Dilutions are useful in science when making solutions or growing an acceptable number of bacterial colonies to count. There are three formulas used to work microbiology dilution problems: finding individual dilutions, finding serial dilutions, and finding the number of organisms in the original sample.

To find a dilution of a single tube, use the formula: sample/(diluent + sample). The sample is the amount you are transferring into the tube, and the diluent is the liquid already in the tube. When you transfer 1 ml into 9 mls, the formula would be: 1/(1+9) = 1/10. This could also be written as 1:10.

After you have calculated the individual dilutions for each tube, multiply the dilutions when using serial dilutions. Serial dilutions are the culmination of a number of diluted tubes used in order to get smaller dilutions. When a sample diluted 1/100 is added to a sample diluted 1/10, the final dilution would be: (1/100) x (1/10) = 1/1000.

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Use this equation to determine the number of organisms in the original sample once you have found the dilution: number of colonies growing on plate x (1/volume used to put bacteria on plate) x (1/dilution). When a student uses 1ml on a plate from a tube diluted 1/100, and the plate grew 230 colonies, the formula would be: 230 x (1/1ml) x (1/(1/100)) = 23000 or 2.3 x 10^4.