No, we do understand math. And mass and weight, and cumulative error, and . . . And even OCD.
Okay. Lets start with the caveat that scales measure weight, not mass. Here's an explanation of the difference at
https://en.wikipedia.org/wiki/Mass_versus_weight
All of the scales being discussed here measure weight (as explained in the link above, the force due to gravitational acceleration of a massive object), and are digital types relying on load cells. The typical real world accuracy of such devices is about .03%, or 3 grams over 10 kg range. Most are less accurate, with typical food scales around .05%, or 1 gram over 2.5 kg range. Virtually all work on the same principle, a voltage is applied to an electronic load cell which is deformed, which changes its resistance, which changes the voltage, which is then converted into a digital signal, which is then displayed.
https://en.wikipedia.org/wiki/Strain_gauge
Regarding multiple weighings vs a single weighing:
Typically multiple weighings of items on a smaller scale with better accuracy and resolution will be more accurate than a single weighing of items combined. This is because load cells designed to withstand large loads without breaking or being permanently deformed cannot be designed to have the amount of deformation necessary to produce the high resolutions available in smaller scales. Dividing up larger loads into smaller groups for weighing purposes doesn't change their weight. It does increase the measurement accuracy. For example: Four separate weighings of items on a scale with a +/- .1 grams resolution results in a possible cumulative error of .8 grams - and it will always be more accurate than a single weighing on a scale with a +/- 1 gram resolution and a possible 2 gram error. Trust the math, not the machine.
But it's pretty much a pointless endeavor anyway, as there are so many other factors that affect measured weight to a MUCH greater degree.
Gravitational differences are one. The gravitational force acting on a mass varies by as much as 0.7% over the face of the earth. Most of this is due to latitude and centrifugal force, as both the earth and the object are moving/spinning. This force propels the object away from the earth which reduces the gravitational effect. This rotation also creates the Earth's equatorial bulge, which increases the distance of the object from the earth's center of mass. Altitude further reduces the gravitational effect due to increased distance between the object being weighed.
All told that pack that weighs 10 kg (22lbs) at the south pole weighs about 70 grams less on a mountain summit in Peru near the equator (0.7% difference). More realistic would be the 0.6% difference between places like Oslo and Mexico City.
https://en.wikipedia.org/wiki/Gravity_of_Earth
Further compounding the issue are the effects of local density differences on the Earth, and even the effects of solar and lunar tidal forces.
http://www.calpoly.edu/~gthorncr/ME3...yofGravity.pdf
One must also consider the effects of moisture. Fabrics and insulation absorb and exude moisture as relative humidity changes. This would result in noticeable/measureable weight gains and losses with sleeping bags, clothing, etc. Then add the effect of actually wearing and sleeping in these items, which can really load them up with moisture. Even an ultralight sleeping bag can easily retain 100 grams or more of water weight in humid conditions.
In the final analysis, both environmental factors and gravity affect gear weight by a factor of 100 times more than scale accuracy. There really is no absolute measure of weight when it comes to gear. Weight changes due to variables like geographical location and environment. Even mass actually changes due to humidity.
And then there's the calibration issue. What standard did you use to calibrate the scale? How often is it checked? And so on . . .
What does your pack REALLY weigh? Well, where are you? And what's the weather like? Maybe it's not the answer an OCD hiker wants to hear. But it's the reality.