How is 10^4 derived? Please show all calculation steps. # of cells per mL = (Average)*DF*10^4 %3D

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### Derivation of the 10^4 Factor in Cell Counting

**Question:**  
How is 10^4 derived? Please show all calculation steps.

**Cell Counting Equation:**  
\[
\text{# of cells per mL} = (\text{Average}) \times \text{DF} \times 10^4
\]

**Explanation:**  
In cell counting using a hemocytometer, the factor \(10^4\) comes into play based on three critical components of the cell counting process:

1. **Volume of the Counting Chamber**:
   - The hemocytometer has a counting chamber where the depth is 0.1 mm (or 0.0001 cm) and the area is usually 1 mm² (or 0.01 cm²). 
   - Therefore, the volume of this chamber is:
     \[
     \text{Volume} = \text{Area} \times \text{Depth} = (0.01 \text{ cm}^2) \times (0.01 \text{ cm}) = 0.0001 \text{ cm}^3
     \]
   - Since 1 cm³ = 1 mL, the volume becomes 0.0001 mL.

2. **Scaling Factor**:
   - When counting cells, we usually count the number in a smaller grid of the net (e.g., 1 mm² of the hemocytometer corresponds to 0.1 mm depth, resulting in 0.0001 mL).
   - To convert this number to the number of cells per mL, we need to multiply by \( \frac{1}{\text{Volume of a chamber}} \):
     \[
     \frac{1}{0.0001 \text{ mL}} = 10^4
     \]
   
3. **Dilution Factor (DF)**:
   - If a sample is diluted before counting, we need to take into account the dilution factor. The dilution factor \( \text{DF} \) corrects for any pre-counting dilution so that we get an accurate number of cells per mL in the original sample.

Putting it all together, the number of cells per mL is defined as:
\[
\text{# of cells per mL} = (\text{Average number of cells counted}) \times \text{DF} \times 10^
Transcribed Image Text:### Derivation of the 10^4 Factor in Cell Counting **Question:** How is 10^4 derived? Please show all calculation steps. **Cell Counting Equation:** \[ \text{# of cells per mL} = (\text{Average}) \times \text{DF} \times 10^4 \] **Explanation:** In cell counting using a hemocytometer, the factor \(10^4\) comes into play based on three critical components of the cell counting process: 1. **Volume of the Counting Chamber**: - The hemocytometer has a counting chamber where the depth is 0.1 mm (or 0.0001 cm) and the area is usually 1 mm² (or 0.01 cm²). - Therefore, the volume of this chamber is: \[ \text{Volume} = \text{Area} \times \text{Depth} = (0.01 \text{ cm}^2) \times (0.01 \text{ cm}) = 0.0001 \text{ cm}^3 \] - Since 1 cm³ = 1 mL, the volume becomes 0.0001 mL. 2. **Scaling Factor**: - When counting cells, we usually count the number in a smaller grid of the net (e.g., 1 mm² of the hemocytometer corresponds to 0.1 mm depth, resulting in 0.0001 mL). - To convert this number to the number of cells per mL, we need to multiply by \( \frac{1}{\text{Volume of a chamber}} \): \[ \frac{1}{0.0001 \text{ mL}} = 10^4 \] 3. **Dilution Factor (DF)**: - If a sample is diluted before counting, we need to take into account the dilution factor. The dilution factor \( \text{DF} \) corrects for any pre-counting dilution so that we get an accurate number of cells per mL in the original sample. Putting it all together, the number of cells per mL is defined as: \[ \text{# of cells per mL} = (\text{Average number of cells counted}) \times \text{DF} \times 10^
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