**Viable Counts: Dilution Arithmetic - Basics**

The answer to the dilution problem is in scientific notation:

**a**x10^{b}

The variable **a** is the coefficient. Variable **b** is the exponent. Remember that:

4x10^{5} = 400,000

3x10^{6} = 3,000,000

2x10^{7} = 20,000,000

1x10^{8} = 100,000,000

Dilution

###### Dilution Example 1

If a sample has 4x10^{8} (or 400,000,000) bacteria and it is diluted as follows:

1ml sample

__9ml diluent__

10ml resulting dilution

The resulting dilution has 4x10^{7} bacteria.

###### Dilution Example 2

If a sample has 4x10^{8} (or 400,000,000) bacteria and it is diluted as follows:

1ml sample

__99ml diluent__

100ml resulting dilution

The resulting dilution has 4x10^{6} bacteria.

###### Dilution Example 3

If a sample has 4x10^{8} (or 400,000,000) bacteria and it is diluted as follows:

1ml sample

__999ml diluent__

1,000ml resulting dilution

The resulting dilution has 4x10^{5} bacteria.

###### Dilution Example 4

If a sample has 4x10^{8} (or 400,000,000) bacteria and it is diluted as follows:

1ml sample

__19ml diluent__

20ml resulting dilution

The resulting dilution has 2x10^{7} bacteria (=400,000,000 x (1/20))

###### Dilution Example 5

If a sample has 4x10^{8} (or 400,000,000) bacteria and it is diluted as follows:

1ml sample

__399ml diluent__

Total 400ml

The resulting dilution has 1x10^{6} bacteria (=400,000,000 x (1/400))

## Inoculation and Incubation

After diluting the sample plates are inoculated. Typically, 100 µl is inoculated which is 0.1 ml.

If the dilution has 4x10^{3} (or 4,000) bacteria then the inoculation will have an average of 4x10^{2} (or 400) bacteria. In the Plate Count Simulation the resulting incubation would end up with TNTC meaning To Numerous To Count.

If the dilution has 5x10^{2} (or 500) bacteria then the inoculation will have an average of 5x10^{1} (or 50) bacteria. In this simulation the resulting incubation would end up with numbers between 46 and 54. Some variation is included in the plating computation to simulate the variations in actual bacteria growth.