Don't know a ginger- specific rule. But for most herbs, 3:1 fresh to dry works. Failing better in for, start with 1/3 of the fresh amount called for, taste & adjust.
From livestrong,com, "You may need to experiment to find just the right amount to use in your dish. The Cook's Thesaurus reports that 1 tablespoon of fresh ginger root is equal to 1/4 teaspoon of ground ginger. At Food.com the recommended equivalent is 1 tablespoon of fresh ginger for 1/8 teaspoon of ground ginger."
Better info than my guesstimate; I''ll use your ratios now.
rachel, perhaps the other posters have a very different experience from mine, but if you are trying to use powdered ginger in an Asian dish,
that just doesn't work, in my book. Ground ginger is intended for baking and has a very different effect from freshly grated or chopped peeled ginger. I don't know what recipe you have in mind, but if it were Asian, and I could not obtain fresh gingerroot, I, personally, would not make that recipe. I'm rarely a stickler like this, but ginger is different!! Fresh ginger root does last a long time in the frig, but it can also be kept in the freezer and partially peeled, grated or sliced as needed.
I'm with Le Bec Fin on this one - the two have vastly different tastes to me and are not swappable.