了解 vs 明白 vs 知道 - what is the difference, and when should I use each one? 了解, 明白, and 知道 seem to be fairly synonymous in Mandarin, but there does seem to be some subtle differences between them.

What exactly is the difference? When should I use each one? Could you give me an example sentence to show when each of these terms would be the most appropriate?
知道 means you just know something, you don't need to understand it.
了解, you understand it.
明白, you understand something, and have a clear idea of what it is about. 

I think the order of them is: 知道&lt;了解&lt;=明白

for 了解, it can also means 'to investigate'. e.g 小白, 你去了解一下这事情怎么发生的.