Interesting negative decimal number notation I was studying logarithms, and had to solve the problem:

If $\log 8 = 0.90$, find $\log 0.125$. 

I found out the answer to be $-0.90$. That was easy. But my text book has given the answer as:
$$-0.90 = \bar{1}.10$$
Now what that bar above $1$ is for ? My understanding is that it is used to signify a repeating digit. But how can $-0.90 = \bar{1}.10$ ? 
Can someone please explain this to me.
Thank you!
 A: This was a very common notation when decimal logarithms were involved. The starting point is that if
$$
M/N=10^k
$$
for two positive numbers $M$ and $N$, then their decimal logarithms have the same mantissa (fractional part) and we can write
$$
\log_{10} M= k + \log_{10} N
$$
In particular, any number $M>0$ can be uniquely written as
$$
M=10^k N
$$
with integer $k$ and $1\le N<10$. So the logarithmic tables were compiled, say, for numbers from $1$ to $1000$, but only showed the mantissa; when the logarithm of, say, $10.4$ was needed, one looked at $104$ finding the mantissa to be $01703$ and so could conclude $\log_{10}10.4=1.01703$. If one knows the decimal logarithm of $2$
$$
\log_{10}2=0.30103
$$
(equality is meant as “approximate”), then $\log_{10}0.02=-2+0.30103$, which was written as
$$
\log_{10}0.02=\overline{2}.30103
$$
to ease lookup in logarithmic tables, because, as already said, only mantissas were shown.
In your case, $0.125=1/8$, so 
$$
\log_{10}0.125=-\log_{10}8 = -3\log_{10}2=-0.90309=-1+0.09691=\overline{1}.09691
$$
(use the “complement to $9$” rule for writing the mantissa).
