Ginger is a popular ingredient in Japanese cooking and its been used in my class numerous of times. I always tell my students the best way to preserve ginger as it usually dries out pretty fast in the refrigerator.
The trick is to drop it in a jar, cover it with tap water, put the lid on and keep it in the fridge. This way you can keep it fresh for up to 1 month. You will know when it's bad as it will become too soft to use. In time of use, just take it out of the water and use as much as you need and return the rest in the jar. You will need to change the water every time you use it as it gets mucky.
I'm Miyuki and I teach Japanese Home cooking at my home in Tokyo.