You are welcome, AnthonyZ.
What makes a direct conversion between percents and the 4.0 scale impossible is that
one person might have obtained an average of 95.0 by scoring 95 in every class. That is normally at the “A” level, so that performance would be a 4.0. Another person might have obtained an average of 95.5, obtained by scoring 99 in half of the classes and 92 in the other half. At my old high school, that would give the second person a 3.5 unweighted average on the 4.0 scale, even though the average GPA in terms of percents is actually higher than the first person’s. Which one is the better student would be open to interpretation. This just illustrates the extremes that could be involved.
My old high school resolved this problem by converting all GPA’s of 94.0 and up to a 4.0 unweighted. That would be conceivable, because someone might have 94 in every since class, and it would have been a true 4.0. However, more likely, a person with a 94.0 average has some grades below 94 (making them B’s at my old school), and other grades above 94.
If ranking is based on percents, and a student is after a very high ranking, it might make more sense for the student to turn in 97-99 performances in most classes, at the cost of an occasional 92, rather than scoring 94 or 95 across the board.
I don’t think any means of conversion would be 100% fair, though the long way that I suggested would probably be the most accurate.
But, more than likely, Yale will look at the 4.07 unweighted as reported by your school, and move on to other aspects of your application.