A culture of 8108 cellsml was diluted as follows 01 ml into

A culture of 8×10^8 cells/ml was diluted as follows:
0.1 ml into 99.9 ml
1.0 ml into 9 ml
1.0 ml into 999 ml
Plate 0.2 ml
What is the total dilution factor?
How many colonies are expected to grow on the plate?

Solution

First, 0.1 ml into 99.9 ml is added. This is roughly 0.1/100 or 1/1000; so, dilution factor becomes 10^-3

1ml of 10^-3 is added to 9ml. So, it becomes 1/10^th of 10^-3. So, dilution factor now becomes 10^-4.

Now, 1ml of 10^-4 is added to 999ml (~1000ml). So, now dilution factor becomes 10^-7.

Therefore, the total dilution factor is 10^-7.

0.2 ml of 10^-7 is plated.

10^0 dilution has 8*10^8 cells/ml

10^-7 dilution will have 8*10^8 * 10^-7 = 80 cells/ml

In 1ml, 80 cells are there.

So, in 0.2ml number of cells = 0.2*80 = 16cells.

So, number of expected colonies = 16