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:
