I was fascinated by slide-rules and learned how to use one, and then used it exclusively for a Physics I, and Chemistry course in college. (I'm a 90s kid) It turns out, that the types of problems you have to solve there lend themselves very well to the slide rule.
To use one, you have to understand that log(A*B) = log(A) + log(B), and also understand that the calculations across powers of ten result in the same digits. i.e. 25 * 4 = 100, but also 0.25 * 0.4 = 0.100 Same digits, but the decimal place moves. Tracking the decimal place (in your head) as you continue calculations is the toughest part, but it isn't really that difficult.
Since the "rule" of the slide rule is laid out logarithimically, (i.e. the lines get closer together the closer you get to the right), when you add together the distance from the edge of the outer to the edge of the inner, you are actually adding together log(A) and Log(B). So multiplication is done just by "adding" the two distances together, i.e. looking to see what number across from B on the A scale.
Physics & Chemistry are a bunch of calculations that are a string of multiplication and division. And because A*B/(C*D) = A/B * C/D freely, you can just accumulate the end result by adding and subtracting on the slide rule, while keeping a running total of what decimal places you are adding on/off.
The slide rule is one of the reasons that "scientific notation" is a thing. As you write a number in scientific notation, you are effectively preparing it *directly* for being applied to the slide rule. You see immediately the whole+partial number that is the distance you are going to slide on the rule, and you see directly the powers of ten that you are tracking during the calculation.
Further, because of the limitations of precision (you can only slide the rule so precisely. Maybe you can enter 1.27, but not 1.275); the slide rule naturally maintains significant digits for you. You don't have to wonder if you have bonkers unrealistic precision in your result. (A simple example: 1 / 3 = 0.3333333333333 on a calculator, but there is no way you could guarantee OR measure that accurately). The slide rule will never give you a result like that beyond your significant digits.
It is actually a beautiful instrument, but I admit it has its niche in real-world applications like physics and chemistry, and not more abstract subjects like maths.