Up until 1300, the old foot was longer and the mile was 5000 feet. In 1300 they redefined 10 old feet to be 11 new smaller feet, an acre was now 66x660 feet instead of 60x600, and eventually the mile was 8x660 = 5280.
In practice these are just big numbers you memorize. 5280 feet in a mile, 63360 inches in a mile, 1760 yards in a mile...
It's not like you often have to do math with them, outside of school math problems. A year isn't precisely 365 days, and months are all different lengths. It's just more of the same type of thing; doesn't actually cause problems when distances are usually expressed in miles anyway.
From polling my American friends, ask them how many yards in a mile and they'll answer 5280. They don't really know how the system work and can only vaguely remember (one of) these numbers.
The system is not meant for units to be converted.
Sure you can use 3/5 - an easy Fibonacci fraction. Or about 5/8. Or 8/13. These fractions have the advantage of being easy to produce and having different prime factors that cancel more easily with some numbers.
> just think of a kilometer as slightly more than 3/5ths of a mile.
I can confidently assure you that right about now there are a bunch of Europeans reading your message multiple times, trying to figure out what 3/5ths of a mile even means, asking themselves if this is satire.
Wow, I didn't think of poor imperial kids, that are definitely forced to remember all these numbers. But now I'm really sorry for them.
2^5 and 5 is nice, 3 can be tolerated, but 11? Who in their right mind would come up with something like this? Why not just round it to 5000?