Normalization for Chi square test

In the version of this test that I am familiar with, individual data is categorical, not quantitative like your examples. And the expected and observed values should be frequencies of some category (a count of how many times it occurs), not some individual's quantitative measurement. The numbers that go in to the $E_i$ and $O_i$ positions are unitless, as they are just counts.

So for example, in a box with mixed fruit, maybe 12 pieces were bananas, but you were expecting 15 to be bananas. You will have the term $$\frac{(12-15)^2}{15}$$ and there is no way to rescale units as you did. Writing $$\frac{(12000-15000)^2}{15000}$$ would correspond to a very different scenario. There you would have seen 12000 bananas when you were expecting 15000. And the corresponding $P$ value should be a lot smaller, because it should be a lot less likely to be off by 3000 out of 15000 than 3 out of 15, when you consider the variance from one piece of fruit to the next on its chances to be a banana. So $\chi^2$ should be a lot larger in the latter case.