Q.84. 𝐀𝟏𝟎𝟎𝝁𝐥 aliquot ( 𝟏𝟎^−𝟒 dilution) of the bacterial culture plated on the nutrient agar gave 4
colonies. The bacterial stock concentration (in million cells /𝐦𝐥, rounded off to one decimal place) is ____

Calculating Bacterial Stock Concentration from Dilution Plating

A 100 µl aliquot from a 10⁻⁴ dilution of a bacterial culture
produces 4 colonies on nutrient agar.
This allows estimation of the viable cell concentration in the original stock.

The calculated stock concentration is:
0.4 million cells/ml.

Calculation Method

Each colony represents one viable cell (CFU) present in the plated volume of the diluted sample.

Concentration in diluted sample =
Number of colonies / Volume plated

= 4 / 0.1 ml = 40 cells/ml

Applying the dilution factor:

Stock concentration = 40 × 10⁴ = 400,000 cells/ml

Expressed in millions:

400,000 cells/ml = 0.4 million cells/ml

Formula Used

Stock concentration (cells/ml) =
(Number of colonies / Volume plated in ml) × Dilution factor

Step-by-Step Derivation

• Convert volume:
  100 µl = 0.1 ml
• CFU/ml in 10⁻⁴ dilution:
  4 / 0.1 = 40 CFU/ml
• Original stock concentration:
  40 × 10⁴ = 4 × 10⁵ cells/ml
• Convert to millions:
  4 × 10⁵ = 0.4 million cells/ml

Although ideal colony counts range from 30–300 colonies per plate,
a lower count (4 colonies) is still valid for calculation in exam-style problems.

Common Pitfalls Explained

• Forgetting volume conversion:
  Treating 100 µl as 1 ml leads to a 10× overestimation
  (incorrectly giving 4.0 million cells/ml).
• Ignoring dilution factor:
  Using 40 cells/ml directly ignores the 10⁻⁴ dilution.
• Wrong unit conversion:
  Million cells/ml requires dividing by 10⁶;
  400,000 / 1,000,000 = 0.4.
• Rounding errors:
  0.40 correctly rounds to 0.4.

Applications in Microbiology

Dilution plating is a standard technique for estimating
colony-forming units (CFU) in microbiology labs.
It is widely used in clinical diagnostics, food microbiology,
environmental testing, and research laboratories.