the following :-

`1/(sqrt5+sqrt2)`

Rationalise the denominator of the following :-

`1/(sqrt7-2)`

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

Find :-

`64^(1/2)`

Find :-

`32^(1/5)`

Find :-

`125^(1/3)`

Find :-

`9^(3/2)`

Find :-

`32^(2/5)`

Find :-

`16^(3/4)`

Find :-

`125^(-1/3)`

Simplify :-

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

Simplify :-

`(1/3^3)^7`

Simplify :-

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

Simplify :-

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

## Solutions for Chapter 1: Number Systems

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

Shaalaa.com has the CBSE Mathematics Class 9 Maths CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 9 Maths CBSE 1 (Number Systems) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

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

Get the free view of Chapter 1, Number Systems Class 9 Maths additional questions for Mathematics Class 9 Maths CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.