From Förberedande kurs i matematik 1

Because \displaystyle \text{lg }0.000\text{1} is defined as the exponent that should stand in the grey box (??) in the equality

\displaystyle 10^{??}=0.001

and we have that

\displaystyle 10^{-3}=0.001

thus \displaystyle \text{lg }0.000\text{1}=-\text{3}.