Chapter 6: Exponents Exercise – 6.3

Question: 1

Express the following numbers in the standard form

(i) 3908.78

(ii) 5, 00, 00, 000

(iii) 3, 18, 65, 00, 000

(iv) 846 × 10⁷

(v) 723 × 10⁹

Solution:

(i) 3908.78 = 3.90878 × 10³

Since, the decimal point is moved three places to the left

(ii) 5, 00, 00, 000 = 5, 00, 00, 000.00

= 5 × 10⁷

Since, the decimal point is moved seven places to the left

(iii) 3, 18, 65, 00, 000 = 3, 18, 65, 00, 000.00

= 3.1865 × 10⁹

Since, the decimal point is moved nine places to the left

(iv) 846 × 10⁷ = 8.46 × 10² × 10⁷

= 8.46 × 10⁹

Since, the decimal point is moved two places to the left

(v) 723 × 10⁹ = 7.23 × 10² × 10⁹

= 7.23 × 10¹¹

Since, the decimal point is moved two places to the left

 

Question: 2

Write the following numbers in the usual form

(i) 4.83 × 10⁷

(ii) 3.21 × 10⁵

(iii) 3.5 × 10³

Solution:

(i) 4.83 × 10⁷ = 483 × 10^(7-2)

= 483 × 10⁵

= 4, 83, 00, 000

Since, the decimal point is moved two places to the right

(ii) 3.21 × 10⁵ = 321 × 10^(5-2)

= 321 × 103

= 3, 21, 000

Since, the decimal point is moved two places to the right

(ii) 3.5 × 10³ = 35 × 10^(3-1)

= 35 × 10²

= 3,500

Since, the decimal point is moved one place to the right

 

Question: 4

Express the numbers appearing in the following statements in the standard form

(i) The distance between the earth and the moon is 384,000,000 metres.

(ii) Diameter of the earth is 1, 27, 56,000 metres.

(iii) Diameter of the sun is 1, 400, 000, 000 metres.

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

Solution:

(i) The distance between the earth and the moon is 3.84 × 10⁸ metres.

Since, the decimal point is moved eight places to the left

(ii) Diameter of the earth is 1.2756 × 10⁷ metres.

Since, the decimal point is moved seven places to the left

(ii) Diameter of the sun is 1.4 × 10⁹ metres.

Since, the decimal point is moved nine places to the left

(iv) The universe is estimated to be about 1.2 × 10¹⁰ years old.

Since, the decimal point is moved ten places to the left