The whole point is by your method, somewhere along the line you converted mass to weight (m?g). The summation of that conversion is g/gc of 1lbf/lbm. After doing many of such calc's one considers it to be understood and omits it from the calc's using simply lb rather than lbf and lbm.And I never will, its a very bad leap to make.
Good link, as it back up what I've been trying to say. For instance, "There has been much confusion (and numerical error!) because of the differences between lbf, lbm, and slug." Or, "1 lbf = 32.174 lbm? ft/s2." Or "It is not proper to say that one lbm equals one lbf, but it is proper to say that one lbm weighs one lbf under standard earth gravity."
In other words, you cannot divide a pound-force by a pound-mass in order to cancel out the term "pounds."
I get a pressure of 624.3lbf/ft?
A force on the bottom of the tank of 62430 lbf.
An area of the bottom of the tank of 100 sf.
And I think I see what is throwing you off. The mass of the water in the tank is 62430 lbm, and the force on the bottom of the tank is 62430 lbf. So since the value of lbm and lbf is the same, they must be the same thing? Therefore, dividing my pressure (lbf) by my density (lbm/ft?) I can cancel out "pounds." But as I mention above, you can't cancel out pounds that way.
Moving on, can we now say height*density is part of an equation to determine volume. Yes, something will cancel out, either height or density, likely height, but in the equation height is necessary to determin area or pressure or force depnding on which parameters are known.
Furthermore, I did post this question in the Electrical Calculations/Engineering forum, but I do not believe the prep or real tests are going to require engineering level nomenclature for the calculations.