You don't understand significant figures.
D@mn dyslexia 0.40 or 0.04 I usually catch those errors but I missed it this time.
Link 1: cups, quarts, gallons, liters, and (g = mL), which as I pointed out is incorrect depending on your level of precision.
Link 2: liters or quarts.
Link 3: says to use w/w but then immediately says to use w/v in the next newer article:
https://sciencing.com/make-five-percent-solution-salt-8076940.html
Link 4: cups.
They overwhelmingly measure water by using volume.
1 g = 1 mL is also correct depending on your level of precision.
Mine currently is what is practical and helpful for someone on this forum to make use of in their endeavor to mix up a safe lacto-ferment brine.
I included link 3 and the link to Purdue University to show that the % weight formula I am using is accepted in the scientific and chemistry communities as an appropriate way to calculate the % concentration of a solution.
My previous understanding of % volume concentration was with only liquids involved; as explained in this article.
https://www.thoughtco.com/calculate-volume-percent-concentration-609534
Thank you for showing me another method to calculate the % concentration. I will come back to this in a bit.
I didn't say that the measurements were not by volume. I stated the calculations were by weight. In all of these calculators if you convert the volume of water to grams at 1 g/mL and select grams for the measurement of salt you will readily see that the calculations are by % weight and not by % volume.
However, after further review I see that these calculators are using a different third formula entirely.
For reference 1 gallon of water weighs ~3785 grams.
Link 1 for a 10% 1 gallon solution 378.5 grams salt
Link 2 for a 10% 1 liter solution 100 grams salt - selecting gallons gives salt in ounces
Link 4 for a 10% 1 gallon solution 379 grams salt.
Deconstructing this their "Web Formula" seems to be: gram Salt = gram Water * % salt.
This leaves us with 3 different ways to calculate the salt needed for a particular concentration of brine.
For the following:
"W" is the weight of water
"V" is volume of water in mL
"X" is the percent concentration of salt
"S" is the weight of salt
2.17 is density of salt in g/mL
Answers below are for 1 gallon and 5% salt are and are shown to the nearest gram.
% Weight Method
S = (W / (1 - X)) - W
S = 199 grams = 35.03 teaspoons = 1/2 cup + 3 Tablespoon + 2 teaspoon
% Volume Method
S = (2.17 * V * X) / (2.17 - X)
S = 194 grams = 34.06 teaspoons = 1/2 cup + 3 Tablespoon + 1 teaspoon
% Web Method
S = W * X
S = 189 grams = 33.27 teaspoons = 1/2 cup + 3 Tablespoon + 1/4 teaspoon
If you use work these equations backwards from say 1 gallon water and 194 grams salt the % concentrations are:
4.88% for % Weight
5.00% for % Volume
5.13% for % Web
These are all safe concentrations of salt for a lacto-ferment brine. Regardless of the method one uses you should get a safe ferment. 5.13% is a bit on the high side but some vegetables such as olives call for up to 10% salt. The biggest difference in the final product will be taste and possibly crunchiness but with good notes the salt levels can be adjusted on future batches.
After all this I am still left with one un-answered question. What is the method used by the folks who came up with the safe range of 2%-5%? I have yet to see a definitive answer on this.
One could split the difference and use the % volume method that
@RPh_Guy has laid out but for or now I will continue to use the % weight method. Pick one that you are comfortable with and go for it.