If you are diluting with a dilution factor of 10 each time, your initial concentration is 1 then the second concentration is 0.1, like you said. In a serial dilution, this will be repeated to dilute the second concentration by a factor of 10, to give a concentration of 0.01. This is a dilution factor of 100 from your initial concentration.
So however many times you dilute, the dilution factor between the initial and final concentration will be greater than the initial dilution.