Sample calculations

 

You will need to perform the calculations explained in this document in order to determine the concentration of bacteria in the standard plate count method.

 

In this method, you will start with a concentrated sample of bacteria and then you will have a number of other tubes where your sample has been diluted.  The bacteria in these tubes will then be put on an agar plate and allowed to grow overnight.  To perform the following calculations, you want to find the plate where between 30 and 300 colonies grew.

 

Each tube will be diluted by a certain factor compared to the previous tube.  This is called the serial dilution (SD). 

 

The serial dilution (SD) = the amount transferred (AT)/total volume (TV)

 

For example, if we transferred 1 ml from tube 1 to tube 2 which had 9 ml of media in it, then the serial dilution would be 1/(1+9) = 1/10 or 10-1.  In order to determine the total volume, you add the amount transferred to the volume of media in the tube that you transferred to.

 

Here is another example:  If you transfer 1 ml from tube 1 to tube 2 which had 99 ml of media in it, then what is the serial dilution?

SD = 1/(1+99) = 1/100 = 10-2

 

Let’s try one more but this one will be a little harder.  If you transfer 0.1 ml from tube 1 to tube 2 which had 9.9 ml of media, then what is the serial dilution?

SD = 0.1/(0.1+9.9) = 0.1/10.  Another way to write this is 1/100.  You just move the decimal point one place to the right in both the numerator and the denominator.  So, the SD = 10-2.

 

Another term that you will need to know is the total dilution.  To calculate the total dilution, you multiply the serial dilutions of all of the tubes that came before.  

 

However, when you multiply numbers with exponents, you must add the exponents.

If we multiply 10-1 and 10-2, the answer is 10-3.

 

Let’s say you want to determine the total dilution of tube 2.  You must know the serial dilutions of tube 1 and of tube 2.  If the serial dilution of tube 1 is 10-1 and the serial dilution of tube 2 is 10-2, then the total dilution of tube 2 is 10-3.  We get this number by multiplying 10-1 and 10-2.

 

One other thing that you must know is that in the standard plate count, the last step is to plate 0.1 ml of bacteria.  If we plated more than this, there would be too much volume of the plate.  However, we want to express the concentration of our original bacteria sample in terms of bacteria/ml.  0.1 ml is 1/10 of 1 ml.  Therefore, if we plate 0.1 ml, in order to determine the final concentration of our initial bacterial sample, we must multiply by 10.  Otherwise, we would be getting the number of bacteria/0.1 ml.  This should become clearer when we do the sample problems.

 

There are 4 steps that you need to go through to determine the concentration of bacteria in your original sample.

 

1.     Find the plate that resulted in between 30-300 colonies.  Which tube did this come from?

 

2.     You need to calculate the serial dilutions of all of the tubes up to and including your tube that resulted in the 30 – 300 colonies.

 

3.     You must determine the total dilution in your tube that resulted in the 30 – 300 colonies.  To do this, multiply all of the serial dilutions up to this tube.

You must then change the negative sign in the exponent to a positive sign.

 

4.     Multiply the number of colonies by the total dilution and by 10 if you plated 0.1 ml.

 

 

Example problems

 

When you do these problems, you may want to draw out what is happening as is pictured below:

 

 

Sample problem 1

 

You are given an undiluted sample of bacteria.  I will use the scheme above in this problem.  From the undiluted sample, you set up 3 additional tubes.  From the undiluted sample, you transfer 1 ml to tube A which has 9 ml of saline or media.  From tube A, you then transfer 0.1 ml of bacteria to tube B which has 9.9 ml of saline or media.  From tube B, you transfer 1 ml of bacteria to tube C which has 9 ml of saline or bacteria.  You then take 0.1 ml of bacteria from the undiluted tube, from tube A, from tube B and from tube C.  You plate these bacteria on agar plates and let them incubate for 24 hours.

 

After 24 hours, you observe the plates.  The plate that you streaked with the undiluted bacteria has too many colonies to count.  The plate that you streaked from tube A has 600 colonies.  The plate that you streaked from tube B has 250 colonies and the plate that you streaked from tube C has 20 colonies.  What was the original concentration of your bacteria in the undiluted tube?

 

Click here for the answer to problem 1.

 


Sample problem 2

 

You are given an undiluted sample of bacteria.   From the undiluted sample, you set up 3 additional tubes.  From the undiluted sample, you transfer 1 ml to tube A which has 9 ml of saline or media.  From tube A, you then transfer 1 ml of bacteria to tube B which has 99 ml of saline or media.  From tube B, you transfer 0.1 ml of bacteria to tube C which has 9.9 ml of saline or bacteria.  You then take 0.1 ml of bacteria from the undiluted tube, from tube A, from tube B and from tube C.  You plate these bacteria on agar plates and let them incubate for 24 hours.

 

After 24 hours, you observe the plates.  The plate that you streaked with the undiluted bacteria has too many colonies to count.  The plate that you streaked from tube A has 600 colonies.  The plate that you streaked from tube B has 400 colonies and the plate that you streaked from tube C has 50 colonies.  What was the original concentration of your bacteria in the undiluted tube?

 

Click here for the answer to problem 2.