This is incorrect.
Short answer: for darn near every single instance that is important to fishkeepers, 1 ppm is equal to 1 mg/L.
Long answer: A ppm is a like divided like quantity. 1 mL of fluid A in 1000L of a different fluid B is 1 ppm of A by volume. 1 mg of substance A in 1 kg (=1000 g) of substance B is 1 ppm of A by mass. There are the two most common in physical quantities, and you will see both ppm by volume and ppm by mass in chemistry frequently.
An example used by quality control professionals would be if a a company is manufacturing 1 million widgets a day and 9 of them fail the quality standards, you will sometimes see the quality reported at 9 ppm quality failure rate. For ppm (and the similar ppt, parts per thousand, ppb, parts per billion (though be careful on a forum like this to mention whether it is American or British billion), pph, parts per hundred better known as percent) it doesn't matter what the measurement is, but both the numerator and denominator have to have the same unit.
So, now we look at 1 mg/L. That actually has two different types of measurements in the numerator and denominator. The numerator is mass (mg) and the denominator is volume (L). So, how is that a ppm? Well, you can use a liquid's density to convert the mass to a volume measurement.
For example, liquid ammonia at 25 deg C has a density of approximately 0.606 g/cm^3 ( see http
/en.wikipedia.org/wiki/Ammonia_%28data_page%29 ). 1 cm^3 is the same as 1 mL. So, let's say that there is 100 mg of ammonia in your 100 L tank, which would of course be a concentration of 1 mg/L. 100 mg = 0.1 g. 0.1g * (1 mL / 0.606 g) = 0.165 mL This is the volume of ammonia in your 100 L tank in this example. Doing the division, and this actually turns into 1.65 ppm by volume of ammonia in the water.
That actually looks like a significant difference. However, the final piece of the puzzle is that ammonia and water don't just remain in their pure-component densities when mixed. That is, they don't just mix linearly. I.e. the density of a mixture that is 10% ammonia and 90% water is not equal to 0.1*(density of pure ammonia) + 0.9*(density of pure water). At very small concentrations, the density of ammonia in a mixture of water is very, very close to the density of the water itself.
And that's the real trick. In liquid, when there is only a very, very small amount of a substance, it typically takes on the properties of what it is dissolved in. So, essentially, the liquid ammonia has a density of 1.00 g/cm^3, the density of pure water at 25 deg C.
So, when there is only a tony amount of something dissolved in water, a mg/L is the same as a ppm by vol.
So finally, that is why I wrote above that for any value of any significance to fishkeepers, a mg/L is the same as a ppm. Fishkeeping may get up to a few 100 ppm when measuring nitrates, for example, but usually not more than that. 100 ppm is still a very small amount. To put into more familiar terms 100 ppm = 0.1 ppt = 0.01 pph = 0.01%. Very tiny. ppm only loses meaning when you start getting very high. For example, a 50/50 mixture would technically be 500,000 ppm. At that point, a mg/L and a ppm would not be the same any more.
what?! are you sure? because on the box it is like the second best conditions next to 0 mgl
