Plate Counts & Serial Dilutions (CFU/mL)
Turn colonies on a plate into how many cells were in the original sample, by undoing the dilution and the plated volume.
A plate count is the most common measurement in a microbiology lab, and it is the one students get wrong most often, because the number you count is never the answer. You count colonies on a plate that received a fraction of a millilitre of a sample you already diluted a thousandfold, and the question asked how many cells were in one millilitre of the original. Get the arithmetic backwards and you are off by a factor of a thousand, which in a clinical lab is the difference between a contaminated water supply and a clean one. The same shape of calculation runs through drug dosing, pollutant concentration, and cell counts before a transfection. Learn it once here and you stop guessing whether to multiply or divide.
- Common Core · HSN-Q.A.1Use units as a way to understand problems and to guide the solution of multi-step problems.
- Common Core · HSN-Q.A.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Ohio · Ohio HS N.Q.1Reason quantitatively and use units to solve problems, including unit analysis.
- Multiply and divide fractions: A dilution factor is a fraction, and undoing it is division by that fraction.
- Read and write scientific notation: Plate counts land in the hundreds of thousands, so answers are reported as powers of ten.
- Set up a ratio and a proportion: CFU per mL is a rate, and every step here is scaling a rate up or down.
Prerequisites are inferred: pending teacher review.
Re-learn the skill with worked practice and clear examples.
The whole calculation in one formula, worked slowly: CFU per mL equals colonies divided by the volume plated, times the dilution factor.
You plate 0.1 mL of a 1 to 1000 dilution and count 58 colonies. What is the CFU per mL of the original sample?
Draft- A.5.8 x 10^4
- B.5.8 x 10^6
- C.5.8 x 10^3
- D.5.8 x 10^5
Show the worked solution ▾
Answer: D. 5.8 x 10^5
- Step 1: Divide by the volume plated: 58 divided by 0.1 mL is 580 per mL of the diluted liquid.
- Step 2: Multiply by the dilution factor: 580 times 1000 is 580,000.
- Step 3: Write it in scientific notation: 580,000 is 5.8 x 10^5 CFU/mL.
Why it's right: 58 / 0.1 x 1000 = 580,000, which is 5.8 x 10^5 CFU/mL.
- A: 5.8 x 10^4 is 58,000: it multiplies by the 1000 but never undoes the 0.1 mL, so the plated volume is treated as a whole millilitre.
- B: 5.8 x 10^6 multiplies by an extra ten, usually by dividing by 0.01 instead of 0.1.
- C: 5.8 x 10^3 is 5,800: it undoes the 0.1 mL correctly but then scales by a dilution factor of 10 instead of the 1000 the sample actually received.
Aligned to HSN-Q.A.1 · reading level ~grade 8
Three plates from the same sample read 9 colonies, 84 colonies and 512 colonies. Which one do you use for the calculation?
Draft- A.The 9, because it is easiest to count
- B.Average all three
- C.The 84, because it is in the countable range
- D.The 512, because more colonies is more data
Show the worked solution ▾
Answer: C. The 84, because it is in the countable range
- Step 1: Recall the range: A plate count is only trusted between about 30 and 300 colonies.
- Step 2: Test each plate: 9 is below 30, so chance dominates. 512 is above 300, so colonies have merged and the count is low. 84 sits in the range.
Why it's right: Only the 84 falls in the countable range, so only that plate gives a number worth scaling back up.
- A: Below 30 colonies, one or two stray cells move the final answer by a large percentage.
- B: Averaging pulls the untrustworthy plates back into an answer they should have been excluded from.
- D: Above 300 colonies merge into each other, so the count reads low no matter how carefully you count.
Aligned to HSN-Q.A.3 · reading level ~grade 8
- A student picks which of three plates to count before doing any arithmetic at all.
Fill these in as you work through the lesson.
- CFU (one colony, from one cell or one clump):
- Dilution factor (how many times smaller you made it):
- Countable range (about 30 to 300 colonies):
- Volume plated (usually 0.1 mL, not 1 mL):
CFU/mL = ( ) divided by ( ) times ( ).
- Why do dilution factors multiply instead of adding?
- Why does dividing by 0.1 mL make the number ten times bigger?
- A plate reads 12 colonies. Why can you not just use it?
- What can a plate count never tell you, no matter how carefully you count?
58 colonies, 0.1 mL plated, 1 to 1000 dilution. Step 1: 58 / 0.1 = 580 per mL of the diluted liquid. Step 2: 580 x 1000 = 580,000. Step 3: report 5.8 x 10^5 CFU/mL, two significant figures, on this medium under these conditions.