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

## Chapter 1 - Number Systems

#### Page 5

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?

Q 2 | Page 5

Find six rational numbers between 3 and 4.

Q 3 | Page 5

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

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.

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.

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.

#### Page 8

Q 1 | 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.

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.

Q 3 | Page 8

Show how sqrt5 can be represented on the number line.

#### Page 14

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

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.]

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

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.

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.

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?

Q 7 | Page 14

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

Q 8 | Page 14

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

Q 9.1 | Page 14

Classify the following number as rational or irrational :-

sqrt23

Q 9.2 | Page 14

Classify the following number as rational or irrational :-

sqrt225

Q 9.3 | Page 14

Classify the following number as rational or irrational :-

0.3796

Q 9.4 | Page 14

Classify the following number as rational or irrational :-

7.478478...

Q 9.5 | Page 14

Classify the following number as rational or irrational :-

1.1010010001...

#### Page 18

Q 1 | Page 18

Visualise 3.765 on the number line, using successive magnification.

Q 2 | Page 18

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

#### Page 24

Q 1 | 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

Q 2 | Page 24

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)

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?

Q 4 | Page 24

Represent sqrt9.3  on the number line.

Q 5 | Page 24

Rationalise the denominators of the following :-

(i) 1/sqrt7

(ii) 1/(sqrt7-sqrt6)

(iii) 1/(sqrt5+sqrt2)

(iv) 1/(sqrt7-2)

#### Page 26

Q 1 | Page 26

Find :-

(i) 64^(1/2)

(ii) 32^(1/5)

(iii) 125^(1/3)

Q 2 | Page 26

Find :-

(i) 9^(3/2)

(ii) 32^(2/5)

(iii) 16^(3/4)

(iv) 125^(-1/3)

Q 3 | Page 26

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)

## 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.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. These NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using NCERT solutions for Class 9 Mathematics 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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