Math Problem Statement

A plate with 111 colonies was inoculated with 100 μL Volume of a 10^-9 Dilution. Given the formula OCD = CFU / (V × D), what is the Original Colony Density?

Solution

The problem asks for the Original Colony Density (OCD) using the formula:

OCD=CFUV×DOCD = \frac{\text{CFU}}{V \times D}

Where:

  • CFU is the number of colony-forming units, which is 111.
  • V is the volume in mL. Since the volume given is 100 μL, this converts to 0.1mL0.1 \, \text{mL} (since 100μL=0.1mL100 \, \mu L = 0.1 \, \text{mL}).
  • D is the dilution factor, which is 10910^{-9}.

Now, plugging in these values:

OCD=1110.1×109=1111010=1.11×1012CFU/mLOCD = \frac{111}{0.1 \times 10^{-9}} = \frac{111}{10^{-10}} = 1.11 \times 10^{12} \, \text{CFU/mL}

The correct answer is:

1.11×1012CFU/mL1.11 \times 10^{12} \, \text{CFU/mL}

Let me know if you would like more details or have any other questions!

Here are some related questions:

  1. How does dilution impact the original colony density?
  2. What is the significance of using CFU/mL in microbiology experiments?
  3. How do you convert between microliters (μL) and milliliters (mL)?
  4. What does the dilution factor tell you in the context of bacterial growth?
  5. How does the volume of inoculation affect colony counts?

Tip: When using formulas with units, always ensure the units are consistent, such as converting μL to mL if required.

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Math Problem Analysis

Mathematical Concepts

Microbiology Colony Density Calculation
Unit Conversion
Algebra

Formulas

OCD = CFU / (V × D)

Theorems

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Suitable Grade Level

College/University Level (Microbiology/Biology)