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