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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× 105 + 7× 104 + 9 × 103 + 4 × 102 + 0 × 101 + 4 × 100
ii) 3006194
= 3 × 1000000 + 0 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 10 + 4 × 1
= 3 × 106 + 0 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 4 × 100
iii) 2806196
= 2 × 1000000 + 8 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 × 101 + 6 × 100
= 2 × 106 + 8 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 6 × 100
iv) 120719
= 1 × 100000 + 2 × 10000 + 0 × 1000 + 7 × 100 + 1 × 10 + 9 × 1
= 1 × 105 + 2 × 104 + 0 × 103 + 7 × 102 + 1 × 101 + 9 × 100
v) 20068
= 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8 × 1
= 2 × 104 + 0 × 103 + 0 × 102 + 6 × 101 + 8 × 100
Question 2.
Find the number from each of the following expanded forms :
a. 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
b. 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
c. 3 × 104 + 7 × 102 + 5 × 100
d. 9 × 105 + 2 × 102 + 3 × 101
Solution:
a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
= 8 × 10000 + 6 × 1000 + 0 × 100 + 4 × 10 + 5 × 1
= 80,000 + 6000 + 0 + 40 + 5
= 86,045
b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
= 400000 + 5000 + 300 + 2
= 4,05,302
c) 3 × 104 + 7 × 102 + 5 × 100
= 40000 + 500 + 5
= 130,7051
d) 9 × 105 + 2 × 102 + 3 × 101
= 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 × 107
ii) 70,00,000
7 × 106
iii) 3,18,65,00,000
3.1865 × 109
iv) 3,90,878
3.90878 × 105
v) 39087.8
3.90878 × 103
vi) 3908.78
3.90878 × 103
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 × 108 m
b) Speed of light in vacuum is 300,000,000 m/s
= 3 × 108 m/s
c) Diameter of the Earth is 1,27,56,000 m.
1.2756 × 107 m
d) Diameter of the Sun is
1,400,0, 000m.
1.4 × 109m
e) Number of average stars in a galaxy = 100,000,000m.
= 1 × 1011 m
f) The universe is estimated to be about 12,000,000,000 years old.
= 1.2 × 1010 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 × 1020 m
h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
= 6.023 × 1022 molecules
i ) The earth has 1,353,000,000 cubic km of sea water.
= 1.353 × 109 cubic km
j) The population of India was about 1,027,000000 in March, 2001.
= 1.027 × 109