Suppose that an economy has 9 million people working full-time. it also has 1 million people who are actively seeking work but currently unemployed as well as 2 million discouraged workers who have given up looking for work and are currently unemployed. what is this economy's unemployment rate?

The unemployment rate will be of 10% of the economy. We can only have in mind the Million people who are actively seeking work in here which is in itself what is taken into account when talking about economy's unemployment rate. Remember also that the unemployment rate that is consistent with full employment known as the natural rate of unemployment.