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Exponents And Powers

Question
CBSEENMA7001018
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Identify the greater number, wherever possible, in each of the following?

(i) 43 or 34 (ii) 53 or 35

(iii) 28 or 82 (iv) 1002 or 2100

(v) 210 or 102

Solution

(i) 43 = 4 × 4 × 4 = 64

34 = 3 × 3 × 3 × 3 = 81

Therefore, 34 > 43

(ii) 53 = 5 × 5 × 5 =125

35 = 3 × 3 × 3 × 3 × 3 = 243

Therefore, 35 > 53

(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

82 = 8 × 8 = 64

Therefore, 28 > 82

(iv)1002 or 2100

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

2100 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 × 1024

1002 = 100 × 100 = 10000

Therefore, 2100 > 1002

(v) 210 and 102

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

102 = 10 × 10 = 100

Therefore, 210 > 102

Some More Questions From Exponents and Powers Chapter

Say true or false and justify your answer:

(i) 10 × 1011 = 10011 (ii) 23 > 52

(iii) 23 × 32 = 65 (iv) 30 = (1000)0

Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192 (ii) 270

(iii) 729 × 64 (iv) 768

Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

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

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

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.

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