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I am unsure the grade marking for the university of greenwich but for most UK universities a 68 is a 2.1 and does not fall into the borderline zone.
You would have to get a grade such as 69.4 for it to be considered as a borderline grade (I think) because a 69.4 is just shy of a first and such a frustraing grade to get! If you for example you got a 69.5 that that would be rounded to a 70 (1:1).
Universities usually consider your average grades and performance on coursework and exams and sometimes your tutor might be asked what kind of a student you were etc if your grade fallsinto the borderline zone.
Hope this wasnt too confusing!
This will be different at each uni's as some uni's might round up if you have 69.5 but have 3 firsts overall. Does your uni have a degree calculator that you could use to tell you what classification you will get ? If not the best thing to do would be to contact your course leader who should be able to help you more.
68% is classified as upper second class honours, check this document out it has all the information on which class the grades falls in.
Sections D6 ("Degree Classification") and D7 ("Borderline Judgments") are relevant.
I can’t remember the criteria but it’s something like x number of credits in 2nd or 3rd year have to be the classification above for your overall classification to be rounded up to the next one.