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**Question 1:**

**Express the following numbers in standard form:**

(i) 6020000000000000

(ii) 0.00000000000943

(iii) 0.00000000085

(iv) 846 Ã— 10^{7}

(v) 3759 Ã— 10^{âˆ’4}

(vi) 0.00072984

(vii) 0.000437 Ã— 10^{4}

(viii) 4 Ã· 100000

**Answer 1:**

To express a number in the standard form, move the decimal point such that there is only one digit to the left of the decimal point.

(i) 6020000000000000 = 6.02 x 10^{15} (The decimal point is moved 15 places to the left.)

(ii) 0.0000000000943 = 9.43 x 10âˆ’12 (The decimal point is moved 12 places to the right.)

(iii) 0.00000000085 = 8.5 x 10^{âˆ’10} (The decimal point is moved 10 places to the right.)

(iv) 846 x 10^{7} = 8.46 x 10^{2} x 10^{7} = 8.46 x 10^{9} (The decimal point is moved two places to the left.)

(v) 3759 x 10^{âˆ’4} = 3.759 x 10^{3} x 10^{âˆ’4} = 3.759 x 10^{âˆ’1} (The decimal point is moved three places to the left.)

(vi) 0.00072984 = 7.984 x 10^{âˆ’4} (The decimal point is moved four places to the right.)

(vii) 0.000437 x 10^{4} = 4.37 x 10^{âˆ’4} x 10^{4} = 4.37 x 100 = 4.37 (The decimal point is moved four places to the right.)

(viii) 4/100000 = 4 x 100000^{âˆ’1} = 4 x 10^{âˆ’5} (Just count the number of zeros in 1,00,000 to determine the exponent of 10.)

**Question 2:**

**Write the following numbers in the usual form:**

(i) 4.83 Ã— 10^{7}

(ii) 3.02 Ã— 10^{âˆ’6}

(iii) 4.5 Ã— 10^{4}

(iv) 3 Ã— 10^{âˆ’8}

(v) 1.0001 Ã— 10^{9}

(vi) 5.8 Ã— 10^{2}

(vii) 3.61492 Ã— 10^{6}

(viii) 3.25 Ã— 10^{âˆ’7}

**Answer 2:**

(i) 4.83 x 10^{7} = 4.83 x 1,00,00,000 = 4,83,00,000

(ii) 3.02 x 10^{âˆ’6} = 3.02/10^{6} = 3.02/10,00,000 = 0.00000302

(iii) 4.5 x 10^{4} = 4.5 x 10,000 = 45,000

(iv) 3 x 10^{âˆ’8} = 3/10^{8} = 3/10,00,00,000 = 0.00000003

(v) 1.0001 x 10^{9} = 1.0001 x 1,00,00,00,000 = 1,00,01,00,000

(vi) 5.8 x 10^{2} = 5.8 x 100 = 580

(vii) 3.61492 x 10^{6} = 3.61492 x 10,00,000 = 3614920

(viii) 3.25 x 10^{âˆ’7} = 3.25/10^{7} = 3.25/1,00,00,000 = 0.000000325

**Question 3:**

**Answer 3:**

(d) 4/9

To square a number is to raise it to the power of 2. Hence, the square of (âˆ’2/3) is

**Question 4:**

**Answer 4:**

(c) -1/8

The cube of a number is the number raised to the power of 3. Hence the cube of âˆ’1/2 is

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