In the properties shelf (activated by the N key in the 3D viewport) in object mode, one of the four transform types in the top pane, is labeled "scale". You can enter specific values there with a pretty good precision. However, these are still percentage values. There is an analogous panel in the properties editor under the object context tab. These are also percentage values.
Note though that you can take advantage of the ability to use a regular expression to achieve a degree of precision in entering scale values. Suppose that you have an object which has a dimension of 73 units, and you want that same dimension scaled to 87 units. After you select your method of entry, whether using the S key, or by entering the values in one of the panels I mentioned above, you can enter the string ( 8 7 / 7 6 ), which will be interpreted as an expression to scale the dimension by 87 / 76 thx, providing you an exact dimension.