We commonly use multiple dilutions of a single sample in procedures for estimating concentrations of serum proteins or counting cells is suspension. Frequently, these will be very high dilutions. By making a series of small dilutions rather than one large dilution, we minimize the use of excess reagents and decrease the chance of making measurement errors. Serial dilutions are a series of equal small dilutions used to obtain a large final dilution. For example, we might want to do 5 serial two-fold dilutions. We could do this by adding 1 mL of solute to 1 mL of solvent, mixing, transferring 1 mL of this mixture to another mL of solvent, mixing, transferring to 1 mL of solvent and so on. The dilution would be 1/2 in the first tube, 1/4 in the second, then 1/8, 1/16 and finally 1/32 in the final tube. Likewise, we could perform serial 5-fold dilutions by transferring 1 mL of solute into 4 mL of solvent . The dilutions for 5 of these steps would be 1/5, 1/25, 1/125, 1/625 and 1/3125. You can see the savings in solvent clearly in the latter example as only 25 mL of solvent was necessary to this 3,000+-fold dilution. I find that it helps to think in terms of parts when working with x-fold dilutions. For example, a 5-fold dilution is composed of 5 parts, 1 of solute and 4 of solvent; a 10-fold dilution has 1 part solute, 9 parts solvent. However, in these and other problems, make sure that you keep careful track of units (mL vs µL, etc).