The original concentration is 5.1 × 10⁹ CFU / ml
In order to attain a countable plate, the number of CFU must be present in between 10 and 200 per ml.
Let us take 0.1 ml and dilute it to 1 ml.
This minimizes the concentration to 5.1 × 10⁹ × 10⁻¹ = 5.1 × 10⁸ CFU/ml
In order to minimize the concentration in between 10 and 200, it can be reduced to 5.1 × 10¹
The final concentration = 5.1 × 10¹ CFU/ml
Initial concentration = 5.1 × 10⁹ CFU/ml
Volume of sample with 5.1 × 10¹ CFU = 5.1 × 10¹ CFU × (1 ml / 5.1 × 10⁹ CFU)
= 1.0 × 10⁻⁸ ml
This is the volume to be taken to obtain countable value, 51 CFU.