The tool Outback is using is called a divider/compass.
To find the point to drill the center of the scale on the pivot end just use the divider and measure from one side of the scale to the other side. Then put that against a ruler. Let say it measures 1/2". Adjust the divider closer until it reads 1/4" according to the ruler. Now put the divider against one side of the scale. The other leg will be in the middle of the scale. Mark it and drill.
Hope this helps, :)