This sort of thread gives me great concern as an engineer and, in this case, a very experienced practising weights engineer - my WCA (AV1), as a sideline, was the first issued when the present system came into vogue mid-1976. When it comes to weighing, I've weighed well over 1000 aircraft from the smallest up to Boeings and similar.
One needs to understand, very clearly, that the accuracy of the empty weight data with which you start your sums … is NOT accurate to the nth degree. The data always includes a variety of errors which, on occasion, can be relatively significant. For instance -
(a) scales - the underlying scales requirements are in CAO 100.7 (
www.legislation.gov.au/Details/F2018C00475) at 4.2. Never mind that most of the older scales actually don't go close to meeting this standard. No scale is dead accurate - all have inherent errors in their design and construction. Furthermore, the calibrations are, at best, a bit dodgy and contrived and, if in use the calibration conditions aren't approximated reasonably, the reading one gets can be somewhere between fanciful and outright conjectural.
(b) distance measurements - weighing with platform scales (usual for lighties) involves measuring reaction arms and jig points to establish the datum plane. This ALWAYS involves approximations and errors. Things are a bit better for jackpad weighings as the jack points are established accurately by the OEM. However, there is no free lunch anywhere and, in this situation, jackpad weighings increase the error potential in the weighing numbers. So you still end up with only an approximate result ...
End result is that the stuff you start with for your calculations is accurate, at the absolute best for a lightie, probably to no more than 5kg and 5mm. If the weighing is done without lots and lots of care and attention, the errors easily can be considerably worse.
So what ?
What benefit/value/validity can there be in running your calculations to precisions of a squillion decimal places ? Utterly pointless and silly. My suggestion is that the calculations should be done to one decimal more precise than the purported accuracy desired in the answer. In this way you avoid needless roundoff error accumulation. If you are running the sums with an electronic calculator, by all means run the accumulator to whatever floating point significance the device might have - no point not doing so.
The examiner is between a rock and a hard place. He is charged with doing his best to establish (by means of part sampling of syllabus competence) that the candidate has learnt a few things and can do the usual sums. One of the ways he might go about this is to discriminate to a slightly higher precision than justified by engineering reality in his available answers - I have no problem at all with that approach. However, there is absolutely no value to be had in looking at precision to a million decimal places and, in reality, this leads to negative training and quite misconceived ideas at the candidate level.
I'm a bit up to my ears at the moment but I will run the problem the OP has raised when I get some spare time and come back with a more reasonable solution precision for your consideration.
As always, Bob approaches this stuff with a good, level head and his counsel should be listened to attentively.
