Answer :

(i) Characteristic is 3


Mantissa is 0.072


From the antilog table antilog 0.072 = 1.180


Now as the characteristic is 3, therefore we will place the decimal after 3+1=4 numbers in 1180


antilog 3.072 = 1180


(ii) Characteristic is 1


Mantissa is 0.759


From the antilog table antilog 0.759 = 5.741


Now as the characteristic is 1, therefore we will place the decimal after 1+1=2 numbers in 5741


antilog 1.759 = 57.41


(iii) Characteristic is ̅1 = –1


Mantissa is 0.3826


From the antilog table antilog 0.382 = 2.410


Mean Value of 6 is 0.003


Thus, antilog 0.3826 = 2.410+0.003 = 2.413


Now as the characteristic is –1, therefore we will move decimal


–1+1=0 places left in 2.413


antilog ̅1.3826 = 0.2413


(iv) Characteristic is ̅3 = –3


Mantissa is 0.6037


From the antilog table antilog 0.603 = 4.009


Mean Value of 7 is 0.006


Thus, antilog 0.6037 = 4.009+0.006 = 4.015


Now as the characteristic is –3,


therefore we will move decimal


–3+1=2 places left in 4.015


antilog ̅3.6037 = 0.004015


(v) Characteristic is 0


Mantissa is 0.2732


From the antilog table antilog 0.273 = 1.875


Mean value 2 is 0.001


Thus, antilog 0.2732 = 1.875+0.001 = 1.876


Now as the characteristic is 0, therefore we will place the decimal after 0+1=1 numbers in 1876


antilog 0.2732 = 1.876


(vi) Characteristic is ̅2 = –2


Mantissa is 0.1798


From the antilog table antilog 0.179 = 1.510


Mean Value of 8 is 0.003


Thus, antilog 0.1798 = 1.510+0.003 = 1.513


Now as the characteristic is –2, therefore we will move decimal


–2+1=1 places left in 1.513


antilog ̅2.1798 = 0.01513


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