One nice thing about mi/km conversions (and ℉/℃ conversions which have been mentioned in the comments) is that once you have a way to do them mentally that works well for you, you are done.

I once worked out a way to quickly figure sales tax for my area using just a small number of operations that are easy to do in my head.

"Easy" means that it just involved things like taking 10%, or multiplying or dividing by 2, or adding or subtracting, or rounding to a given precision, and that it did not require keeping too many intermediate results in memory.

It worked great. And then the sales tax rate changed.

I have a vague recollection of then writing a program that would brute force check all short combinations of my "easy" operations to find ones that worked for a given tax rate. But I can't find that program now, and may have only thought about writing it.