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Age 14 to 16
Challenge Level
Imagine that you create a four-step dilution series, where the amounts of culture passed from one stage to the next and the amount of medium added at each stage are multiples of 10 between 10ml and 100ml each time. In each case there are initially 100,000 cells/ml; the final concentration is given in the diagram as a rounded number.
You can input your numbers into the dilution calculator.
Experiment with the dilution series to investigate these questions:
- What are the lowest/highest possible final concentrations?
- How could you create final concentrations of 10, 100, 160, 20, 125 and 1875 cells/ml?
- At each stage of dilution, how many different dilution factors are possible?
- Could you, or how would you, create an exact 1/11, a 1/17, and a 1/23 dilution?
- Could you, or how would you, create an exact 1/21 or 1/46 dilution?
- Explore impossible dilutions.
NOTES AND BACKGROUND
Dilution series are used in laboratories progressively to dilute a concentrated solution into a dilute solution. Diluting in the standard ratio 1:9 will create a solution of 10% of the concentration, otherwise called a 1/10 dilution. Successive 1/10 dilutions reduce the concentration by a factor of 10 each time, although other dilutions (as seen in this question) can be made by choosing other ratios.
Dilution series are used in laboratories progressively to dilute a concentrated solution into a dilute solution. Diluting in the standard ratio 1:9 will create a solution of 10% of the concentration, otherwise called a 1/10 dilution. Successive 1/10 dilutions reduce the concentration by a factor of 10 each time, although other dilutions (as seen in this question) can be made by choosing other ratios.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.