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## Chapter 13 Exponents and Powers Exercise 13.3

Question 1: Write the following numbers in the expanded forms:
279404

= (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

= (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

= (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

= (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

= (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 ×10)
⁴ + (6 × 10)³ + (0 × 10)² + (4 × 10)¹ + (5 × 10)

= (8 × 10000) + (6 × 1000) + (0 × 100) + (4 × 10) + (5 × 1)
= 80000 + 6000 + 0 + 40 + 5
= 86045

(b) (4 ×10)⁵ + (5 × 10)³ + (3 × 10)² + (2 × 10)

= (4 × 100000) + (0 × 10000) + (5 × 1000) + (3 × 100) + (0 × 10) + (2 × 1)
= 400000 + 0 + 5000 + 300 + 0 + 2
= 405302

(c) (3 ×10)⁴ + (7 × 10)² + (5 × 10)

= (3 × 10000) + (0 × 1000) + (7 × 100) + (0 × 10) + (5 × 1)
= 30000 + 0 + 700 + 0 + 5
= 30705

(d) (9 ×10)⁵ + (2 × 10)² + (3 × 10)¹

= (9 × 100000) + (0 × 10000) + (0 × 1000) + (2 × 100) + (3 × 10) + (0 × 1)
= 900000 + 0 + 0 + 200 + 30 + 0
= 900230

Question 3: Express the following numbers in standard form:
(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.

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.
The standard form of the statement is 3.84 × 10⁸ m.

(b) Speed of light in vacuum is 300,000,000 m/s.
The standard form of the statement is 3 × 10⁸ m/s.

(c) Diameter of the Earth is 1,27,56,000 m.
The standard form of the statement is 1.2756 × 10⁷ m.

(d) Diameter of the Sun is 1,400,000,000 m.
The standard form of the statement is 1.4 × 10⁹ m.

(e) In a galaxy there are on an average 100,000,000,000 stars.
The standard form of the statement is 1 × 10¹¹ stars.

(f) The universe is estimated to be about 12,000,000,000 years old.
The standard form of the statement is 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.
The standard form of the statement is 3 × 10²² m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
The standard form of the statement is 6.023 × 10²² molecules.

(i) The earth has 1,353,000,000 cubic km of sea water.
The standard form of the statement is 1.353 × 10⁹ cubic km.

(j) The population of India was about 1,027,000,000 in March, 2001.
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