A serial dilution is a sequence of identical steps, and because each one multiplies rather than subtracts, the total runs away from intuition very quickly.
final concentration = initial ÷ (dilution factor)ⁿ
Starting at 100,000,000 CFU per millilitre and performing five one-in-ten steps, the serial dilution calculator gives 1,000 CFU per millilitre, a total dilution of 100,000 times. The five steps were each small and the result is five orders of magnitude.
Ten steps is ten billion
Run five more of the same steps and the total dilution is 10,000,000,000 times, leaving 0.01 CFU per millilitre. That is not a hundredth of an organism, since organisms do not come in hundredths. It means roughly one organism in every hundred millilitres, and at that point a single millilitre sample most likely contains nothing at all.
This is the basis of plate counting. You dilute until the expected count per plate lands in a countable range, typically 30 to 300 colonies, then multiply back up by the dilution factor. Getting that range right is the whole skill, because a plate with 2,000 colonies cannot be counted and a plate with 2 cannot be trusted.
Why logs are the working unit
Once numbers span ten orders of magnitude, percentages stop communicating. A treatment that reduces a million organisms to ten is a 99.999 per cent reduction, and one that reduces a million to one is 99.9999 per cent. Written out, those look like the same number with a typo. As a log reduction they are 5 and 6, and the difference is obviously a factor of ten in survivors.
That is why disinfection and sterilisation standards are written in logs. It is not jargon for its own sake: it is the only notation in which the difference between adequate and inadequate is visible at a glance. A 6-log reduction is the common sterilisation benchmark, and the gap between it and a 4-log reduction is a hundredfold in what survives, while the percentages differ in the fourth decimal place.
Dilution arithmetic in the other direction
Most lab dilutions are not serial but single step, where the question is how much stock to take to reach a target concentration. That is the C₁V₁ = C₂V₂ relation, and the dilution calculator solves it for whichever term you are missing.
The reason to use a serial dilution instead of one enormous single step is accuracy. Diluting one in ten thousand in a single pipetting operation means measuring a volume so small that the error dominates the result. Four one-in-ten steps reach the same place using volumes you can actually measure, at the cost of compounding four small errors instead of making one large one.
For getting the starting concentration right in the first place, molarity converts a mass and a molar mass into a concentration.