Exponents and Powers
Exercise 13.3
Question 1: Write the following numbers in the expanded forms:
(a) 279404
Answer: `2 xx 10^5 + 7 xx 10^4 + 9 xx 10^3 + 4 xx 10^2 + 4 xx 10^0`
(b) 3006194
Answer: `3 xx 10^6 + 6 xx 10^3 + 1 xx 10^2 + 9 xx 10^1 + 4 xx 10^0`
(c) 2806196
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:
- `8 xx 10^4 + 6 xx 10^3 + 0 xx 10^2 + 4 xx 10^1 + 5 xx 10^0`
- `4 xx 10^5 + 5 xx 10^3 + 3 xx 10^2 + 2 xx 10^0`
- `3 xx 10^4 + 7 xx 10^2 + 3 xx 10^1`
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`
(c) 3,18,65,00,000
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`