What is meant by the yield of an industrial process, such as the extraction of a metal from a commerical ore deposit?
The term "percent yield" is a means of measuring the effectiveness of a process. This process could either be an industrial process or a chemical reaction. Basically you take a measure of the raw materials that you put into the process. If the process or reaction ran at 100% efficiency and gave a 100% yield, you then calculate the amount of product or material that would be produced (this is called the theoretical yield). Then after the reaction or process is complete, measure the actual amount of material produced. Divide the actual amount by the theoretical amount and multiply by 100 to get the percent yield.
Let's take the example you gave above, the extraction of metal from an ore. If you started with 10 tons or ore let's say the theoretical yield of the process is 4 tons. In other words, if the process worked perfectly at 100% efficiency, 4 tons of metal would be produced from 10 tons of ore. But the actual amount of metal obtained at the end of the process is 3 tons. Divide 3 into 4 and multiply by 100:
3/4 * 100 = 75%
The yield for the process is 75%.