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## Karnataka State Syllabus Class 7 Maths Chapter 13 Exponents and Powers Ex 13.3

Question 1.

Write the following numbers in the expanded forms :

279404, 3006194, 2806196, 120719, 20068

Solution:

i) 279404

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

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

ii) 3006194

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

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

iii) 2806196

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

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

iv) 120719

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

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

v) 20068

= 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8 × 1

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

Question 2.

Find the number from each of the following expanded forms :

a. 8 × 10^{4} + 6 × 10^{3} + 0 × 10^{2} + 4 × 10^{1} + 5 × 10^{0}

b. 4 × 10^{5} + 5 × 10^{3} + 3 × 10^{2} + 2 × 10^{0}

c. 3 × 10^{4} + 7 × 10^{2} + 5 × 10^{0}

d. 9 × 10^{5} + 2 × 10^{2} + 3 × 10^{1}

Solution:

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

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

= 80,000 + 6000 + 0 + 40 + 5

= 86,045

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

= 400000 + 5000 + 300 + 2

= 4,05,302

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

= 40000 + 500 + 5

= 130,7051

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

= 900000 + 200 + 30

= 9,00,230

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

(vi) 3908.78

Solution:

i) 5,00,00,000

5 × 10^{7}

ii) 70,00,000

7 × 10^{6}

iii) 3,18,65,00,000

3.1865 × 10^{9}

iv) 3,90,878

3.90878 × 10^{5}

v) 39087.8

3.90878 × 10^{3}

vi) 3908.78

3.90878 × 10^{3}

Question 4.

Express the number appearing in the following statements in standard form.

Solution:

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

= 3.84 × 10^{8} m

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

= 3 × 10^{8} m/s

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

1.2756 × 10^{7} m

d) Diameter of the Sun is

1,400,0, 000m.

1.4 × 10^{9}m

e) Number of average stars in a galaxy = 100,000,000m.

= 1 × 10^{11} m

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

= 1.2 × 10^{10} years old

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

= 3 × 10^{20} m

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

= 6.023 × 10^{22} molecules

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

= 1.353 × 10^{9} cubic km

j) The population of India was about 1,027,000000 in March, 2001.

= 1.027 × 10^{9}