If a 17%-efficient system becomes "10 times more efficient", what is the absolute efficiency? Or is this not possible? Sometimes in reading around the net, I see things like "This car could be ten times more efficient if the drivetrain and engine were replaced by batteries and electric-motor wheels."
If I'm not mistaken, the usual tank-to-wheel efficiency of the average car is 17%. Ten times this would be 170%, which is just not possible. So what does "ten times more efficient" really mean? I suspect it's exponential or logarithmic in some way, but I can't even guess the formula.
Or maybe most tech blogs are dumb and don't know what they're really saying mathematically? Maybe it's just not possible?
In general, if something is x % efficient, and you want it to be p times more efficient, what would be the result, y %?
 A: It would be, as you say, numerical nonsense, and the "ten" was probably invented.  
But suppose we are in the land of Humpty Dumpty words which mean whatever the speaker wants them to mean and going from $99.9\%$ efficiency to $99.99\%$ was seen as broadly as good an improvement as going from $0.01\%$ to $0.1\%$ efficiency. Then we can try to find some moderately useful interpretation, even if nobody else takes the same approach. 
Then if conventional measure of efficiency (energy output divided by energy input) before was $\eta_b$ and the efficiency after was $\eta_a$, you might imagine somebody instead dividing energy output by energy lost and so saying the improvement in efficiency was $\displaystyle \dfrac{\eta_a / \left(1- \eta_a \right)}{\eta_b / \left(1- \eta_b \right)}$.
If this is $p$ then you will have $\eta_a = \dfrac{p\, \eta_b / \left(1- \eta_b \right)}{1+p\, \eta_b / \left(1- \eta_b \right)}$. 
For example if $p=10$  and $\eta_b =0.17$ then this might suggest $\eta_a\approx 0.672$.  A welcome feature of this approach is that if $p=0.1$  and $\eta_b =0.672$ then this might suggest $\eta_a\approx 0.17$.           
