Even though international regulations adopted a unique measuring system some time ago, some conventional measuring units are still used to measure various quantities (bar for pressure, tons for weight, not to mention anglo-saxon units).
Both in chemistry and photography we have to deal with ratios which express the concentration of a solution, and we want to go a little further into these.


Diluting a solution
There is a doubt which sometimes arises into the photographers' mind while dealing with bottles and glasses in the darkroom: what is the difference between a 1:X diluted solution and a 1+X one?

There isn't any really!
Nevertheless, in someone's opinion, the "1:X" formula indicates 1 part of solute in X total parts of solution, while "1+X" indicates 1 part of solute plus X parts of solvent.
The correct understanding is that X always indicates how many parts of solvent. So, 1:X and 1+X mean the same thing.
It is possible, though, to find 1:100 to indicate a 1:99 ratio, but the difference is very small indeed.
On the contrary, if you think about a 1:3 solution things change dramatically: by mixing correctly 1 part of solute with 3 parts of solvent you get a 25% solution, while following the wrong idea described above you would be mixing 1 part in two parts of solvent, getting a 33,3% solution!


Concentration
Three kinds of measurement are fundamental to define a concentration:

1-  the molar ratio (moles of solute / total no. of moles, also known as "molar fraction").
This ratio is independent from temperature and pressure, and is valid for any chemical, even in gaseous state.
Even though this method has advantages, it is not commonly used , except in chemical labs.

2-  the ratio between the solute's mass and the total mass (solute plus solvent).
This ratio, often normalized as percentage, is also independent from temperature because masses do not vary as temperature changes. Because of this it is often used in trading chemical compounds, where large amounts of solutions are handled and shipped, and price is set on the quantity of solute contained in the solution. For example, you will always find something like "conc.=xx% (m/m)" or "x% (w/w)" on liquid chemicals. In the last formula "w" is referred to weight.


3-  ratio between the solute's mass and the total volume (solute plus solvent).
This ratio varies with temperature, for liquids modify their volume accordingly to temperature's changes while masses don't. Nevertheless this way of expressing concentration is widely used, because it is much more handy to use a graduated beaker to measure liquids instead of using a scale.
For precision's sake one must say that international standards volumes are measured in cubic meters or their powers of ten rather than liters. Anyway, the same international conventions states that the liter  can be used as a special name for the cubic decimeter .
Because volume varies with temperature, both densities and concentrations expressed in m/v have to state which temperature they are referred to (usually 20 or 25°C).
Then it's necessary to know the liquid density to convert a concentration measured in m/m to the one expressed in m/v, that is the ratio between a certain chemical's mass and its volume for a given temperature.


For example:
Our goal is to prepare one liter of sulfuric acid solution at 10% m/v, to be able to measure small amounts of acid in a graduated beaker: 10 ml of the solution contain exactly 1 g of sulfuric acid.
Commercially available sulfuric acid has a concentration of 96% m/m and its density is 1,835 kg/dm3 at 20°C.
It means that 1 kg of solution is contained in 1000/1,835=544,96 ml, of which 96% is sulfuric acid. Thus, 100 g of sulfuric acid are contained in (100/1,835)/0,96=56,766... ml of concentrated solution, which can be rounded to 57 ml.
To prepare our 10% m/v solution we must take 57 ml of the concentrated acid and slowly and carefully dissolve it into ca. 800 ml of water. This must be done while stirring, adding the acid to the water and NEVER water to acid because the solution process produces much heat and accidental spills will be of diluted, instead of concentrated, acid. The solution will then be allowed to cool down before transferring it to a graduated beaker, where water will be added to the final volume of one liter. One must remember that graduated containers report the temperature at which the scales are valid. If the solution will be brought to the final volume while still hot, when cooled it could show a shrinkage which can reach and even surpass 5%.
A suggestion for "chemists": the water to be added to reach the final volume will be poured in small amounts in the first container where the solution has been made, and the transferred to the graduated container. Doing it this way any small trace of acid still left in the first container will be brought into solution.


Other ways to express concentration
Despite of International System recommendations, some common ways to express the above concept are still used. Among these:

alcohol degrees

volumes

Baumé degrees

Alcohol degrees are widely known: they express concentration as alcohol ml in 100 ml of solution.
Volumes are use for hydrogen peroxide and mean how many volumes of gaseous oxygen can be extracted from one volume of liquid hydrogen peroxide. Hydrogen peroxide percentage expresses instead the weight of hydrogen peroxide in 100 grams of solution. For conversion utilities and factors see the appropriate paragraph "Tables and conversions".
Baumé degrees are a measure of density in non-metric units. Because density, for a given solute dissolved in a given solvent, is a function of concentration, one can use a density measure to express concentration. The use of density as a measure of concentration comes from its being easy to measure, for example by using a densitometer as one does to measure acid concentration in lead-based batteries. Anyway the conversion from density to concentration is meant to be made with specific tables, for each given chemical. For a precise definition of Baumé degrees see the appropriate paragraph "Tables and conversions".


Oddities
It often happens that different way of expressing dilutions are found in the Old Techniques, where recipes are simply copied from one book to another for decades without further variations. Even though these way of expressing dilution does not match what above said at point 1,2 and 3, authors still refers to as "per cent".
An example is given by preparation of an arabic gum solution to be used in gum dichromate. It is read: "prepare a 40% solution of Arabic gum by mixing 40 g of gum in 100 cc of water . Since gum is extremely viscous it is difficult to bring this solution to volume, the method above is preferred. The solution is not a 40%, because the final volume will be higher than 100 ml (ca. 130 ml) and the exact concentration will be approximately 30,8% m/v (40g/130ml). It would be more precise to refer to the formula above as a solution of gum and water 40+100.
Some books still give instructions this way and we will stick to these wherever inevitable. In any case, however, we will do all we can to precisely define concentration of solutions avoiding improper terms.