# MP Board Class 7th Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

## MP Board Class 7th Maths Solutions Chapter 13 Exponents and Powers Ex 13.3

Question 1.
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

Question 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 = 86045
(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100 = 405302
(c) 3 × 104 + 7 × 102 + 5 × 100 = 30705
(d) 9 × 105 + 2 × 102 + 3 × 101 = 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
(vi) 3908.78
Solution:
(i) 50000000 = 5 × 107
(ii) 7000000 = 7 × 106
(iii) 3186500000 = 3.1865 × 109
(iv) 390878 = 3.90878 × 105
(v) 39087.8 = 3.90878 × 104
(vi) 3908.78 = 3.90878 × 13

Question 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 gala×y there are on an average 100,000,000,000 stars.
(f) The universe is estimated to be about 12,0,000,000 years old.
(g) The distance of the Sun from the centre of the Milky Way Gala×y 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 1,027,0,000 in March, 2001.
Solution:
(a) 3.84 × 108 m
(b) 3 × 108 m/s
(c) 1.2756 × 107 m
(d) 1.4 × 109 m
(e) 1 × 1011 stars
(f) 1.2 × 1011 years
(g) 3 × 1020 m
(h) 6.023 × 1022 molecules
(i) 1.353 × 109 cubic km
(j) 1.027 × 109