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Chapter 2: Powers Exercise – 2.3

Question: 1

Express the following numbers in standard form:

(i) 6020000000000000

(ii) 0.0000000000943

(iii) 0.00000000085

(iv) 846 × 107

(v) 3759 × 10-4

(vi) 0.00072984

(vii) 0.000437× 104

(viii) 4 ÷ 100000 

Solution:

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

(i) 6020000000000000 = 6.02 × 1015 (The decimal point is moved 15 places to the left.)

(ii) 0.0000000000943 = 9.43 × 10-12 (The decimal point is moved 12 places to the right.)

(iii) 0.00000000085 = 8.5 × 10-10  (The decimal point is moved 10 places to the right.)

(iv) 846 × 107 = 8.46 × 102 × 107 = 8.46 × 109 (The decimal point is moved two places to the left.)

(v) 3759 × 10-4 = 3.759 × 103 × 10-4 = 3.759 × 10-1 (The decimal point is moved three places to the left.)

(vi) 0.00072984 = 7.984 × 10-4 (The decimal point is moved four places to the right.)

(vii) 0.000437 × 104 = 4.37 × 10-4 × 104 = 4.37 × 100 = 4.37  (The decimal point is moved four places to the right.)

(viii) 4 ÷ 100000 = 4 × 100000-1 = 4 × 10-5 (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 × 107

(ii) 3.02 × 10-6

(iii) 4.5 × 104

(iv) 3 × 10-8

(v) 1.0001 × 109

(vi) 5.8 × 102

(vii) 3.61492 × 106

(viii) 3.25 × 10-7

Solution:


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