Re: decimal system
The only thing it makes easier is not having to track the size of arbitrary units, most of which were not defined by people interested in what you're pretending they're interested in. It's not that decimal is the best base; there's basically nothing about it that makes it better than any other base and, compared to 12 or 16, you could argue it's worse. However, since we have all decided to use it for most of our numbers, it makes sense to continue using it rather than make people work in other bases, because the same people who explain how great feet are for measuring things because what if you have a thing that's exactly one foot long and need to cut it into thirds (you don't need to, and if it's a meter, you can still do it) would complain vociferously if we accepted that and also informed them that all other numbers were going to get reported in base 12 too.
As for degrees on a compass, there's a factor that probably should be in whatever divisor you use for that: 4, so you can still have due north, east, south, and west. Other than that, you can divide it in any way you like. Whether that's 100 decgrees, and if you need something more precise you divide those in tenths, or 360 degrees, or 400 gradians, or 144 dozendegrees, it will work. For most purposes, the difference between 77 and 78 degrees east-northeast doesn't matter, and when it does, nothing says an integer number of 1/360 off your reference is going to include the right value.