A mathematically perfect fermentation is calculated. So as if the yeast were a scissors, which makes alcohol from sugar without leaving anything and consuming itself. In practice, such a degree of fermentation can not be achieved.
Many possibly interesting values are displayed. Some results may be surprising:
Thus, the type of sugar makes more of a difference than most might suspect. In particular, there are major differences between the double sugars (sucrose and maltose) and the single sugars (glucose and fructose). This is mainly due to the fact that a double sugar does not simply consist of two single sugars, but of two singple sugars minus one water molecule. So when double sugars are fermented, water molecules are consumed. So like this:

This means that you get more alcohol from 1kg of double sugar than from 1kg of single sugar. From 100g double sugar 53.8g alcohol and from 100g single sugar only 51.1g alcohol.
There are further differences, for example, in that the solutions of the various types of sugar all have a slightly different density. Thus, a sugar solution with a measured density of 1.07kg/lt results mathematically in 12.4%abv for glucose and 12.1%abv for fructose. Because for this density, 190g/lt glucose or 186g/lt fructose are needed.
And the refractive indices are not uniform either: Thus, a refractive index of 1.36 means between 185 and 193g/l of sugar, depending on the type of sugar, and between 12.4 and 13.0%abv after fermentation, mathematically.
Correct measurements and calculations should therefore actually take into account the type of sugar. In the case of sugar water and rum, it is sucrose; in the case of cereals, it is mainly maltose and glucose; and in the case of fruit, it is a different mix of glucose, fructose and sucrose, depending on the type of fruit.