I don't see the issue at all, consider whatever as a fraction, or just add a denominator of 1:

"9 times larger" => multiply the numerator of the fraction with 9

"9 times smaller" => multiply the denominator of the fraction with 9

Consider a bag of identical resistors with resistance R

Add 9 of them in series: the resistance is 9 times larger.

Add 9 of them in parallel: the resistance is 9 times smaller.

Its the series vs parallel dictionary wars all over again...

Check my other comment.

It's an idiom, much like "you are pulling my hair". Are you actually pulling my hair? Of course not; taken literally, many English phrases make no sense. But they are common elements of the language and everyone understands them, so they aren't problematic.

This is the same. Taken literally, "9x smaller" is nonsense, but everyone who hears that phrase knows exactly what mathematical operation you are referring to, thus it's a totally acceptable way to express that you mean to say 11.11% as large.

11% is also a really saying a fraction, 11 per-cent or 11/100, but there's nothing wrong with that feeling more natural to some and it is at least a nice shorthand way for the written form. "A ninth the size" is a similar alternative. All are really fine, there's always someone who has trouble with a given representation compared to another.

When I hear 9x smaller, I visualize 9 small items taken as much space as the big one, I find it quite clear.