What is the final sample dilution in a multiple dilution series with dilutions of 1/4 (tube 1), 1/2 (tube 2), 1/5 (tube 3), and 1/10 (tube 4)?

Calculating Final Sample Dilution in a Multiple Dilution Series

The final sample dilution in a multiple dilution series with dilutions of 1/4 (tube 1), 1/2 (tube 2), 1/5 (tube 3), and 1/10 (tube 4) is 1/400.

Understanding Serial Dilution Calculations

When performing multiple dilutions in series, the final dilution is calculated by multiplying all individual dilution factors together. This follows standard laboratory dilution principles as outlined in clinical laboratory guidelines 1.

Step-by-Step Calculation:

1. Identify each dilution factor:

   • Tube 1: 1/4 (dilution factor = 4)
   • Tube 2: 1/2 (dilution factor = 2)
   • Tube 3: 1/5 (dilution factor = 5)
   • Tube 4: 1/10 (dilution factor = 10)

2. Multiply all dilution factors together:

   • 4 × 2 × 5 × 10 = 400

3. Express final dilution as a fraction:

   • Final dilution = 1/400

Importance of Proper Dilution Calculations

Accurate dilution calculations are critical in laboratory settings for several reasons:

• Analytical accuracy: Proper dilution ensures measurements fall within the analytical measurement range of instruments 1
• Result interpretation: For immunoassays and microbiological testing, correct dilution factors are essential for accurate reporting 1
• Sample preparation: When preparing samples for analysis, understanding the final dilution helps in calculating the actual concentration in the original sample 1

Common Pitfalls to Avoid

• Confusing dilution ratio with dilution factor: The dilution ratio (e.g., 1:10) represents the proportion of sample to total volume, while the dilution factor (10) represents how many times more dilute the solution is compared to the original 1
• Forgetting to multiply sequential dilutions: Each dilution in a series compounds the previous one; they must be multiplied together, not added 2
• Misinterpreting final concentrations: To determine the actual concentration in the original sample, multiply the measured concentration by the total dilution factor (400 in this case) 1

Practical Applications

In laboratory settings, serial dilutions are commonly used for:

• Microbial enumeration using plate count methods 3
• Preparation of standard curves for analytical procedures 1
• Antibody titer determinations in immunoassays 1
• Antimicrobial susceptibility testing 2

Understanding the final dilution is essential for accurately interpreting results and ensuring reliable laboratory data.