RBSE Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

Question 1.
Write the following numbers in the expanded form:
(i) 279404
Answer:
279404
Here, 279404 = 200000 + 70000 + 9000 + 400 + 0 + 4
= 2 × 100000 + 7 × 10000 + 9 × 1000 + 4 × 100 + 0×10 + 4×1
= 2 × 10⁵ + 7 × 10⁴ + 9 × 10³ + 4 × 10² + 0 × 10¹ + 4 × 10⁰
= 2 × 10⁵ + 7 × 10⁴ + 9 × 10³ + 4 × 10² + 4 × 10⁰

(ii) 3006194
Answer:
3006194 = 3000000 + 0 + 0 + 6000 + 100 + 90 + 4
= 3 × 1000000 + 0 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 4 × 1
= 3 × 10⁶ + 0 × 10⁵ + 0 × 10⁴ + 6 × 10³ + 1 × 10² + 9 × 10¹ + 4 × 10⁰
= 3 × 10⁶ + 6 × 10³ + 1 × 10² + 9 × 10¹ + 4 × 10⁰

(iii) 2806196
Answer:
2806196 = 2000000 + 800000 + 0 + 6000 + 100 + 90 + 6
= 2 × 1000000 + 8 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 6 × 1
= 2 × 10⁶ + 8 × 10⁵ + 0 × 10⁴ + 6 × 10³ + 1 × 10² + 9 × 10¹ + 6 × 10²⁰
= 2 × 10⁶ + 8 × 10⁵ + 6 × 10³ + 1 × 10² + 9 × 10¹ + 6 × 10⁰

(iv) 120719
Answer:
120719 = 100000 + 20000 + 0 + 700 + 10 + 9
= 1 × 100000 + 2 × 10000 + 0 × 1000 + 7 × 100 + 1 × 10 + 9 × 10⁰
= 1 × 10⁵ + 2 × 10⁴ + 7 × 10² + 1 × 10¹ + 9 × 10⁰

(v) 20068
Answer:
20068 = 20000 + 0 + 0 + 60 + 8
= 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8 × 1
= 2 × 10⁴ + 0 × 10³ + 6 × 10² + 6 × 10¹ + 8 × 10⁰
= 2 × 10⁴ + 6 × 10¹ + 8 × 10⁰

Question 2.
Find the number from each of the following expanded forms:
(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰
Answer:
8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰
= 8 × 10000 + 6 × 1000 + 0 × 100 + 4 × 10 + 5 × 1
= 80000 + 6000 + 0 + 40 + 5
= 86045

(b) 4 × 10⁵ + 5 × 10³ + 3 × 10² + 2 × 10⁰
Answer:
4 × 10⁵ + 5 × 10³ + 3 × 10² + 2 × 10⁰
= 4 × 100000 + 5 × 1000 + 3 × 100 + 2 × 1
= 400000 + 0 + 5000 + 300 + 0 + 2
= 405302

(c) 3 × 10⁴ + 7 × 10² + 5 × 10⁰
Answer:
3 × 10⁴ + 7 × 10² + 5 × 10⁰
= 3 × 10000 + 7 × 100 + 5 × 1
= 30000 + 0 + 700 + 0 + 5 = 30705

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹
Answer:
9 × 10⁵ + 2 × 10² + 3 × 10¹
= 9 × 100000 + 2 × 100 + 3 × 10¹
= 900000 + 0 + 0 + 200 + 3 + 10⁰
= 900230

Question 3.
Express the following numbers in standard form:
(i) 5,00,00,000
Answer:
5,00,00,000
Here, 5,00,00,000 = 5 × 10000000 = 5 × 10⁷

(ii) 70,00,000
Answer:
70,00,000
Here, 70,00,000 = 7 × 1000000 = 7 × 10⁶

(iii) 3,18,65,00,000
Answer:
3,18,65,00,000
Here, 3,18,65,00,000 = 3.1865 × 1000000000
= 3.1865 × 10⁹

(iv) 3,90,878
Answer:
3,90,878
Here, 3,90,878 = 3.90878 × 100000
= 3.90878 × 10⁵

(v) 39087.8
Answer:
39087.8
Here, 39087.8 = 3.90878 × 10000
= 3.90878 × 10⁴

(vi) 3908.78
Answer:
3908.78
Here, 3908.78 = 3.90878 × 1000
= 3.90878 × 10³

Question 4.
Express the number appearing in the following statements in standard form:
(a) The distance between Earth and Moon is 384,000,000 m.
Answer:
∵ 3,84,000,000
= 3.84000000 × 10⁸ = 3.84 × 10⁸
∴ The distance between Earth and Moon is 3.84 × 10⁸ m.

(b) Speed of light in vacuum is 3< 0,000,000 m/s.
Answer:
∵ 300000000 = 3 × 10⁸
∴ The speed of light in vacuum is 3 × 10⁸ m/sec.

(c) Diameter of the Earth is 1,27,56,000 m.
Answer:
∵ 1,27,56,000 = 1.2756000 × 10⁷
= 1.2756 × 10⁷
∴ The diameter of the Earth is 1.2756 × 10⁷ m.

(d) Diameter of the Sun is 1,400,000,000 m.
Answer:
∵ 1,400,000,000 = 1.400000000 × 10⁹
= 1.4 × 10⁹ m
∴ The diameter of the Sun is 1.4 × 10⁹m.

(e) In a galaxy, there are on an average 100,000,000,000 stars.
Answer:
∵ 100,000,000,000 = 1 × 10¹¹
∴ In a galaxy, there are an average 1 × 10¹¹ stars.

(f) The universe is estimated to be about 12,000,000,000 years old.
Answer:
∵ 12,000,000,000 = 1.2000000000 × 1010 = 1.2 × 10¹⁰
∴ The universe is estimated to be about 1.2 × 10¹⁰ years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
Answer:
∵ 300,000,000,000,000,000,000
= 3.00,000,000,000,000,000,000 × 10²⁰
= 3 × 10²⁰
∴ The distance of the Sim from the centre of the Milky Way Galaxy is estimated to be 3 × 10²⁰ m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
Answer:
∵ 60,230,000,000,000,000,000,000
= 6.0230,000,000,000,000,000,000
= 6.023 × 10²²
∴ 6.023 × 10²² molecules are contained in a drop of water weighing 1.8 gm.

(i) The Earth has 1,353,000,000 cubic km of seawater.
Answer:
∵ 1,353,000,000 = 1.353000000 × 10⁹ = 1.353 × 10⁹
∴ The Earth has 1.353 × 10⁹ cubic km of seawater.

(j) The population of India was about 1,027,000,000 in M

arch 2001.
Answer:
∵ 10,27.000,000 = 1.027000000 × 10⁹
= 1.027 × 10⁹
∴ The population of India was about 1.027 × 10⁹.