Exponents and Powers

Exercise 13.3

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

(a) 279404

Answer: 2 × 10⁵ + 7 × 10⁴ + 9 × 10³ + 4 × 10² + 4 × 10⁰

(b) 3006194

Answer: 3 × 10⁶ + 6 × 10³ + 1 × 10² + 9 × 10¹ + 4 × 10⁰

Answer: `2 xx 10^6 + 8 xx 10^5 + 6 xx 10^3 + 1 xx 10^2 + 9 xx 10^1 + 6 xx 10^0`

(d) 120719

Answer: `1 xx 10^5 + 2 xx 10^4 + 7 xx 10^2 + 1 xx 10^1 + 9 xx 10^0`

(e) 20068

Answer: `2 xx 10^4 + 6 xx 10^1 + 8 xx 10^0`

Question 2: Find the number from each of the following expanded forms:

Answer: (a) 86040, (b) 405302, (c) 30730

Question 3: Express the following numbers in standard form:

(a) 5,00,00,000

Answer: `5 xx 10^7`

(b) 70,00,000

Answer: `7 xx 10^6`

Answer: `3.1865 xx 10^9`

(d) 3,90,878

Answer: `3.90878 xx 10^5`

(e) 39087.8

Answer: `3.90878 xx 10^4`

(f) 3908.78

Answer: `3.90878 xx 10^3`

Question 4: Express the number appearing in the following statements in standard form:

The distance between Earth and Moon is 384,000,000 m.

Answer: `3.84 xx 10^8`
Speed of light in vacuum is 300,000,000 m/s.

Answer: `3 xx 10^8`
Diameter of the Earth is 1,27,56,000 m.

Answer: `1.2756 xx 10^7`
Diameter of the Sun is 1,400,000,000 m.

Answer: `1.4 xx 10^9`
In a galaxy there are on an aevarge 100,000,000,000 stars.

Answer: `1 xx 10^(11)`
The universe is estimated to be about 12,000,000,000 years old.

Answer: `1.2 xx 10^(10)`
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: `3 xx 10^(20)`
60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

Answer: `6.023 xx 10^(22)`
The earth has 1,353,000,000 cubic km of sea water.

Answer: `1.353 xx 10^9`
The population of India was about 1,027,000,000 in March 2001.

Answer: `1.027 xx 10^9`