Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3

Question 1.

Write the following numbers in the expanded forms:

(i) 279404

(ii) 3006194

(iii) 2806196

(iv) 120719

(v) 20068

Solution:

(i) 279404:

We have:

279404 = 2 x 100000 + 7 x 10000 + 9 x 1000 + 4 x 100 + 0 x 10 + 4 x 1

= 2 x 10^{5} + 7 x 10^{4} + 9 x 10^{3} + 4 x 10^{2} + 0 x 10^{1} + 4 x 10^{0}

= 2 x 10^{5} + 7 x 10^{4} + 9 x 10^{3} + 4 x 10^{2} + 4 x 10^{0}

(ii) 3006194:

We have:

3006194 = 3 x 1000000 + 0 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 + 4 x 1

= 3 x 10^{6} + 0 x 10^{5} + 0 x 10^{4} + 6 x 10^{3} + 1 x 10^{2} + 9 x 10^{1} + 4 x 10^{0}

= 3 x 10^{6} + 6 x 10^{3} + 1 x 10² + 9 x 10^{1} + 4 x 10^{0}

(iii) 2806196:

We have:

2806196 = 2 x 1000000 + 8 x 100000 + 0 x 10000 + 6 x 1000 + 1 x 100 + 9 x 10 + 6 x 10^{0}

= 2 x 10^{6} + 8 x 10^{5} + 0 x 10^{4} + 6 x 10^{3} + 1 x 10^{2} + 9 x 10^{1} + 6 x 10^{0}

= 2 x 10^{6} + 8 x 10^{5} + 6 x 10^{3} + 1 x 10^{2} + 9 x 10^{1} + 6 x 10^{0}

(iv) 120719:

We have:

120719 = 1 x 100000 + 2 x 10000 + 0 x 1000 + 7 x 100 + 1 x 10 + 9 x 1

= 1 x 10^{5} + 2 x 10^{4} + 0 x 10^{3} + 7 x 10^{2} + 1 x 10^{1} + 9 x 10^{0}

= 1 x 10^{5} + 2 x 10^{4} + 7 x 10^{2} + 1 x 10^{1} + 9 x 10^{0}

(v) 20068:

We have:

20068 = 2 x 10000 + 0 x 1000 + 0 x 100 + 6 x 10 + 8 x 1

= 2 x 10^{4} + 0 x 10^{3} + 0 x 10^{2} + 6 x 10^{1} + 8 x 10^{0}

= 2 x 10^{4} + 6 x 10^{1} + 8 x 10^{0}

Question 2.

Find the number from each of the following expanded forms:

(a) 8 x 10^{4} + 6 x 10^{3} + 0 x 10^{2} + 4 x 10^{1} + 5 x 10^{0}

(b) 4 x 10^{5} + 5 x 10^{3} + 3 x 10^{2} + 2 x 10^{0}

(c) 3 x 10^{4} + 7 x 10^{2} + 5 x 10^{0}

(d) 9 x 10^{5} + 2 x 10^{2} + 3 x 10^{1}

Solution:

(a) 8 x 10^{4} + 6 x 10^{3} + 0 x 10^{2} + 4 x 10^{1} + 5 x 10^{0}

= 8 x 10000 + 6 x 1000 + 0 x 100 + 4 x 10 + 5 x 1

= 80000 + 6000 + 0 + 40 + 5 = 86045

(b) 4 x 10^{5} + 5 x 10^{3} + 3 x 10^{4} + 2 x 10^{0}

= 4 x 100000 + 5 x 1000 + 3 x 100 + 2 x 1

= 400000 + 5000 + 300 + 2 = 405302

(c) 3 x 10^{4} + 7 x 10^{2} + 5 x 10^{0}

= 3 x 10000 + 7 x 100 + 5 x 1

= 30000 + 700 + 5 = 30705

(d) 9 x 10^{5} + 2 x 10^{2} + 3 x 10

= 9 x 100000 + 2 x 100 + 3 x 10

= 900000 + 200 + 30

= 900230

Question 3.

Express the following numbers in standard form:

(i) 5,00,00,000

(ii) 70,00,000

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

(iv) 3,90,878

(v) 39087.8

Solution:

(i) 5,00,00,000:

We have: 50000000 = 5 x 10000000 = 5 x 10^{7}

Thus, the standard form of 50000000 is 5 x 10^{7}.

(ii) 70,00,000:

We have: 70,00,000 = 7 x 1000000 = 7 x 10^{6}

Thus, the standard form of 70,00,000 is 7 x 10^{6}.

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

We have: 3186500000 = 3.186500000 x 10^{9} = 3.1865 x 10^{9}

Thus, the standard form of 3186500000 is 3.1865 x 10^{9}.

(iv) 3,90,878:

We have: 390878 = 3.90878 x 10^{5}

Thus, the standard form of 390878 is 3.90878 x 10^{5}.

(v) 39087.8:

We have: 39087.8 = 3.90878 x 10^{4}

Thus, the standard form of 39087.8 is 3.90878 x 10^{4}.

(vi) 3908.78:

We have: 3908.78 = 3.90878 x 10^{3}

Thus, the standard form of 3908.78 is 3.90878 x 10^{3}.

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.

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

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

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

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

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

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,0, 000,000,000,000,000 m.

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

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

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

Solution:

(a) ∵ 384.0. 000 = 3.84000000 x 10^{8} = 3.84 x 10^{8}

∴ The distance between Earth and Moon is 3.84 x 108 m.

(b) ∵ 300000000 = 3 x 108

∴ The speed of light in vacuum is 3 x 10^{8} m/s.

(c) ∵ 1,27,56,000 = 1.2756000 x 10^{7} = 1.2756 x 10^{7}

∴ The diameter of the Earth is 1.2756 x 10^{7} m.

(d) ∵ 1.400.0. 000 = 1.400000000 x 10^{9} = 1.4 x 10^{9}

∴ The diameter of Sun is 1.4 x 10^{9} m.

(e) ∵ 100.0. 000.000 = 1 x 10^{11}

∴ In a galaxy, there are on an average 1 x 10^{11} stars.

(f) ∵ 12000000000 = 1.2 x 1010

∴ The universe is estimated to be about 1.2 x 10^{10} years old.

(g) ∵ 300.0. 000.000.000.000.000 = 3 x 100,000,000,000,000,000,000 = 3 x 10^{20}

∴ The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 3 x 10^{20 }m.

(h) ∵ 60.230.0. 000.000.000.000.000 = 6.0230000000000000000000 x 10^{22} = 6.023 x 10^{22}

∴ 6.023 x 10^{22} molecules are contained in a drop of water weighing 1.8 gm.

(i) ∵ 1.353.0. 000 = 1.353000000 x 10^{9} = 1.353 x 10^{9}

∴ The Earth has 1,353 x 10^{9} cubic km of sea water.

(j) ∵ 1.027.0. 000 = 1,027000000 x 10^{9} = 1.027 x 10^{9}

∴ The population of India was about 1.027 x 10^{9} in March, 2001.