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Q1. Write the base and exponent of the following numbers. Also write the expanded form and the value. (i) 3⁴ (ii) (-4)³ (iii) 1⁸

Solution

Number Base Exponent Expanded form Value 3⁴ 3 4 3 x 3 x 3 x 3 81 (-4)³ -4 3 -4 x -4 x -4 -64 1⁸ 1 8 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 1

Q2. 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.

Q3. Express the following numbers in exponent form. (i) 343000 (ii) 2048

Solution

(i) 343000 = 343 x 1000 = 7 x 7 x 7 x 10 x 10 x 10 = 7³ x 10³. (ii) 2048 = 2 x 1024 = 2 x 2 x 512 = 2 x 2 x 2 x 256 = 2 x 2 x 2 x 2x 128 = 2 x 2 x 2 x 2 x 2 x 64 = 2 x 2 x 2 x 2 x 2 x 2 x 32 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 16 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 8 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2¹¹

Q4. Express the number 451900000 in the form K x 10ⁿ (where K is a number and n is a integer) in 4 different ways.

Solution

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

Q5. Which one is greater 3⁴ or 4³?

Solution

Here, 3⁴ = 3 x 3 x 3 x 3 = 81 And, 4³ = 4 x 4 x 4 = 64 Since, 81 > 64 Therefore, 3⁴ > 4³.

Q6. Write the following statements as repeated multiplication and then express in exponent form: (i) 3 multiplied by 3 for 7 times (ii) 2 multiplied by 2 for 5 times (iii) 7 multiplied by 7 for 10 times

Solution

(i) 3 multiplied by 3 for 7 times = 3 x 3 x 3 x 3 x 3 x 3 x 3 = 3⁷ (ii) 2 multiplied by 2 for 5 times = 2 x 2 x 2 x 2 x 2 = 2⁵ (iii) 7 multiplied by 7 for 10 times = 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 7¹⁰

Q7. 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

Q8. The distance between Sun and Saturn is 1,433,500,000,000 m. Express this distance in standard form.

Solution

The distance = 1,433,500,000,000 m = 14335 x 100000000 m = 14335 x 10⁸ m = 1.4335 x 10¹² m

Q9. Write the following numbers in the usual form: a) 5.61 x 10⁵ b) 2.5 x 10³

Solution

In usual form a) 5.61 x 10⁵ = 5.61 x 100000 = 561000 b) 2.5 x 10³ = 2.5 x 1000 = 2500

Q10. Simplify: (i) (-5)³   (ii) (-2)³ x (-3)².

Solution

(i) (-5)³ = -5 x -5 x -5 = -125(ii) (-2)³ x (-3)² = -2 x -2 x -2 x -3 x -3 = -8 x 9 = -72