Hair count is certainly important, however, the handling and placement of grafts supersedes this. If you feel the need to count your extraction sites you may find a discrepancy as you will be unaware of your surgeon's transection rate (grafts that are extracted that are partially/not fully intact) as well as the number of hairs per follicle. It is common practice for surgeons to give patients the number of follicles extracted including the number of hairs per follicle for example 300 1 hair follicles, 600 2 hair follicles and so on.
The other point to be discussed here is that if you had a sparse donor area I hope that you considered the option of strip surgery as it provides a greater yield than FUE.
Generally if you trust your doctor, you shouldn't have to double check the grafts you got by counting them. If you really want to count the implanted hairs, you should ask someone to tediously count them for you. I am sure it can be done if you're determined. You can probably take a high resolution photo and try to do it yourself as well.
The simple answer is, there is no way to be sure without counting every single hair or follicular unit immediately after the procedure. Most doctors and their assistants are honest, but some are not; the bottom line is that it is very difficult, if not impossible, for a patient to know for sure. Your math is correct......but if you were medicated or distracted or dozed off your punch count may have been inaccurate. That said, there is a certain "look" that a hair transplant of X or Y number of follicular units should have at the end of a year given the area that was addressed, and this is something that can only be evaluated once you have your final result. Even the most honest and skilled surgeons have had patients from time to time who do not achieve the expected result from a certain number of grafts, and there can be many reasons for this, but these patients are by far the exception to the rule. I would suggest being patient and waiting to see what things look like after a year. You may be pleasantly surprised.
Hairs and grafts are 2 different things so it depends on what they are counting. Some clinics also charge by attempts or physical numbers or viable looking grafts/hairs. The variables are many so its important to know what exactly you are being charge for and that the clinic is honest and with a good reputation. We often see patients from other clinics who get 2-3x the # of grafts needed to produce the same resutls we get with a fraction of that number.
That depends upon the honesty and integrity of the doctor. Unfortunately, too many doctors 'fake it' that is the numbers because each grafts is tied to a particular fee. I write extensive against this but it can be difficult to tell. There are even more pitfalls that you need to look out for. the graft counts in FUE, for example, might reflect pass attempts at FUE like with the ARTAS robot, and what is the doctor actually charging you for?
Call me if you want