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Chapter 13 Exponents and Powers Ex 13.3 Solutions

Question - 1 : -
Write the following numbers in the e×panded forms:
279404, 3006194, 2806196, 120719, 20068

Answer - 1 : -

(i) 279404 = 2 × 100000 + 7 × 10000 + 9 × 1000 + 4 × 100 + 0 ×10 + 4
= 2 × 105 + 7 × 104 + 9 × 1032 +4 × 102 + 0 × 101 + 4 × 100
(ii) 3006194 = 3 × 1000000 + 0 × 100000 + 0 × 10000 + 6 × 1000 + 1 × 100 + 9 ×10 + 4
= 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 ×10 + 6
= 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 × 105 + 2 × 104 + 0 × 103 +7 × 102 + 1 × 101 + 9 × 100
(v) 20068 = 2 × 10000 + 0 × 1000 + 0 × 100 + 6 × 10 + 8
= 2 × 104 + 0 × 103 + 0 × 102 +6 × 101 + 8 × 100

Question - 2 : - Find the number from each of the following expandedforms:
(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

Answer - 2 : -

(a) 8 × 104 + 6 ×103 + 0 × 102 + 4 × 101 + 5 × 100
= 8 × 10000 + 6 × 1000 + 0 × 100 + 4 × 10 + 5 × 1
= 80000 + 6000 + 0 + 40 + 5 = 86045

(b) 4 × 105 + 5 × 103 + 3 × 102 +2 × 100
= 4 × 100000 + 5 × 1000 + 3 × 100 + 2 × 1
= 400000 + 5000 + 300 + 2 = 405302

(c) 3 × 104 + 7 ×102 + 5 × 100
= 3 × 10000 + 7 × 100 + 5 × 1
= 30000 + 700 + 5 = 30705

(d) 9 × 105 + 2 × 102 + 3 × 101
= 9 × 100000 + 2 × 100 + 3 × 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
(vi) 3908.78

Answer - 3 : -

(i) 5,00,00,000 = 5 × 1077
(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 × 104
(vi) 3908.7 8 = 3.90878 × 103

Question - 4 : -
Express the number appearing in the following statements in standard form:
(a) The distance between Earth and Moon is 384.0. 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 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 300,000,000,000,000,000,000 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.

Answer - 4 : -

(a) 384,000,000 m = 3.84 × 108 m
(b) 300,000,000 m/s = 3 × 108 m/s
(c) 1,27,56,000 m = 1.2756 × 1072 m
(d) 1,400,000,000 m = 1.4 × 109 m
(e) 100,000,000,000 stars = 1 × 1011 stars
(f) 12,000,000,000 years old = 1.2 × 1010 yearsold
(g) 300,000,000,000,000,000,000 m = 3 × 1020 m
(h) 60, 230, 000, 000, 000, 000, 000, 000 molecules = 6.023 × 1022 molecules
(i) 1,353,000,000 cubic km = 1.353 × 109 cubickm
(j) 1,0,27,000,000 = 1.027 × 109

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