Instead of determining slope by measuring distances we can measure it directly. There are tools (inclinometers) which measure slope, tilt, etc. Of course if we use one of these, it is a good idea to take more than one measurement and at different locations. For example, on that 3 mile stretch of road, it is highly unlikely that it is a 2.5% grade at every single point. So, using an inclinometer at several locations and then calculating an average of those measurements would yield a much better indication of the road's slope.
Another way to determine slope is with a level. Roofers (among others) use this method.
One end of the level is placed along the slope of a roof and the lower end is lifted until the bubble indicates it is perfectly horizontal. The rise is then measured. Roofers and carpenters generally use a 1 foot level and the rise is measured in inches and so the slope of the roof (or pitch as they call it) is stated as inches per 12 inches. So, the pitch of a roof can be 1 in 12, 2in 12, and so on.
Besides roads and roofs the concept of slope is quite essential in the design of wheelchair ramps. For this purpose, the slope should never be greater than 1 in 12. In designing a wheelchair ramp for the elderly, a gentler slope of 1 in 18 should be considered. If the ramp will be exposed to the weather, icy conditions should be taken into account for safety.