If ${\log }_{10}3=0.4771$, then the number of zeros between decimal point and first significant figure in ${81}^{-20}$ is

Given ${\log }_{10}3=0.4771$

Now ${\log }_{10}{81}^{-20}=-20{\log }_{10}81$

$=-20{\log }_{10}{3}^4$

$=-20\times 4{\log }_{10}3$

$=-80\left(0.4771\right)$

$=-38.168$

$=-38-0.168$

$=-39+1-0.168$

$=-39+0.832$

$=\overline{39}.832$

$\therefore$ Number of 0 ‘s between decimal point and first significant figure in is 38