Orientation Lab Example Math Problems

Example Math Problems

  1. You diluted a bacterial culture through 6 rounds (6 wells) of dilution. After plating 100µL, you count 43 colonies. What was the concentration of bacteria in the culture? (The common unit of concentration/density of bacteria is CFU (colony forming units) / mL).

    Working backwards from the Petri dish to the sample works best:

    43 colonies on the dish = 43 bacterial cells

    [43 bacterial cells / 100µL (amount plated)] × (1000µL/mL) = 430 CFU/mL

    So that makes 4.3 × 102 CFU/mL in the well that was plated

    Or, 4.3 × 102 CFU/mL / (1/10 dilution) = 4.3 × 103 CFU/mL in the fifth well

    Or, 4.3 × 103 CFU/mL / (1/10 dilution) = 4.3 × 104 CFU/mL in the fourth well
    ...
    Or, 4.3 × 106 CFU/mL / (1/10 dilution) = 4.3 × 107 CFU/mL in the first well

    Finally, 4.3 × 107 CFU/mL / (1/10 dilution) = 4.3 × 108 CFU/mL in the culture



  1. You have been informed that a tube of bacteria has a density of 6.7 × 104 CFU/mL. What well should you sample and how many colonies should you expect?


First off, you want Petri dishs with easily countable numbers of colonies (30-300). Too few and you can get an imprecise measurement; too many and you won't be able to count them all.

If you plated 100µL (.1 mL) of the sample directly:

6.7 × 104 CFU/mL * .1 mL = 6700 CFU (or 6700 colonies); quite uncountable.

Plating of the first titer well:

6.7 × 104 CFU/mL × (1/10 dilution) = 6.7 × 103 CFU/mL in the first well

6.7 × 103 CFU/mL × .1 mL = 670 CFU; still outside of the acceptable range

Plating of the second well:

6.7 × 104 CFU/mL × (1/10 dilution) × (1/10 dilution) × .1 mL = 67 CFU;

So, you would want to dilute to the second well and expect 67 colonies on the Petri dish.

In-class problems

  1. You diluted a bacterial culture through 4 rounds (4 wells) of dilution. After plating 100µL and incubating, you count 72 colonies. What was the concentration of the bacteria in the culture?




  1. A sample of bacteria should have a concentration of 4.4 × 107 CFU/mL; how many colonies at what dilution (what well) would you use to confirm this?




At home (for self-gratification)

  1. You discover that the microtiter plate (used in Problem 3) actually was filled with only 170µL of saline (instead of 270µL). What is the corrected concentration of bacteria?