The original concentration in a sample is 5.1 x 10^9 cfu/ml. which sample volume should yield a countable plate

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.