The mantissa of ${\log }_{10}\frac{1}{16}=-1.2040$  is 

Given ${\log }_{10}\frac{1}{16}=-1.2040=(-1)+(-0.2040)$

Add and subtract 1, then we get

$=(-1-1)+(1-0.2040)$

$=-2+0.7960$

$=\overline{2}.7960$

${\log }_{10}\left(\frac{1}{16}\right)=\overline{2}.7960$

$\therefore$ Required mantissa is 0.7960