Originally Answered: Why do people say a pound of fat is 3500 calories?
Calories for foods refer to the reaction with oxygen, this is what happens when you literally set some food on fire. The number "9" is actually an approximation. Around 1900, nutritionists (mainly one, Atwater) built a huge chamber where someone stayed in bed for day(s) and they measured the heat produced. The amount of energy (as heat) was similar to the amount produced when setting the food on fire and so these approximations got started.
The first mention for such an "equation", came from Lulu Hunt Peters at 1918. She was merely a physician, fascinated by Atwater's work and she made approximations, so that calories (then unknown to the US public) would catch up. Her book became a bestseller, being the 1st weight loss book directly for the public. But the equation is far from how much energy a pound of fat gives. Fact is that we can never know for sure how much it gives, but we can control it so that it gives much less. This is what low-carb and carb-control diets actually do.
When you eat carbohydrates an hormone called insulin is released, the same hormone is the one that transfers fat to the cells. So, if you don't eat carbohydrates together with fat then fat doesn't get stored and it gets out of the body. How? With water (sweating or going to the toilet), because fat is insoluble in blood/water. Thus, the fat you eat doesn't always give the same amount of energy, you may lose it before it's used. It depends on how much carbohydrates you eat and how much insulin is released, how much water you lose daily, etc.
Bottom line: forget this equation and forget calories.