The precision is different, but the accuracy is exactly the same.

No, the accuracy is not the same. Due to magnetic drift over time, and
due to values of convenience (such as when there are too many parallel
runways).

is closer to the reason. Runways are not merely "rounded off", rather,
the last digit of their magnetic heading is ruthlessly ripped away after
the roundoff process has taken place.
That's simply a savings in representation. Just as the "minus" sign is
dropped from temperatures above a certain altitude in the winds aloft
forecast.

That kind of change is significant, especially when what is left looks
like a (different) number.

Jose
--
Money: what you need when you run out of brains.
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