If you entered 3.625" as your Wall Component width, I would expect that AutoCAD has maintained that dimension "internally", but that your drawing file has its linear precision set to 1/4", so the displayed number gets rounded to the nearest quarter inch.
Check the linear precision setting in the Drawing Setup dialog, on the Units tab. If you want to see numbers to the 1/8", you need to set the precision to at least 1/8". 
When working in imperial units, I usually have the length type set to Engineering (feet, inches and decimal inches), and the precision set to at least five decimal places, because I want to see it if a particular dimension is 0.120" or 0.130", rather than exactly 0.125". Architectural units set to the "equivalent" 1/32" precision would show all three of those numbers as 1/8". Maybe not a big deal for just one dimension (yes, I know that a tolerance of 1/4" in the field would be extraordinarily precise for the actual construction), but I prefer to have my drawings be as precise as possible so that I really know what I "should" have and then do my design to allow for field tolerances, rather than have the drawing itself be a hot mess before field tolerance comes into play.
David Koch
AutoCAD Architecture and Revit User
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