When I was in high school, we got graded on the 13-scale, which had ten steps spaced out a little towards the low and high ends in order to give the extreme grades a stronger effect on your average. The reason we have to use a numerical scale in Denmark is that the university prerequisites all depend on your grade average, and it’s hard to calculate averages from a letter scale. About half-way through my BA degree, the universities transitioned to the new 12-scale, which has 7 steps distributed in such a way that the students’ old averages on the 13-scale are fairly close to their averages when converted to the new scale. The 12-step grading scale goes like this:

12 – Excellent
10 – Very good
7 – Good
4 – Fair
02 – Adequate
00 – Inadequate (failed)
-3 – Unacceptable (failed)

The zeroes in front of 0 and 2 are there to prevent you from adding a 1 in front of your grade, as if that really matters in an age where all this stuff is handled digitally.

Now, this new scale was originally implemented to make it easier to compare to the European standard ECTS grading scale, which goes A, B, C, D, E, Fx, F. Unhappily, despite looking almost exactly like the American grading scale, the ECTS scale doesn’t actually map properly to the U.S. one. Here’s how Wikipedia compares the two scales:

ECTS – U.S.
A – A (4.0)
B – A−/B+
C – B (3.0)
D – C+
E – C (2.0)
FX – F
F – F

In other words, if you get a C (a 7) at a Danish university, it will actually be equivalent to a B at an American university. I’m sorry to say you will see why it’s important for me to explain this once I post my Game Theory paper (and the grade I got for it) some time over the weekend