Chemistry - Are food calorie values really integers?
Solution 1:
They're not exact numbers. These numbers aren't exact for three reasons:
Each type of carb, protein, and fat has a different caloric value. These are overall averages for each class.
Even if you were dealing with a single pure compound, the value couldn't be exact because there is individual variation in how much of that compound is metabolized based on digestion, absorption, etc.
Even if #1 and #2 were not issues, the number still couldn't be exact, because it is a measured value, and measured values are never exact. Only counted numbers, and values that are exact by defintion (e.g., the speed of light) are exact.
To get a better idea of how these values are determined, and the issues and uncertainties associated with measuring them, I'd recommend reading through:
Food and Agriculture Organization of the United Nations. FAO food and nutrition paper. Chapter 3: Calculation of the energy content of foods - energy conversion factors. Food and Agriculture Organization of the United Nations, 1979.
Here is a direct link to chapter 3:
http://www.fao.org/3/Y5022E/y5022e04.htm
Solution 2:
It doesn't "take one calorie to burn", you gain one calorie by burning.
Now noting obviously what everybody else has said about selection of the type of fat affecting the precise amount of energy available from one gram (which in practice will be measured in a calorimeter), but what this is really saying is that by metabolising some specified fraction of a gram of fuel you can do (approximately) one calorie of work, e.g. raising the temperature of water by some specified amount or moving your muscles in such a way that they lift a weight by some specified number of centimeters.
So no, it's not an integer: it's an approximation to the amount of work you'd have to do to prevent the food you've just eaten being stored as flab, and to get an accurate figure you'd have to do an assay of an identical portion of that food taking into account both its chemical composition and its digestibility (e.g. an increased amount of fibre in the specimen might not change the result of the physical calorimetric test, but might change the availability of the nutrients to the digestive system).