Math Problem Statement

For a 1 × 10^-1 dilution, you plated 0.120 mL. If you counted 300 colonies, how many CFU/mL would you have?

Solution

To solve the problem:

The formula for calculating CFU/mL is:

CFU/mL=Number of ColoniesVolume Plated (mL)×Dilution Factor\text{CFU/mL} = \frac{\text{Number of Colonies}}{\text{Volume Plated (mL)}} \times \text{Dilution Factor}

Given:

  • Number of colonies = 300
  • Volume plated = 0.120mL0.120 \, \text{mL}
  • Dilution factor = 1×101=0.11 \times 10^{-1} = 0.1

Now substitute into the formula:

CFU/mL=3000.120×10\text{CFU/mL} = \frac{300}{0.120} \times 10

Step-by-step:

  1. Divide 300 by 0.120: 3000.120=2500\frac{300}{0.120} = 2500
  2. Multiply by 10: 2500×10=25,000CFU/mL2500 \times 10 = 25,000 \, \text{CFU/mL}

Answer: 25,000 CFU/mL

Let me know if you want more clarification or have any questions!

Additional Questions:

  1. How does the dilution factor influence CFU/mL calculations?
  2. What is the importance of plating a consistent volume in such calculations?
  3. How would the CFU/mL change if only 150 colonies were counted?
  4. What is the significance of CFU/mL in microbiology?
  5. Why is it necessary to multiply by the inverse of the dilution factor?

Tip: Always ensure you include the proper dilution factor when calculating CFU/mL to avoid errors in your final result.

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Math Problem Analysis

Mathematical Concepts

Proportions
Dilution Calculations
Microbial Colony Counting

Formulas

CFU/mL = (Number of Colonies / Volume Plated) × Dilution Factor

Theorems

Principle of Proportionality in Dilutions

Suitable Grade Level

Undergraduate Microbiology or Biology