Question

If the characteristic of logarithm to the base $10$ of $0.000234$ is $p$, then value of $8+p$ is

Answer 1

$0.000234$
Number of zeros before the first significant digit is $3$
$\therefore$ Characteristic of ${\log }_{10}0.000234$ is $-(3+1)=-4$
$p=-4\Rightarrow 8+p=4$

Alternate :
${\log }_{10}0.000234$
$={\log }_{10}(2.34\times {10}^{-4})$
$={\log }_{10}2.34-4{\log }_{10}10$
$=m-4$, where $0<m<1$
$\therefore$ Characteristic of ${\log }_{10}0.000234$ is $-4$
$p=-4\Rightarrow 8+p=4$