*Adapted and significantly modified by JMB (2008) from C.W.
Brady. ÒDilutions and dilution
calculations,Ó Unpublished.
University of Wisconsin, Whitewater *

Bacteria are often present in such huge numbers that they can be difficult to count. Yet accurate counts are necessary for a variety of reasons like, for instance, assessing the quality of water or the safety of food. There are a number of counting techniques but most rely on the dilution of the sample to reduce the bacterial numbers down to a quantity that can be counted accurately.

Dilution requires the thorough mixing of a small, accurately measured sample with a large volume of sterile water, saline or other appropriate liquid called the diluent or a dilution blank. Accurate dilutions of a sample are obtained through the use of pipettes and the dilution blanks are precisely measured when prepared before the measuring experiment. For ease of calculation, dilutions are done in multiples of 10 or 100.

A single dilution is calculated as follows:

Dilution = __ volume of the sample __

total volume of the sample + diluent volume

For example the dilution of 1 mL into 9 mL equals:

__ 1 __ which is the same as __ 1 __ which is written 1/10 or 10^{-1}

1+9 10

This can be called, Òa one to ten dilution.Ó

When doing very high dilutions (like 1/10,000 or 1/1,000,000), it is more accurate to do the dilution in a series of smaller dilutions rather than in one giant dilution. This is called a dilution series or a serial dilution.

In a serial dilution, the final total dilution is a product of each individual dilution in the series. Thus, a series of 5, Òone to ten dilutions equals Òa one to one hundred thousandÓ dilution:

(1/10)
x (1/10) x (1/10) x (1/10) x (1/10) = 1/100,000 = 10^{-5} dilution

A typical dilution series is shown below:

Practice doing the calculations in the following examples: