There's a unit discontinuity between metric weight* and volume.
The metric system uses a set of simple units: metre, gram, second, etc. Those are then modified as needed by prefixes that indicate a multiplier. So we get a thousand meters is a kilometre, and a thousandth of a metre is a millimetre.
The most esoteric units are then constructed from the simple ones. For example the unit of force, the newton, is that amount necessary to accelerate a mass of one kilogram by one metre per second every second.
It turns out that in order to have a usable system of units, it matters which units you choose as your base units. Actually using metres, grams, and seconds turns out to not work well at all. One attempt, around the beginning of the last century (I think,) at creating a usable system was the "centimetre-gram-second" system, in which the unit of energy is the "erg", which is annoyingly small: 1 mWh = 36,000,000 ergs. The metric system as we know it is the "metre-kilogram-second" system. It works very well in most cases, but the use of a kilogram -- 1,000 grams -- as a base unit can mess with your head.
The density of water, and most other similar liquids, including VG, PG and Nicotine, is almost exactly 1 kilogram per litre. That is a very nice result and very easy to remember.
If a litre of water weighs a kilogram, then a thousandth of a litre must weigh a thousandth of a kilogram. If the kilogram was a simple unit, we could say that 1 milli-litre weighed 1 milli-kilogram. Unfortunately it doesn't work like that. We have to use grams as the simple unit. So 1 milli-litre weighs 1 gram.
10mg/ml is 0.010 grams per ml, and since a ml is about a gram, it is about 0.01ml/ml, or 0.01 x 100 = 1%.
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* Mass. I know. If you know that then you know the rest and I'm not talking to you. OTOH, if this footnote makes no sense, ignore it. ;-)