Maybe this is just me being very naive, but how does it help? It doesn't actually change the properties of the underlying numbers.

10 (decimal) is not divisible by 3, and rewriting it in base 12 as A won't change that. You simply get 29.4 instead of 33.3...

If a kilo, for example, was made of 12 x 12 x 12 (1728) grams instead of 1000 grams, then you could sell stuff by the half-kilo, third-kilo, and 1/12 kilo without going into decimals. The number 1728 would still be written as 1000 in base 12, but 1/3 kilo would be 400 grams instead of 333.3333... as it is now. Useful if you're a grocer.

Other applications, like documenting how much oil to put in a car or whatever, there would be more options for picking memorable numbers. Like, my motorcycle takes 1.6L of oil. It could be 1 represented as 1 2/3 L, which is more visually intuitive. Not sure if I explained that well enough, maybe someone else has got a better metaphor handy...

Is it some American thing that measuring things as fractions is easier than decimals? To me being used with metric system 1.6L is equally intuitive as 1 2/3, maybe even more intuitive.

It's just hardwired in the brain how much 0.6, or 60%, represents, I think internally my brain finds the closest easy references like 10%, 25%, 33%, 50% or 75% and then interpolates or adds or removes chunks of 10%, the rest is rounding errors. I mean, i dont have to think consciously if 0.69 is more or less than 75% and i know exactly where both 66.66% and 75% is and can place it somewhere in between.

I agree that fractions are a very American thing. A lot of stuff is expressed as fractions here. But I bet a lot of people couldn't tell you whether 5/16 is more then 1/3 or not.

Another thing is that multiplying and dividing by 2 and 5 is easier in base-10. For example, to divide by 5 you multiply the number by 2 (just add it to itself) and then divide by 10 (a right shift).

On the other hand, to divide by 3 you basically need to do long division.