A friend of mine are having a discussion right now about whether or not a GPA of 1.999 is equal to a GPA of 2.0. He knows, as I do, that .999999 repeating is 1.0 (because there’s no number between the two), but he disagrees with me on the idea that, given there is no GPA between 1.999 and 2.000, a GPA of 1.999 must be equal to a GPA of 2.000, and thus must be a GPA of 2.000.
What say the Teeming Millions?
You can argue that a GPA of 1.999 equals a GPA of 2.0, but not that it equals a GPA of 2.000. If you’re showing the decimals, they must be significant, and you can’t round them to a number with the same amount.
Just because there isn’t a number between two other numbers doesn’t mean they’re equal (it’s necessary, but not sufficient, I believe). Among the integers, there is no integer between 2 and 3, but 2 is not equal to 3, for example.
Arjuna34
But there are plenty of numbers between 2 and 3. We’re not talking about integers here but numbers.
The reason GPA is important is for admission into a school, job applications, and bragging rights. The logical approach is the correct number of decimal places that are appropriate for the answer. For GPA, one decimal place is all that is needed for the above needs and to use any more decimal places than that would seem silly.
In other words, you would be perfectly justified in rounding up 1.999 to 2.0. I agree with this.
Well, if we accept the idea that 1.999 is equal to 2.000 because there are no GPA numbers between them, then 2.001 must be equal to 2.000 by the same reasoning, and 2.002 must be equal to 2.001 for the same reasons, and …(repeat 1998 times)… 4.000 must be equal to 3.999 for the same reasons. So all possible GPAs are equal.
This makes no sense whatsoever, but it follows from the false premise. The part about repeating decimals is not relevant to this question- that’s true of continuous number systems but not for discontinuous systems (such as the integers, or thousandths, as your GPA example is.)
The difference is negligable, but not zero. 2.0 is conventional to ignore this negligable difference, but 2.000 as in the OP is factually incorrect.
Normally a GPA is given to three decimal places; thus there is no GPA between 1.999 and 2.000, as the OP mentioned. This case is equivalent to looking for an integer between two adjacent integers. Multiply the GPA by 1000 and we are talking about integers 
Arjuna34
However, the Student Organizations, Activities and Programs board requires all officers of SOAP-sponsored clubs/activities/etc to maintain a GPA of 2.0. So it’s not silly, thus why I ask:).
What I would tell your friend is to stop bitching. He has made it at least to the middle of his second year of school; he should have learned how to get better grades by now.
Tell him to stop dinking off.
Assuming that your school gives grades on a four point scale, discrete to only a tenth of a grade (in other words, your grade in a specific class can be 3.3 but not 3.33) then the earliest you get have a GPA of 1.999 is 67 credit hours.
That is more than enough time to get your act together.
How’s that for a parent-like lecture?