CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.
Class 7 Maths NCERT Solutions Chapter 13 Exponents and Powers Ex 13.3
Question 1.
Write the following numbers in the expanded forms :
Solution:
(i) 279404 = 2 × 100000 + 7 × 10000 x 9 × 1000 + 4 × 100 + 0 × 10 + 4 × 1
= 2 × 105 + 7 × 104 +9 × 103 + 4 × 102 + 0 × 101 + 4 × 100
(ii) 3006194 = 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 × 10°
(iii) 2806196 = 2 × 1000000 + 8 × 100000 + 0 × 10000 + 6 × 1000 +1 × 100 + 9 × 101 + 6 × 100
= 2 × 106 + 8 × 105 + 0 × 104 + 6 × 103
(iv) 120719 = 1 × 100000 + 2 × 10000 + 0 × 1000 + 7 × 100 + 1 × 10 + 9 × 1
= 1 × 105 + 2 × 104 + 0 × 103 + 7 × 102 +1 × 101 + 9 × 100
(v) 20068 = 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8 × 1
= 2 × 104 + 0 × 103 + 0 × 102 + 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
Solution:
8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
= 8 × 10000 + 6 × 1000 + 0 × 100 + 4 × 10 + 5 × 1
= 86045
(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
Solution:
4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
= 4 × 100000 + 5 × 1000 + 3 × 100 + 2
= 405302
(c) 3 × 104 + 7 × 102 + 5 × 100
Solution:
3 × 104 + 7 × 102 + 5 × 1
= 3 × 10000 + 7 × 100 + 5 × 1
= 30705
(d) 9 × 105 + 2 × 102 + 3 × 101
Solution:
9 × 105 + 2 × 102 + 3 × 101
= 9 × 100000 + 2 × 100 + 30
= 900230
Question 3.
Express the following numbers in standard form:
(i) 5,00,00,000
Solution:
5,00,00,000 = 5 × 10000000 = 5 × 107
(ii) 70,00,000
Solution:
70,00,000 = 7 × 1000000 = 7 × 106
(iii) 3,18,65,00,000
Solution:
3,18,65,00,000 = 3.1865 × 1000000000 = 3.1865 × 109
(iv) 3,90,878
Solution:
3,90,878 = 3.90878 × 100000 = 3.90878 × 105
(v) 39087.8
Solution:
39087.8 = 3.90878 × 10000 = 3.90878 × 104
(vi) 3908.78
Solution:
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.
Solution:
The mean distance between Earth and Moon = 384,000,000 m = 3.84 × 100000000 m = 3.84 × 108 m
(b) Speed of light in vaccum is 300,000,000 m/s.
Solution:
Speed of light in vaccum
= 300,000,000 m/s
= 3.0 × 100000000 m/s
= 3.0 × 108 m/s
(c) Diameter of the Earth is 1,27,56,000 m.
Solution:
Diameter of the Earth 1,27,56,000 m
= 1.2756 × 10000000 m = 1.2756 × 107
(d) Diameter of the Sun is 1,400,000,000 m.
Solution:
Diameter of the Sun
= 1,400,000,000 m = 1.4 × 1000000000 m = 1.4 × 109 m
(e) In a galaxy there are on4m average 100,000,000,000 stars.
Solution:
In a galaxy there are on an average
= 100,000,000,000 stars = 1 × 100000000000 stars = 1 × 1011 stars
(f) The universe is estimated to be 12,000,000,000 years old.
Solution:
The universe is estimated to be 12,000,000,000 years old
= 12 × 1,000,000,000 = 1.2 × 1010 year
(g) The distance of the Sun from the center of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
Solution:
The distance of Sun from the centre of the Milky Way Galaxy is estimated to be
= 300,000,000,000,000,000,000
= 3 × 100000000000000000000
= 3 × 1020 m
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
Solution:
Number of molecules contained in a drop of water weighing 1.8 gm = 60,230,000,000,000,000,000,000
= 6.023 × 10000000000000000000000 = 6.023 × 1020
(i) The Earth has 1,353,000,000 cubic km of seawater.
Solution:
The Earth has 1,353,000,000 cubic km of seawater i.e.,
1.353 × 1,000,000,000 = 1.353 × 109 cubic km.
(j) The population of India was about 1,027,000,000 in March, 2001.
Solution:
The population of India was about in March 2001 = 1,027,000,000 = 1.027 × 1000000000 = 1.027 × 109