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:

  1. `8 xx 10^4 + 6 xx 10^3 + 0 xx 10^2 + 4 xx 10^1 + 5 xx 10^0`
  2. `4 xx 10^5 + 5 xx 10^3 + 3 xx 10^2 + 2 xx 10^0`
  3. `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:

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

    Answer: `3.84 xx 10^8`

  2. Speed of light in vacuum is 300,000,000 m/s.

    Answer: `3 xx 10^8`

  3. Diameter of the Earth is 1,27,56,000 m.

    Answer: `1.2756 xx 10^7`

  4. Diameter of the Sun is 1,400,000,000 m.

    Answer: `1.4 xx 10^9`

  5. In a galaxy there are on an aevarge 100,000,000,000 stars.

    Answer: `1 xx 10^(11)`

  6. The universe is estimated to be about 12,000,000,000 years old.

    Answer: `1.2 xx 10^(10)`

  7. 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)`

  8. 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)`

  9. The earth has 1,353,000,000 cubic km of sea water.

    Answer: `1.353 xx 10^9`

  10. The population of India was about 1,027,000,000 in March 2001.

    Answer: `1.027 xx 10^9`

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