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Q1. Mass of earth is approximately 5,970,000,000,000,000,000,000,000 kg. Express this mass in standard form.

Solution

Mass of earth = 5,970,000,000,000,000,000,000,000 kg = 597 x 10000000000000000000000 kg = 597 x 10²² kg = 5.97 x 10²⁴ kg

Q2. Express the following in usual form: (i) 1.002 x 10⁶ (ii) 5.54 x 10⁷

Solution

(i) 1.002 x 10⁶ = 1.002 x 1000000 = 1002000 (ii) 5.54 x 10⁷ = 5.54 x 10000000 = 55400000

Q3. Write the following in standard form. (i) 458000 (ii) 1780000 (iii) 85000

Solution

(i) 458000 = 4.58 x 100000 = 4.58 x 10⁵. (ii) 1780000 = 1.78 x 1000000 = 1.78 x 10⁶. (iii) 85000 = 8.5 x 10000 = 8.5 x 10⁴.

Q4. Compare the following pair of numbers. (i) 2.5 x 10³ and 3.5 x 10² (ii) 2⁵ and 5²

Solution

(i) 2.5 x 10³ and 3.5 x 10² Or, 2.5 x 1000 and 3.5 x 100 Or, 2500 and 350 Clearly, 2500 > 350 Therefore, 2.5 x 10³ > 3.5 x 10² (ii) 2⁵ and 5² Or, 2 x 2 x 2 x 2 x 2 and 5 x 5 Or, 32 and 25 Clearly, 32 > 25 Therefore, 2⁵ > 5²

Q5. Express the number 451900000 in the form K x 10ⁿ where K is a number and n is an integer in 4 different ways.

Solution

Here the number is: 451900000 This can be written as 4519 x 100000 Thus, the 4 different ways are: 4519 x 10⁵, 451.9 x 10⁶, 45.19 x 10⁷, 4.519 x 10⁸

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