NCERT Solutions(Part - 2) - Exponents and Powers Class 7 Notes | EduRev

Mathematics (Maths) Class 7

Created by: Praveen Kumar

Class 7 : NCERT Solutions(Part - 2) - Exponents and Powers Class 7 Notes | EduRev

The document NCERT Solutions(Part - 2) - Exponents and Powers Class 7 Notes | EduRev is a part of the Class 7 Course Mathematics (Maths) Class 7.
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Exercise 13.3 

Question 1: 

Write the following numbers in the expanded form: 

279404, 

3006194, 

2806196, 

120719, 

20068 

Answer 1: 

(i) 2,79,404 

= 2,00,000 + 70,000 + 9,000 + 400 + 00 + 4
= 2x100000 + 7x 10000+ 9x1000 + 4 x 100+ 0x 10 + 4x1
= 2x105+7x104 +9x103 + 4 x102+ 0x101+4x100

(ii) 30,06,194 

= 30,00,000 + 0 + 0 + 6,000 + 100 + 90 + 4
= 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6 x 1000 + 1x100 + 9x10 + 4x1
= 3x106 + 0x105 +0x104 +6 x103+1x102 +9x10+4x100

(iii) 28,06,196 

= 20,00,000 + 8,00,000 + 0 + 6,000 + 100 + 90 + 6
= 2x1000000 + 8x 100000+ 0x 10000 +6 x 1000 + 1 x 100 + 9 x 10 + 6 x 1
= 2 x106+8x105+0x104 + 6x103+1x102+9x10+6x100

(iv) 1,20,719 

= 1,00,000 + 20,000 + 0 + 700 + 10 + 9
= 1 x 100000 + 2 x 10000 + 0x 1000 + 7x100 + 1x 10+9x1
= 1 x 105 + 2 x 10+ 0 x 103 + 7 x 102 + 1 x 101 + 9 x 100

(v) 20,068 

= 20,000 + 00 + 00 + 60 + 8

= 2 x 10000 + 0 x 1000 + 0 x 100 + 6 x 10 + 8 x 1

NCERT Solutions(Part - 2) - Exponents and Powers Class 7 Notes | EduRev

Question 2: 

Find the number from each of the following expanded forms: 

(a) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100 

(b) 4 x 105 + 5 x 103 + 3 x 102 + 2 x 100 

(c) 3 x 104 + 7 x 102 + 5 x 100 (d) 9 x 105 + 2 x 102 + 3 x 101 

Answer 2: 

(a) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100
= 8 x 10000 + 6x 1000 + 0 x 100 + 4 x 10 + 5 x 1
= 80000 + 6000 + 0 + 40+5 
= 86,045

(b) 4 x 105 + 5 x 103 + 3 x 102 + 2 x 100
= 4 x 100000 + 0 x 10000 + 5 x 1000 + 3 x 100 + 0 x 10 + 2 x 1
= 400000 + 0 + 5000 + 3000 + 0 + 2 
= 4,05,302

(c) 3 x 104 + 7 x 10z + 5 x 100
= 3 x 10000 + 0 x 1000 + 7 x 100 + 0 x 10 + 5 x 1
= 30000 + 0 + 700 + 0 + 5 
= 30,705

(d) 9x 105 + 2 x 102 + 3 x 101 
= 9 x 100000 + 0 x 10000 + 0 x 1000 + 2 x 100 + 3 x 10 + 0 x 1
= 900000 + 0 + 0 + 200 + 30 + 0 
= 9,00,230

Question 3: 

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 

Answer 3: 

(i) 5,00,00,000 = 5 x 1,00,00,000 = 5 x 107

(ii) 70,00,000 = 7 x 10,00,000 = 7 x 106

(iii) 3,18,65,00,000 = 31865 x 100000

= 3.1865 x 10000 x 100000 = 3.1865 x 109

(iv) 3,90,878 = 3.90878 x 100000 = 3.90878 x 105

(v) 39087.8 = 3.90878 x 10000 = 3.90878 x 104

(vi) 3908.78 = 3.90878 x 1000 = 3.90878 x 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. 

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

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

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

(e) In a galaxy there are on an average 100,000,000,0000 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.

Answer 4: 

(a) The distance between Earth and Moon = 384,000,000 m
= 384x 1000000 m
= 3.84 x 100 x 1000000
= 3.84x108 m

(b) Speed of light in vacuum = 300,000,000 m/s
= 3 x 100000000 m/s
= 3x108 m/s

(c) Diameter of the Earth = 1,27,50,000 m
= 12756 x 1000 m
= 1.2756 x 10000 x 1000 m
= 1 2756x107 m

(d) Diameter of the Sun = 1,400,000,000 m
= 14 x 100,000,000 m
= 1.4 x 10 x 100,000,000 m
= 1.4 x 109 m

(e) Average of Stars = 100, 000, 000,000
= 1 x 100,000,000,000
= 1x1011

(f) Years of Universe = 12,000,000,000 years
= 12 x 1000,000,000 years
= 1.2 x 10 x 1000,000,000 years
= 1.2 x 1010 years

(g) Distance of tlie Sun from the centre of the Milky Way Galaxy
= 300,000,000,000,000,000,000 m
= 3 x 100,000,000,000,000,000,000 m
= 3 x 1020 m

(h) Number of molecules in a drop of water weighing 1.8 gm
= 60,230,000,000,000,000,000,000
= 6023 x 10,000,000,000,000,000,000
= 6,023 x 1000 x 10,000,000,000,000,000,000
= 6.023 x1022

(i) The Earth has Sea water = 1,353,000,000 km3
= 1,353 x 1000000 km3
= 1,353 x 1000 x 1000,000 km3
= 1.353x109 km3

(j) The population of India = 1,027,000,000
= 1027x1000000 = 1,027x1000x1000000
= 1.027x109

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