I would also use the 0.99999... example and relate it to Zeno's paradox. The arrow does reach its target, therefore the sum of the infinite sequence must be equal to the distance to the target. It's much easier to understand things if you make them concrete, and we KNOW that the arrow reaches its target.

I would put these subjects under the banner of "numerical methods". I was taught this stuff in my CS course but I thought it had gone out of fashion. Probably very useful for mechanical and electrical engineers, not very useful for most fields of practical programming. But then CS isn't really about teaching specific tools and techniques, it's about teaching problem solving and algorithmic thinking, and it really doesn't matter much what problem domain you use to teach those skills.

For those of us in different countries, could you expand on what "senior high school" is?

How do you think the programmers who wrote the drawing programs were taught?