Represent 4 . 7 on the number line.

Given irrational number is 4 . 7 . ( i ) Draw a line and mark a point A on it. ( ii ) Mark a point B such that A B = 4 . 7 cm . ( iii ) Mark a point C on the opposite side of A on this line such that B C = 1 cm . ( iv ) Find the midpoint of A C by drawing perpendicular bisector of A C and let it be O . ( v ) With O as centre and O C = O A as radius, draw a semicircle. ( vi ) Draw a line B D , which is perpendicular to A B at B . ( vii ) Now B D = 4 . 7 , which can be marked in the number line as the value of B E = B D = 4 . 7 .

Represent 6 . 5 on the number line.

Given irrational number is 6 . 5 ( i ) Draw a line and mark a point A on it. ( ii ) Mark a point B such that A B = 6 . 5 cm ( iii ) Mark a point C on the opposite side of A , on this line such that B C = 1 cm . ( iv ) Find the midpoint of A C by drawing perpendicular bisector of A C and let it be O . ( v ) With O as centre and O C = O A as radius, draw a semicircle. ( vi ) Draw a line B D , which is perpendicular to A B at B . ( vii ) Now B D = 6 . 5 , which can be marked on the number line as the value of B E = B D = 6 . 5 .

Find any two irrational numbers between 6 7 and 12 13 .

We need to find two irrational numbers between 6 7 and 12 13 . First we need to find the decimal expansion of 6 7 and 12 13 . 0 . 8 5 7 1 4 2 8 7 6 - 0 6 0 - 5 6 4 0 - 3 5 5 0 - 4 9 1 0 - 7 3 0 - 2 8 2 0 - 1 4 6 0 - 5 6 4 0 . 9 2 3 0 7 6 9 13 1 2 - 0 1 2 0 - 1 1 7 3 0 - 2 6 4 0 - 3 9 1 0 - 0 1 0 0 - 9 1 9 0 - 7 8 1 2 0 - 1 1 7 3 Since the decimal expansion of the given rational numbers are non-terminating and repeating decimal numbers. 6 7 = 0 . 857142 ¯ and 12 13 = 0 . 923076 ¯ We know that a number having non- terminating and non- recurring decimal expansion is an irrational number. Therefore, two irrational numbers between 6 7 and 12 13 are 0 . 8616611666111 . . . and 0 . 8717711777111 . . . .

Find any two irrational numbers between 2 and 3 .

We need to find two irrational numbers between 2 and 3 . A number having non-terminating and non-recurring decimal expansion is an irrational number. 1 . 4 1 4 2 . . . 1 2 . 0 0 0 0 0 0 0 1 24 1 0 0 9 6 281 4 0 0 2 8 1 2824 1 1 9 0 0 1 1 2 9 6 28282 6 0 4 0 0 5 6 5 6 4 3 8 3 6 The decimal expansion of 2 = 1 . 414 . . . . 1 . 7 3 2 . . . . 1 3 . 0 0 0 0 0 0 0 1 27 2 0 0 1 8 9 343 1 1 0 0 1 0 2 9 3462 7 1 0 0 6 9 2 4 28282 1 7 6 3 = 1 . 732 . . . . Therefore, two irrational numbers between 2 and 3 are 1 . 515511555111 … and 1 . 616611666111 … .

The mass of the Earth is 5 . 97 × 10 24 kg and that of the Moon is 0 . 073 × 10 24 kg . What is their total mass?

Given, Total mass of Earth is 5 . 97 × 10 24 kg Total mass of Moon is 0 . 073 × 10 24 kg Total mass = Total mass of Earth + Total mass of Moon = 5 . 97 × 10 24 kg + 0 . 073 × 10 24 kg = 5 . 97 + 0 . 073 × 10 24 kg = 6 . 043 × 10 24 kg Thus, the total mass of Earth and moon is 6 . 043 × 10 24 kg

E M B I B E

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise

Tamil Nadu Board Solutions for Chapter: Real Numbers, Exercise 3: Exercise

Author:Tamil Nadu Board

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Real Numbers, Exercise 3: Exercise

Attempt the free practice questions on Chapter 2: Real Numbers, Exercise 3: Exercise with hints and solutions to strengthen your understanding. Mathematics Standard 9 solutions are prepared by Experienced Embibe Experts.

Questions from Tamil Nadu Board Solutions for Chapter: Real Numbers, Exercise 3: Exercise with Hints & Solutions

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise>Q 1

Represent $\sqrt{4.7}$ on the number line.

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise>Q 1

Represent $\sqrt{6.5}$ on the number line.

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise>Q 2

Find any two irrational numbers between $0.3010011000111 . . .$ and $0.3020020002 . . .$ .

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise>Q 2

Find any two irrational numbers between $\frac{6}{7}$ and $\frac{12}{13}$ .

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise>Q 2

Find any two irrational numbers between $\sqrt{2}$ and $\sqrt{3}$ .

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise>Q 3

Find any two rational numbers between $2.2360679 . . .$ and $2.236505500 . . .$ .

EASY

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Solved Example>Q 3

Express the rational number $\frac{1}{27}$ in recurring decimal form by using the recurring decimal expansion of $\frac{1}{3}$ . Hence write $\frac{59}{27}$ in recurring decimal form.

MEDIUM

9th Tamil Nadu Board

IMPORTANT

Mathematics Standard 9>Chapter 2 - Real Numbers>Solved Example>Q 30

The mass of the Earth is $5.97 \times 10^{24} kg$ and that of the Moon is $0.073 \times 10^{24} kg$ . What is their total mass?