> Do you really expect I mentioned this example, mentioned I wrote some code that solves this issue, and still never looked up or came across an explanation of why most programming languages behave this way?
Well, what you described does not actually solve the issue despite you claiming that it has, so I thought you might be confused. Which is not an insult -- many people are confused about this issue.
And you appear to have misunderstood my comment, which is not about explaining to you why binary arithmetic is imprecise, which you obviously already know. It is about explaining that decimal arithmetic is also imprecise, for the exact same reason, which is something that much fewer people understand.
Your "fix" makes it so that 1/10 + 2/10 == 3/10, but it still doesn't make it so that 1/3 + 1/3 == 2/3. So how is it actually "precise"?
To answer your question about speed: yes, doing things with arbitrarily-sized integers is much slower than doing them with floats (or normal integers for that matter). In the best case, you add at least one branch to every arithmetic operation. And a binary-coded decimal scheme like you described would be even slower still.
It doesn't really matter whether it would make the average website slower, since the average website should not be using floats (OR binary-coded decimals like your scheme) in the first place except for calculating layouts or other numeric calculations where asking whether 0.1 + 0.2 == 0.3 would never come up. For discrete computations they should be using integers -- that's what integers are for.