Imagine you are purifying a protein which accounts for 0.001% of the total protein within a cell. how many steps of purification are required to yield pure protein, assuming a 10 fold purification with each step of purification?

Pure protein = > 100% protein

First step = > new concentration = 0.001 * 10 % = 0.01%

Second step = > new concentration = 0.01%*10 = 0.1%

Third step = > 0.1% * 10 = 1%

Fourth step = > 1% * 10 = 10%

Fifth step=> 10% * 10 = 100%.

So, 5 steps are needed.