A microbiologist performs serial dilutions, reducing a bacterial culture by a factor of 10 at each step. After 6 dilutions, she plates 0.1 mL of the final dilution on an agar plate containing 1×10⁴ bacteria per mL. How many bacteria were plated?

["How Many Bacteria Were Plated? Understanding Serial Dilution in Microbiology", "In microbiology, serial dilutions are essential techniques used to reduce the concentration of bacteria to levels suitable for accurate measurement and analysis. A common application involves diluting a bacterial culture by a factor of 10 at each step, enabling researchers to quantify microbial populations with precision. This article explores a precise example: a microbiologist performs six consecutive 10-fold dilutions, then plates a small volume from the final dilution—a critical step for colony-forming unit (CFU) estimation. We’ll determine exactly how many bacteria are plated when 0.1 mL of the final dilution is used.", "### What Is Serial Dilution?", "Serial dilution involves systematically reducing the concentration of microorganisms by dividing a sample and carrying it forward into fresh medium in progressively smaller proportions. Here, the dilution factor is 10 at each step, meaning every 1 mL of culture is mixed with 9 mL of dilution medium—resulting in a 1:10 dilution ratio.", "### Calculating the Total Dilution Factor", "Each dilution step multiplies the concentration by 1/10. Performing six dilutions sequentially gives a total dilution factor equal to:", "[\n10 \ imes 10 \ imes 10 \ imes 10 \ imes 10 \ imes 10 = 10^6\n]", "This means the original bacterial culture was diluted by a factor of 1,000,000.", "### Starting Culture and Final Dilution", "Assuming the initial culture contains a very high concentration of bacteria—say, ( C_0 )—and knowing that after six 10-fold dilutions, the concentration in the final tube is:", "[\nC_{\ ext{final}} = \frac{C_0}{10^6}\n]", "The microbiologist plates 0.1 mL (i.e., ( 10^{-1} ) mL) of this final dilution onto an agar plate containing ( 1 \ imes 10^{-9} ) bacteria per mL.", "To find the number of bacteria plated, multiply the volume plated by the concentration in that volume:", "[\n\ ext{Bacteria plated} = \ ext{Volume plated} \ imes \ ext{Concentration in plate}\n]", "Substitute the known values:", "[\n= (0.1 , \ ext{mL}) \ imes (1 \ imes 10^{-9} , \ ext{bacteria/mL}) = 1 \ imes 10^{-10} , \ ext{bacteria}\n]", "### Interpretation", "Despite the huge initial concentration, the serial dilution dilutes the sample 1 millionfold. As a result, only ( 1 \ imes 10^{-10} ) bacteria are present in the 0.1 mL plated volume. This low count ensures accurate colony counting—where each colony originates from a single bacterial cell—without overgrowth or dilution errors.", "### Why This Matters in Microbiology", "Serial dilutions allow microbiologists to safely quantify bacterial populations that are otherwise too dense to resolve in a single colony count. Using a standardized volume (e.g., 0.1 mL) ensures reproducibility and compatibility with standard reporting units (CFU/mL). The method hinges on precise dilution factors and accurate microbial viable counts, forming the foundation of microbial enumeration in research and clinical diagnostics.", "### Conclusion", "When a microbiologist performs six 10-fold serial dilutions and plates 0.1 mL onto an agar plate with ( 1 \ imes 10^{-9} ) bacteria per mL, the number of bacteria plated is:", "[\n\boxed{1 \ imes 10^{-10}}\n]", "This calculation illustrates how serial dilution transforms a concentrated culture into a measurable quantity, enabling precise microbial analysis in both research and quality control settings."]