It's well known that (1+1/x)^x approaches the number e, an irrational number close to 2 . 718 281 8, as you increase X to infinity. Is it really? Drag the slider to the left to demonstrate that yes, this is true. Now drag the slider slowly to the right. This just zooms out the graph, no tricks here. Should get even closer and closer to E, wouldn't it -- Wait, what? Well, despite what this graph shows, it is true that the formula approaches Euler's number. And, this graph is mostly correct for... reasonable values of X. But as you increase X to astronomical values, the graph freaks out, returning numbers like 3, 5, and eventually just getting stuck at e=1. This is because the calculator loses precision entirely, because 1/X is so small it's almost 0 (and eventually, the calculator thinks it *is* 0) Even though this means Scratch's math isn't accurate, you should be happy about it - because it means that Scratch is taking some shortcuts with the numbers. This way, it doesn't take 5 minutes to compute 1+1, but it does mean that weird edge cases like this one tend to break it a little bit.
In fact Scratch's calculator coincidentally behaves pretty much identically to the one in my TI-83 grapher at school. So I made this Scratch project, and I didn't even have to cheat and round off numbers on purpose to emulate the grapher. Sweet! :P Teacher demonstrated how to calculate Euler's number based on the compound interest formula, where compounding interest faster and faster causes the principal to grow by a value proportional to e. The worksheet in class went from compounding every month, to every week, even to every second - but it stopped there. And that's because compounding faster than that causes the calculator to produce ridiculous rounding errors such as this one. Teacher got confused and couldn't believe her own graphing calculator. Oops. If you're in her period 8 class - sorry for confusing you and completely derailing the second half of the class! Well, ok, I'm only kinda sorry. Also shoutouts to me having to write e as "2 . 718 281 8" with all those spaces up there because of the phone number filter being LITERALLY A PIECE OF TRASH >:(
