They wouldn’t, they would say their equivalent to 25%. They still have a concept of 1 divided by 4, it’s just that they express it differently because their system is base 9, not base 10.
Like I said, they agree that they each have 1 of 4 pieces. They write that differently, depending on the base.
When all is said and done, they agree with a base ten person that they have 1 of 4 apples.
Just because they say 1 of 4 apples is a different percentage in their base, doesn’t mean they are saying it’s different.
1.0 in base 9 means .999… in base 10
.3 in base 9 is .333… in base 10
3 x .3 in base 9 is 1.0, not .9.
In base 10, 10 parts equal 1.0
In base 9, 9 parts equal 1.0
If you have 3 parts of 3 of 9 parts you have 9 of 9 parts
But in base 10, .333… is equal to .3 in base 9. 3 of each of those only equates to 99.999…% of 1.0.
I am giving a base 10 percentage to a base 9 problem.
In base 10, 1 divided by 9 = .111… or 11.111…%
That is 1.0 cut into 9 pieces, and giving a base 10 percent to a base 9 problem.
So in base 9, “.3” has a base 10 percentage of 33.333…%
There is no “.9” in base 9, so .3 x 3 is not .9, it is 1.0
But stated in base 10 terms, the base 9 “.3 x 3” means the base 10 99.999…%, not 1.0 that it should, in BOTH bases.
This line of reasoning isn’t going to cut it for anybody else. You can’t just keep relying on the base 10 decimal representation of the value to prove something in base 9.
If you could, then you could do the reverse, and prove that because 1/4 is an infinite decimal in base 9, it must not add up to 1 in any base as well.
You agreed that all bases are equally valid earlier in the thread. If they are equally valid, and you do not have a biased reliance on base 10 for your points, then you have to apply the same logic to 1/4.
The word “percent” seems to be another way for you to bring base 10 back into into. The term “percent” itself is as ambiguous as the word “ten” when talking about other bases. Relying on base 10 representations like “percent” is literally the whole problem: you can only show the problem in base 10, and when you try to show the problem exists in other bases, you seem to only be able to do that by converting to base 10 first.
For a person raised in base 9, the symbol “100” refers to the quantity that you would call 81. So something like “3%” to such a person would mean, to you, the base 10 value of 3/81
You can’t throw in the % symbol into this conversation without disambiguating it first.