ajdelange

Recipes 

No, not really. I am talking about the fact that ppm (or ppb or ppt) is dimensionless and that mg/L is numerically equal to mg/kg only if the solution weighs exactly 1 kg/L which it only does at one (for a particular solute and that must be one that will increase the density of the solution) concentration for each temperature. A molar solution is a w/v solution. A molal solution is a w/w solution but it is weight of solute per unit weight of solvent. In neither case is ppm equal to mg/L.

Yes.

That's the important thing.

Your water report lists calcium at 2150 ug/L. That is an average most likely over the past year. Depending on your water source (river, reservoir, etc.) that number may change slightly or somewhat dramatically over the year depending on several factors, not the least of which are season, temperature . . .

How do you conclude that? No information about number of measurements, precision of measurement, dispersion of measurements or any other statistical data was given by OP. The measurement instrument may or may not have read to 4 significant digits and even if it only read to 2 or 3 the mean (if it is indeed and average and it probably is) would certainly have more digits and if the standard deviation were small enough the SEM could be small enough that 3 or 4 digits could be significant. If your point is that a published value of 2150 ug/L does not mean that the water in question will contain exactly 2150 ug/L but rather some number close to that (with what "close" means unspecified) then it is valid.

Bmorebrew

Recipes 

Should say "is like the difference . . ." My bad - the point was to reinforce your point of technical difference vs. practical.

Curious to me also that the value would be reported as 2150 ug/L as opposed to 2.15 mg/L. I have it backwards in my initial response actually, purposely reporting in such a manner hints that the zero is significant. Reporting as 2.15 mg/L would obviously eliminate any ambiguity over the last zero if it were in fact not significant. However, my guess is that the measurement is made on an ICP/MS, and here minerals on drinking water are run using method 200.8 and done in mg/L.

One would not report more digits than those used in making the measurements.

ajdelange

Recipes 

My guess too. If the Standard Procedure or MOA or Practice or whatever calls for standards whose concentrations are expressed in mg/L then the result should be expressed in mg/L and in water analysis this is usually the case. The example standard I mentioned in #6 is labeled mg/L and any analysis I do using a calibration based on that standard is, thus, to be expressed in mg/L. I could, of course, do some math and convert that strength of that solution to equivalents per liter or moles per liter or % w/w or grains per gill or any other unit I wanted and report in that way but the reason the standard is labeled in mg/L is because the standard practice wants the reporting in mg/L.



Averaging finite precision data to get answers more accurate than the precision is one of the oldest tricks in the book but it must be done with care. In particular, the SEM must justify the carrying of the extra digits. As an example of this if I take 1000 numbers each equal to 2.600 plus a gaussian random variable of standard deviation 1 and then "measure" the value of the result to unit precision (i.e. I can have "measurements" of 0,1,2,3,4 etc and average these I get averages like 2.596, 2.573, 2.576, 2.622 for different "experiments". Clearly, I have been able to measure beneath the "quantizing noise" introduced by the finite precision of my measurement process. Given that the standard deviation in the raw sequence is about 1 count the SEM is 1/sqrt(1000) = 0.03 and so I am justified in reporting at least 1 and perhaps 2 additional digits. Thus my answers could be 2.6 for all four examples or 2.60, 2.57, 2.58, 2.62. The ability to do this obviously depends on assurance that one is free of systematic (bias) error, and that one has a large enough samples (1000 isn't reasonable for checking on the calcium content of ones water)and small enough SD to hold the SEM down.

All this is well and good but the extra significance may not be desired (in which case there is little point in doing all the extra measurements). The protocol often states the number of significant digits to be reported.