Gujarat BoardĀ GSEB Textbook Solutions Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3
Question 1.
Write the following numbers in the expanded forms:
(i) 279404
(ii) 3006194
(iii) 2806196
(iv) 120719
(v) 20068
Solution:
(i) 279404:
We have:
279404 = 2 x 100000 + 7 x 10000 + 9 x 1000 + 4 x 100 + 0 x 10 + 4 x 1
= 2 x 105 + 7 xĀ 104 + 9 x 103 + 4 x 102 + 0 x 101 + 4 x 100
= 2 x 105 + 7 x 104 + 9 x 103 + 4 x 102 + 4 x 100
(ii) 3006194:
We have:
3006194 = 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 + 4 x 1
= 3 x 106 + 0 x 105 + 0 x 104 + 6 x 103 + 1 x 102 + 9 x 101 + 4 x 100
= 3 x 106 + 6 x 103 + 1 x 10Ā² + 9 x 101 + 4 x 100
(iii) 2806196:
We have:
2806196 = 2 x 1000000 + 8 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 + 6 x 100
= 2 x 106 + 8 x 105 + 0 x 104 + 6 x 103 + 1 x 102 + 9 x 101 + 6 x 100
= 2 x 106 + 8 x 105 + 6 x 103 + 1 x 102 + 9 x 101 + 6 x 100
(iv) 120719:
We have:
120719 = 1 x 100000 + 2 x 10000 + 0 x 1000 + 7 x 100 + 1 x 10 + 9 x 1
= 1 x 105 + 2 x 104 + 0 x 103 + 7 x 102 + 1 x 101 + 9 x 100
= 1 x 105 + 2 x 104 + 7 x 102 + 1 x 101 + 9 x 100
(v) 20068:
We have:
20068 = 2 x 10000 + 0 x 1000 + 0 x 100 + 6 x 10 + 8 x 1
= 2 x 104 + 0 x 103 + 0 x 102 + 6 x 101 + 8 x 100
= 2 x 104 + 6 x 101 + 8 x 100
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
Solution:
(a) 8 x 104 + 6 x 103 + 0 x 102 + 4 x 101 + 5 x 100
= 8 x 10000 + 6 x 1000 + 0 x 100 + 4 x 10 + 5 x 1
= 80000 + 6000 + 0 + 40 + 5 = 86045
(b) 4 x 105 + 5 x 103 + 3 x 104 + 2 x 100
= 4 x 100000 + 5 x 1000 + 3 x 100 + 2 x 1
= 400000 + 5000 + 300 + 2 = 405302
(c) 3 x 104 + 7 x 102 + 5 x 100
= 3 x 10000 + 7 x 100 + 5 x 1
= 30000 + 700 + 5 = 30705
(d) 9 x 105 + 2 x 102 + 3 x 10
= 9 x 100000 + 2 x 100 + 3 x 10
= 900000 + 200 + 30
= 900230
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
Solution:
(i) 5,00,00,000:
We have: 50000000 = 5 x 10000000 = 5 x 107
Thus, the standard form of 50000000 is 5 x 107.
(ii) 70,00,000:
We have: 70,00,000 = 7 x 1000000 = 7 x 106
Thus, the standard form of 70,00,000 is 7 x 106.
(iii) 3,18,65,00,000:
We have: 3186500000 = 3.186500000 x 109 = 3.1865 x 109
Thus, the standard form of 3186500000 is 3.1865 x 109.
(iv) 3,90,878:
We have: 390878 = 3.90878 x 105
Thus, the standard form of 390878 is 3.90878 x 105.
(v) 39087.8:
We have: 39087.8 = 3.90878 x 104
Thus, the standard form of 39087.8 is 3.90878 x 104.
(vi) 3908.78:
We have: 3908.78 = 3.90878 x 103
Thus, the standard form of 3908.78 is 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 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 on 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 300,0, 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) āµ 384.0. 000 = 3.84000000 x 108 = 3.84 x 108
ā“ The distance between Earth and Moon is 3.84 x 108 m.
(b) āµ 300000000 = 3 x 108
ā“ The speed of light in vacuum is 3 x 108 m/s.
(c) āµ 1,27,56,000 = 1.2756000 x 107 = 1.2756 x 107
ā“ The diameter of the Earth is 1.2756 x 107 m.
(d) āµ 1.400.0. 000 = 1.400000000 x 109 = 1.4 x 109
ā“ The diameter of Sun is 1.4 x 109 m.
(e) āµ 100.0. 000.000 = 1 x 1011
ā“ In a galaxy, there are on an average 1 x 1011 stars.
(f) āµ 12000000000 = 1.2 x 1010
ā“ The universe is estimated to be about 1.2 x 1010 years old.
(g) āµ 300.0. 000.000.000.000.000 = 3 x 100,000,000,000,000,000,000 = 3 x 1020
ā“ The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 3 x 1020 m.
(h) āµ 60.230.0. 000.000.000.000.000 = 6.0230000000000000000000 x 1022 = 6.023 x 1022
ā“ 6.023 x 1022 molecules are contained in a drop of water weighing 1.8 gm.
(i) āµ 1.353.0. 000 = 1.353000000 x 109 = 1.353 x 109
ā“ The Earth has 1,353 x 109 cubic km of sea water.
(j) āµ 1.027.0. 000 = 1,027000000 x 109 = 1.027 x 109
ā“ The population of India was about 1.027 x 109 in March, 2001.