Sounds like a good plan.Keeping things exact until it's absolutely necessary to approximate them is good practice if you care about the correctness of your result.
Seems to me it's ultimately a losing proposition whatever you do. Any real world calculation will involve messy things like PI, root 2, e, and the like. Never mind simple messy things like 1/3. Once you get into that your calculations are by definition not "exact". So the question is how hard do you want to, or need to, work to get workably close to the right results. It's then a trade off between accuracy vs computational work (speed) and memory usage.
Exactly. Which involves a division one way or another to get the single thing you need rather than the two numbers you are given.I'd put it as close to exactly one third of the way from zero to one as I could.
Thanks for the scheme collatz. Now we can have a good giggle at how unreadable and slow scheme is
More seriously I think scheme is a wonderful thing. At least conceptually.
Story goes that when Brendan Eich was hired by Netscape to make a scripting language for the browser he wanted to make something inspired by Self. Which is in turn inspired by Self. The management said no way, make something that looks like a normal language (C, Java, Pascal...) that people can understand.
So we got JS. Looks a bit like Java but with some of the sophisticated features of Self/Lisp.