it really bothers me how loosely most people--students, educators, and researchers alike--treat units

@Felthry Units?

@BatElite when doing math. A lot of people seem to just strip the units off, do the math, and then stick on the units again at the end

@Felthry Ah in that sense.

I've never learned anything other than to strip off the units. IDK how you'd do it otherwise.

@BatElite Units are quantities that you can do math to too. A newton times a meter *is* a joule. SI prefixes multiply like exponents; μ times k is m, for instance. You do math to the units too, not just to the numbers, and it helps _so much_ with keeping things straight and not making simple mistakes because if you do all your math and then the units work out to give you kilograms when you expected a speed, you know you did something wrong

@BatElite I guess most people don't think of things like this but it's so incredibly confusing to us... I can't understand how it makes sense for people to strip the units off before doing math

@Felthry AFAIK what you talk about makes sense, but I've learned to treat the two groups as separate equations.
Like, the numbers separately gives the value you're looking for.
You can then do the conversions and math stuff on the units to get an eventual value, potentially with a value to scale what you got earlier. (which in metric is often a power of ten) But that scaling is usually sort of half-implicit??

(I might be simplifying, not using any advanced maths in my current life. ^^;)

@Felthry I know sort of what you mean though, for example we learned to convert metres per second to kilometres per hour by deviding/multiplying by 3,6. since

1km = 1000m
1h = 3600s

So while m/s is a fraction of (1/1 = 1), km/h converted to m/s is (1000/3600 = 1/3,6). I can't explain well, bleh. :<

Which is very simple for both of us I'm sure (I wonder if I could manage the kind of maths you do. :P)

@BatElite The kinds of math we do are frequently more calculus than arithmetic, so it depends on whether you think calculus is doable or not I suppose!