NCERT Solutions Class 7 Mathematics
Chapter – 13 (Exponents and Powers)
The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 13 Exponents and Powers Exercise 13.3 has been provided here to help the students in solving the questions from this exercise.
Chapter : 13 Exponents and Powers
Exercise – 13.3
1. Write the following numbers in the expanded forms:
279404, 3006194, 2806196, 120719, 20068
Solution –
279404
The expanded form of the number 279404 is,
= (2 × 100000) + (7 × 10000) + (9 × 1000) + (4 × 100) + (0 × 10) + (4 × 1)
= (2 × 105) + (7 × 104) + (9 × 103) + (4 × 102) + (0 × 101) + (4 × 100)
3006194
The expanded form of the number 3006194 is,
= (3 × 1000000) + (0 × 100000) + (0 × 10000) + (6 × 1000) + (1 × 100) + (9 × 10) + 4
= (3 × 106) + (0 × 105) + (0 × 104) + (6 × 103) + (1 × 102) + (9 × 101) + (4 × 100)
2806196
The expanded form of the number 2806196 is,
= (2 × 1000000) + (8 × 100000) + (0 × 10000) + (6 × 1000) + (1 × 100) + (9 × 10) + 6
= (2 × 106) + (8 × 105) + (0 × 104) + (6 × 103) + (1 × 102) + (9 × 101) + (6 × 100)
120719
The expanded form of the number 120719 is,
= (1 × 100000) + (2 × 10000) + (0 × 1000) + (7 × 100) + (1 × 10) + (9 × 1)
= (1 × 105) + (2 × 104) + (0 × 103) + (7 × 102) + (1 × 101) + (9 × 100)
20068
The expanded form of the number 20068 is,
= (2 × 10000) + (0 × 1000) + (0 × 100) + (6 × 10) + (8 × 1)
= (2 × 104) + (0 × 103) + (0 × 102) + (6 × 101) + (8 × 100)
2. Find the number from each of the following expanded forms:
(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
(c) 3 × 104 + 7 × 102 + 5 × 100
(d) 9 × 105 + 2 × 102 + 3 × 101
Solution –
(a) 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
= (4 × 100000) + (0 × 10000) + (5 × 1000) + (3 × 100) + (0 × 10) + (2 × 1)
= 400000 + 0 + 5000 + 300 + 0 + 2
= 405302
(c) 3 × 104 + 7 × 102 + 5 × 100
= (3 × 10000) + (0 × 1000) + (7 × 100) + (0 × 10) + (5 × 1)
= 30000 + 0 + 700 + 0 + 5
= 30705
(d) 9 × 105 + 2 × 102 + 3 × 101
= (9 × 100000) + (0 × 10000) + (0 × 1000) + (2 × 100) + (3 × 10) + (0 × 1)
= 900000 + 0 + 0 + 200 + 30 + 0
= 900230
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
Solution –
(i) 5,00,00,000
The standard form of the given number is 5 × 107
(ii) 70,00,000
The standard form of the given number is 7 × 106
(iii) 3,18,65,00,000
The standard form of the given number is 3.1865 × 109
(iv) 3,90,878
The standard form of the given number is 3.90878 × 105
(v) 39087.8
The standard form of the given number is 3.90878 × 104
(vi) 3908.78
The standard form of the given number is 3.90878 × 103
4. 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) The distance between Earth and Moon is 384,000,000 m.
384,000,000 m = 3.84 × 108 m
(b) Speed of light in vacuum is 300,000,000 m/s.
300,000,000 m/s = 3 × 108 m/s
(c) Diameter of the Earth is 1,27,56,000 m.
1,27,56,000 m = 1.2756 × 1072 m
(d) Diameter of the Sun is 1,400,000,000 m.
1,400,000,000 m = 1.4 × 109 m
(e) In a galaxy there are on an average 100,000,000,000 stars.
100,000,000,000 stars = 1 × 1011 stars
(f) The universe is estimated to be about 12,000,000,000 years old.
12,000,000,000 years old = 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.
300,000,000,000,000,000,000 m = 3 × 1020 m
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
60, 230, 000, 000, 000, 000, 000, 000 molecules = 6.023 × 1022 molecules
(i) The earth has 1,353,000,000 cubic km of sea water.
1,353,000,000 cubic km = 1.353 × 109 cubic km
(j) The population of India was about 1,027,000,000 in March, 2001.
1,0,27,000,000 = 1.027 × 109
