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NCERT solution class 7 chapter 13 Exponents and powers 13.3 mathematics

EXERCISE 13.3


Page No 263:

Question 1:

Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Answer:

279404 = 2 × 105 + 7 × 104 + 9 × 103 + 4 × 102 + 0 × 101 + 4 × 100

3006194 = 3 × 106 + 0 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 4 × 100

2806196 = 2 × 106 + 8 × 105 + 0 × 104 + 6 × 103 + 1 × 102 + 9 × 101 + 6 × 100

120719 = 1 × 105 + 2 × 104 + 0 × 103 + 7 × 102 + 1 × 101 + 9 × 100

20068 = 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 × 10+ 5 × 10+ 3 × 10+ 2 × 100

(c) 3 × 104 + 7 × 102 + 5 × 100

(d) 9 × 105 + 2 × 102 + 3 × 101

Answer:

(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100

= 86045

(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100

= 405302

(c) 3 × 104 + 7 × 102 + 5 × 100

= 30705

(d) 9 × 105 + 2 × 102 + 3 × 101

= 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:

(i) 50000000 = 5 × 107

(ii) 7000000 = 7 × 106

(iii) 3186500000 = 3.1865 × 109

(iv) 390878 = 3.90878 × 105

(v) 39087.8 = 3.90878 × 104

(vi) 3908.78 = 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, 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, 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:

(a) 3.84 × 108 m

(b) 3 × 108 m/s

(c) 1.2756 × 107 m

(d) 1.4 × 109 m

(e) 1 × 1011 stars

(f) 1.2 × 1010 years

(g) 3 × 1020 m

(h) 6.023 × 1022

(i) 1.353 × 109 cubic km

(j) 1.027 × 109

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