When a sample is diluted, the dilution factor is calculated in the following way. Diluting factor is equal to the volume of the original substance that was added to the diluting agent divided by total volume of the substance after dilution.

Here, the dilution factor is 10^-5. 1 ml of the final sample has 1/10^5 parts of the original sample. As 1 ml of the final sample has 42 cells of S. epidermidis, 1/10^5 m of the original sample had 42 cells of S. epidermidis. The number of cells in 1 ml of the original sample is 42*10^5

The number of cells of S. epidermidis in the original sample is 4.2*10^5