NCERT Solutions Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.3

 

NCERT Solutions Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.3

 

Introduction:

In this exercise, we will learn expressing large numbers in the standard form. For example, sun is located 300,000,000,000,000,000,000 m from the center of our milky way galaxy. We can observe that it is not convenient to write and read, to make it convenient we use powers. like - 3 × 100,000,000,000,000,000,000 = 3×10²⁰m.

NCERT Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.1

NCERT Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.2

NCERT Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.3

 

Class 7 Maths Exercise 11.2 (Page-181)

 

Q1. Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Solution: 

279404 = 2×10⁵+ 7×10⁴+ 9×10³+4×10²+ 0×10¹+4×10⁰

3006194 = 3×10⁶+ 0×10⁵+ 0×10⁴+ 6×10³+ 1×10²+9×10¹+ 4×10⁰

2806196 =  2 ×10⁶+ 8×10⁵+ 0×10⁴+ 6×10³+ 1×10²+9×10¹+ 6×10⁰

120719 = 1×10⁵+ 2×10⁴+ 0×10³+7×10²+ 1×10¹+9×10⁰

20068 = 2×10⁴+ 0×10³+0×10²+ 6×10¹+8×10⁰

 

Solution:

a) 86045

b) 405302

c) 30705

d) 900230

Q3. Express the following numbers in standard form:

i)  5,00,00,000

ii) 70,00,000

iii) 3,18,65,00,000

iv) 3,90,878

v) 39087.8

vi) 3908.78

Solution:

i) 5× 10⁷

ii) 7× 10⁶

iii) 3.1865 × 10⁹

iv) 3.90878× 10⁵

v) 3.90878×10⁴

vi) 3.90878×10³

Q4. Express the number appearing in the following statements in standard form:

(a) The distance between Earth and Moon is 384.0. 000 m.

(b) Speed of light in vacuum is 300,000,000 m/s.

(c) Diameter of the Earth is 1,27,56,000 m.

(d) Diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy there are an average 100,000,000,000 stars.

(f) The universe is estimated to be about 12,000,000,000 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.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

(i) The Earth has 1,353,000,000 cubic km of sea water.

(j) The population of India was about 1,027,000,000 in March 2001.

Solution: 

a) 384,000,000 m = 3.84 × 10⁸m

b) (b) 300,000,000 m/s = 3× 10⁸m⁄s

(c) 1,27,56,000 m = 1.2756× 10⁷m

(d) 1,400,000,000 m = 1.4 × 10⁹m

(e) 100,000,000,000 stars = 1× 10¹¹ stars

(f) 12,000,000,000 years old = 1.2 × 10¹⁰ years old

(g) 300,000,000,000,000,000,000 m = 3× 10²⁰m

(h) 60, 230, 000, 000, 000, 000, 000, 000 molecules = 6.023 × 10²²

(i) 1,353,000,000 cubic km = 1.353× 10⁹ km³

(j) 1,0,27,000,000 = 1.027 × 10⁹