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1 gtt = 0.000000092 sh tn wt.
1 sh tn wt. = 10,886,216.88 gtt
Definition of medical drops of water provided by Merriam-Webster
the smallest practical unit of liquid measure that varies in size according to the specific gravity and viscosity of the liquid and to the conditions under which it is formed.
Definition of US short ton of water provided by WikiPedia
In the United States, a short ton is usually known simply as a “ton”, without distinguishing it from the tonne (1,000 kilograms or 2,204.62262 pounds), known there as the “metric ton”, or the long ton (2,240 pounds or 1,016.0469088 kilograms), known there as the “Imperial ton”. There are, however, some US applications where unspecified tons normally means long tons (for example, Navy ships) or metric tons (world grain production figures).