## Chapter 13 Exponents and Powers Exercise 13.3

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

= (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**

Answer:

Answer:

= (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**

Answer:

Answer:

= (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**

Answer:

Answer:

= (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

Answer:

20068

Answer:

= (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)

(a) (8 ×10)

**⁴ + (6 × 10)³ + (0 × 10)² + (4 × 10)**

**¹ + (5 × 10)**

**⁰**

Answer:

Answer:

= (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)**

**⁰**

Answer:

Answer:

= (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)**

**⁰**

Answer:

Answer:

= (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**

Answer:

Answer:

= (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

Answer:The standard form of the given number is 5 × 10⁷.

(i) 5,00,00,000

Answer:

**The standard form of the given number is 7 × 10⁶.**

(ii) 70,00,000

Answer:

(ii) 70,00,000

Answer:

**The standard form of the given number is 3.1865 × 10⁹.**

(iii) 3,18,65,00,000

Answer:

(iii) 3,18,65,00,000

Answer:

**The standard form of the given number is 3.90878 × 10⁵.**

(iv) 3,90,878

Answer:

(iv) 3,90,878

Answer:

**The standard form of the given number is 3.90878 × 10⁴.**

(v) 39087.8

Answer:

(v) 39087.8

Answer:

**The standard form of the given number is 3.90878 × 10³.**

(vi) 3908.78

Answer:

(vi) 3908.78

Answer:

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

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.

Answer:

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.

Answer:

**(b) Speed of light in vacuum is 300,000,000 m/s.**

Answer:The standard form of the statement is 3 × 10⁸ m/s.

Answer:

**(c) Diameter of the Earth is 1,27,56,000 m.**

Answer:The standard form of the statement is 1.2756 × 10⁷ m.

Answer:

**(d) Diameter of the Sun is 1,400,000,000 m.**

Answer:The standard form of the statement is 1.4 × 10⁹ m.

Answer:

**(e) In a galaxy there are on an average 100,000,000,000 stars.**

Answer:The standard form of the statement is 1 × 10¹¹ stars.

Answer:

**(f) The universe is estimated to be about 12,000,000,000 years old.**

Answer:The standard form of the statement is 1.2 × 10¹⁰ years old.

Answer:

**(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.**

Answer:The standard form of the statement is 3 × 10²² m.

Answer:

**(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.**

Answer:The standard form of the statement is 6.023 × 10²² molecules.

Answer:

**(i) The earth has 1,353,000,000 cubic km of sea water.**

Answer:The standard form of the statement is 1.353 × 10⁹ cubic km.

Answer:

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

Answer:The standard form of the statement is 1.027 × 10⁹.

Answer:

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