Ncert mathematics solutions class 9 Solutions for Chapter 1 number system

Exercises in Chapter 1 number system Grade 9

Number System - Exercise 1.1

Number System - Exercise 1.2

Number System - Exercise 1.3

Number System - Exercise 1.4

Number System - Exercise 1.5

Number System - Exercise 1.6

Questions in Number System - Exercise 1.1

State whether the following statement is true or false.

Every rational number is a whole number.

Which is the rational number between $\frac{3}{5}$ and $\frac{4}{5}$ ?

Which of the following are rational numbers between 3 and 4?

Zero a rational number.

State whether the following statement is true or false.

Every natural number is a whole number.

State whether the following statement is true or false.

Every integer is a whole number.

Find six rational numbers between 3 and 4.

Questions in Number System - Exercise 1.2

State whether the following statement is true or false.

The square roots of all positive integers is irrational.

State whether the following statement is true or false.

Every real number is an irrational number.

State whether the following statement is true or false.

Every irrational number is a real number.

Which image represents √5 on the number line ?

State whether the following statement is true or false.

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

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 √m where m is a natural number.

(iii) Every real number is an irrational number.

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

Questions in Number System - Exercise 1.3

1.101001000100001… is a rational number.

Which is the irrational number between the rational numbers $\frac{5}{7}\ and\ \frac{9}{11}$ ?

√23 is a rational number.

7.478478 is a rational number.

√225 is a irrational number.

Which of this is in p/q form for $0. \overline{001}$ ?

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$ ?

What is the decimal form of $\frac{2}{11}$ ?

What is the decimal form of $\frac{3}{13}$ ?

What is the decimal form of $4\frac{1}{8}$ ?

You know that $\frac{1}{7}$ = 0.142857....

What is the decimal expansion of $\frac{3}{7}$ ?

You know that $\frac{1}{7}$ = 0.142857....

What is the decimal expansion of $\frac{4}{7}$ ?

You know that $\frac{1}{7}$ = 0.142857....

What is the decimal expansion of $\frac{5}{7}$ ?

You know that $\frac{1}{7}$ = 0.142857....

What is the decimal expansion of $\frac{6}{7}$ ?

What is the decimal form of $\frac{1}{11}$ ?

What is the decimal form of $\frac{36}{100}$ ?

You know that $\frac{1}{7}$ = 0.142857....

What is the decimal expansion of $\frac{2}{7}$ ?

What is the decimal form of $\frac{329}{400}$ ?

Which of this is in p/q form for $0. \overline{6}$ ?

0.3796 is an irrational number.

What is the value of 0.99999…. in the form p/q?

Which of this is in p/q form for $0. 4\overline{7}$ ?

Which of the following is the number whose decimal expansions are non-terminating non-recurring?

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.

Classify the following numbers as rational or irrational according to their type:

(i)√23

(ii)√225

(iii) 0.3796

(iv) 7.478478

(v) 1.101001000100001…

Questions in Number System - Exercise 1.4

$\text { Visualise } 4 . \overline{26} \text { on the number line, up to } 4 \text { decimal places. }$

Questions in Number System - Exercise 1.5

Simplify (√5+√2)²

Rationalize the denominator of $\frac{1}{(\sqrt{7}-\sqrt{6})}$ and select the correct option.

Rationalize the denominator of $\frac{1}{(\sqrt{7}-2)}$ and select the correct option.

$\frac{2\sqrt{7}}{7\sqrt{7}}$ is a rational number.

(3 +√23)- √23 is an irrational number.

$\frac{1}{\sqrt{2}}$ is a rational number.

2 –√5 is a rational number.

2 is an irrational number.

Simplify (3+√3)(2+√2)

Simplify (3+√3)(3-√3 )

Rationalize the denominator of $\frac{1}{\sqrt{7}}$ and select correct option.

Simplify (√5-√2)(√5+√2)

Rationalize the denominator of $\frac{1}{(\sqrt{5}+\sqrt{2})}$ and select the correct option.

Simplify each of the following expressions:

(i) (3+√3)(2+√2)

(ii) (3+√3)(3+√3 )

(iii) $(\sqrt{5}+\sqrt{2})^{2}$

(iv) (√5-√2)(√5+√2)

Represent (√9.3) on the number line.

Questions in Number System - Exercise 1.6

Simplify and select the correct option: $2^{\frac{2}{3}}\times2^{\frac{1}{5}}$

Simplify and select the correct option:

$7^{\frac{1}{2}}\times8^{\frac{1}{2}}$

Simplify and select the correct option:

$\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$

Simplify and select the correct option:

$\left(\frac{1}{3^3}\right)^7$

$125^{-\frac{1}{3}}$

64^1/2=?

$125^{\frac{1}{3}}$

$9^{\frac{3}{2}}$ =?

$32^{\frac{2}{5}}$ =?

$16^{\frac{3}{4}}$ =?

$32^{\frac{1}{5}}$

Find:

$\text { (i) } 64^{1 / 2}$

$\text { (ii) } 32^{1 / 5}$

$(\text { iii }) 125^{1 / 3}$

Find:

$\text { (i) } 9^{3 / 2}$

$\text { (ii) } 32^{2 / 5}$

$\text { (iii) } 16^{3 / 4}$

$\text { (iv) } 125^{-1 / 3}$

Simplify:

$\text { (i) } 2^{2 / 3} \times 2^{1 / 5}$

$\text { (ii) }\left(1 / 3^{3}\right)^{7}$

$\text { (iii) } 11^{1 / 2} / 11^{1 / 4}$

$\text { (iv) } 7^{1 / 2} \times 8^{1 / 2}$

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Chapters in this book

Coordinate Geometry

Linear Equations in Two Variables

Introduction to Euclids Geometry

Lines and Angles

Areas of Parallelograms and Triangles

Heron’s Formula

Surface Areas and Volumes

lido-difference

Lido

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