What is the correct way to specify the weight fraction from bulk compositional data with a listed total % (e.g. from XRF, ICP)?

**TL;DR = With bulk composition results, such as from XRF or ICP, is the mass fraction of a given analyte that analyte given as a % or the analyte divided by the given total mass %?**


Perhaps a silly and very elementary question, but I want to be certain as I've been wondering for a while now and never 100% sure if I'm right or not. But I'd like to be to minimise any potential compounding errors.


I've recently received some X-Ray Fluorescence (XRF) bulk composition analysis of some coal fly ash material I'm going to analyse. The full table of results is as below where the units are listed as


* "ppm for solid samples = mg/Kg;
* ppb for solid samples = $\mu$g/Kg ;
* ppm for liquid samples = mg/L;
* ppb for solid samples = $\mu$g/L"


(note that I did try to put everything in Chem SE table format but it was too difficult to do, format and the help page didn't provide too much clarity from my POV):


[![enter image description here](https://i.stack.imgur.com/W5vg0.png)](https://i.stack.imgur.com/W5vg0.png)


Note that the total % from the table above is 100.21%. I presume they're not always 100% due to errors with instrumentation detection limits (etc.).


Note that when I only include those measurements with % units I get this:


[![enter image description here](https://i.stack.imgur.com/llv9b.png)](https://i.stack.imgur.com/llv9b.png)


When I add all the %s up I get a total of 100.405%. If I instead add only those with the same method in the table above I get 98.845%. In either case, they do not equal the mentioned 100.21 % total.


I understand that the mass (or weight) fraction of a given analyte is [given by the formula below](https://en.wikipedia.org/wiki/Mass_fraction_%28chemistry%29) where $w\_i$ and $m\_i$ is the mass/weight fraction and mass of the given analyte respectively and $m\_{tot}$ is the mass of the total mixture:


[![](https://i.stack.imgur.com/MRl3y.png)](https://i.stack.imgur.com/MRl3y.png)


I have been told by some to just assume that the % given for each analyte is the mass fraction but I feel that may not be right and I'd rather less compounding errors than more.


**So with this in mind, my questions are:**


1. Is the mass fraction of SiO2 from the above tables 54.19% as listed or, for a given mass of 100.21 g for the parent material, $\frac{54.19 g}{100.21 g} \times 100\%$ = 54.08%?
2. Can the moisture and LOI analytics be added as part of the total? I.e. should I assume from this table of results that 0.01% of the total mass is H2O and 0.01% is carbon respectively?


