Question

Find (i) $anti\log 1.8652$
(ii) $anti\log 0.3269$
(iii) $anti\log \overline{2}.6709$

Answer 1

(i) Characteristic is $1$. So, the number contains two digits in its integral part.
Mantissa is $0.8652$
From the table, $anti\log 0.865$ is $7.328$
Mean difference of $2$ is $0.003$
$anti\log 0.8652=7.328+0.003=7.331$
$\therefore anti\log 1.8652=73.31$
(ii) Characteristic is $0$. So, the number contains one digit in its integral part.
Mantissa is $0.3269$
From the table, $anti\log 0.326$ is $2.118$
Mean difference of $9$ is $0.004$
$\therefore anti\log 0.3269=2.118+0.004=2.122$
(iii) Characteristic is $-2$. So, the number contains one zero immediately following the decimal point. Mantissa is $0.6709$
From the table, $anti\log 0.670$ is $4.677$
Mean difference of $9$ is $0.010$
$anti\log 0.6709=4.677+0.010=4.687$
$\therefore anti\log \overline{2}.6709=0.04687$