(key)
1) The Federal debt.
- The population of the United States in 1960 was about 179,000,000 people. Express this number in scientific notation. (1.79 x 10 8 persons)
- The U.S. Federal Debt in 1960 was about $290,000,000,000. Express this number in scientific notation. (2.9 x 10 11 dollars)
- Calculate the Federal Debt per person in 1960, express your answer in scientific notation. (1.62 x 10 3 dollars/person)
- The population of the U.S. in December 2009 was about 308,000,000 people. Express this number in scientific notation. (3.08 x 10 8 persons)
- The U.S. Federal Debt in December 2009 was about $12,100, 000,000,000. Express this number in scientific notation. (12.1 x 10 12 dollars)
- Calculate the Federal Debt per person in Dec. 2009. (3.93 x 10 4 dollars per person)
2) Molecules
Avogadro’s number 6.02 x 10 23 (This is the number of particles in a mole.)
Since the formula weight of water is 18.00 grams/mole, and the density of water under the conditions of the experiment is 1.00 grams/ml, how many molecules of water are in
1.00 liter of pure water?
- First calculate the mass of 1.00 liter of water. (1000 grams)
- Next calculate the number of moles in 1000 grams of water.
(1000 g/liter / 18.00 g/mole = 55.6 moles/liter)
- Then determine the number of molecules in this number of moles.
(55.6 moles/liter x 6.02 x 10 23 molecules/mole = 3.35 x 10 25 molecules/liter)
3) Bacteria
A tank used for waste water treatment holds 3.95 x 10 bacteria in the water is 5.6 x 10 6
5 liters. The concentration of
cells per ml. What is the number of bacteria in the tank?
Remember: 1 liter = 1 x 10 3 ml.
(3.95 x 10 5 liters) x (1.000 x 10 3 ml/liter) x (5.6 x 10 6 cells/ml) = 2.2 x 10 15 cells

(key)
1) You dilute a solution of NaCl by mixing 25 ml of the stock with 175 ml of water.
What is the dilution? ___________________
(1/8 or 0.125)
If the concentration of the NaCl stock is 4.0 M, what is the concentration of the diluted solution?
_________________________
(0.50 M)
2) A certain brand of rum has an ethanol concentration of 30% (60 proof). The alcohol is diluted by mixing 2 oz. of rum with 8 oz. of cola.
What is the dilution? __________________________
(1/5)
What is the concentration of alcohol in the mixed drink?
(6%)
3) You dilute a culture of bacteria by mixing 100  l with 9.9 ml of sterile saline.
What is the dilution? ___________________
(HINT: 1 ml = 1000  l)
(1/100 or 0.01)
If the bacterial culture initially had a concentration of 1 x 10 bacteria would be found in 10  l of the diluted culture?
7 cells per ml, how many
______________________
(1000 or 1 x 10 3 )
4) To prepare 100 ml of a 50.0 mM solution of KCl from a stock solution that is 1.00 M,
use:
___________ ml of 1.00 M KCl and _____________ ml of distilled water
(5.00 ml of 1.00 M KCl and 95.0 ml of water.)

(key)
1) A sample of bacteria is diluted as follows:
0.10 ml of the sample is diluted with 9.9 ml of sterile saline,
then 0.10 ml of the diluted sample is diluted with 9.9 ml of sterile saline,
then 1.0 ml of that diluted sample is diluted with 9.0 ml of sterile saline.
What is the total dilution for this serial dilution procedure?
_______________________
(1 x 10 -5 )
2) To prepare a suspension of bacteria with a concentration of 2.0 x 10 4 from a stock culture that has a concentration of 4.0 x 10 8
cells per ml
cells per ml you need to use a dilution of:
_______________________.
(5 x 10 -5 )
3) Assume an overnight culture of a bacterium has a concentration of 5.0 x 10 8 cells/ml.
The culture is diluted as follows:
0.10 ml of the overnight culture is diluted with 9.9 ml of sterile saline,
then 0.10 ml of the diluted sample is diluted with 9.9 ml of sterile saline,
then 0.10 ml of that diluted sample is diluted with 9.9 ml of sterile saline.
What is the concentration of bacteria in the most diluted solution?
_________________
(5.0 x 10 2 cells/ml)
4) A sample of bacteria is diluted as follows:
1.0 ml of the sample is diluted with 5.0 ml of sterile saline,
then 1.0 ml of the diluted sample is diluted with 6.0 ml of sterile saline,
then 1.0 ml of that diluted sample is diluted with 14.0 ml of sterile saline.
What is the total dilution for this serial dilution procedure?
_______________________
(1/630 or 1.59 x 10 -3 )
5) To prepare a suspension of bacteria with a concentration of 3.0 x 10 3 cells per ml from a stock culture that has a concentration of 1.2 x 10 9 dilution of:
cells per ml you need to use a
_______________________.
(2.5 x 10 -6 )
6) Assume an overnight culture of a bacterium has a concentration of 6.0 x 10
The culture is diluted as follows:
8 cells/ml.
0.10 ml of the overnight culture is diluted with 99.9 ml of sterile saline,
then 0.10 ml of the diluted sample is diluted with 99.9 ml of sterile saline.
What is the concentration of bacteria in the most diluted solution?
_________________
(6.0 x 10 2 cells/ml)

(key)
1) A sample of an overnight culture of Staphylococcus epidermidis is diluted by the serial dilution technique and 0.10 ml aliquots of various dilutions are spread on plates of
L-agar. After incubation, the following numbers of colonies are seen. What is the concentration of viable bacteria in the overnight culture. (Include units in your answer.)
Dilution: 10 -4 10 -5 10 -6 10 -7
Number of colonies: too many ~ 600 59 7
Show your calculations here. cfu/ml = ___ (# of colonies) _
(amt. plated) x (dilution) cfu/ml = ____59_______ = 59 x 10 7
(0.1 ml) x (10 -6 )
The concentration of
Staphylococcus epidermidis 5.9 x 10 8 cfu/ml in the overnight culture is: _____________________________________
2) A sample of an overnight culture of Escherichia coli is diluted by the serial dilution technique and 0.10 ml aliquots of various dilutions are spread on plates of L-agar. After incubation, the following numbers of colonies are seen. What is the concentration of viable bacteria in the overnight culture. (Include units in your answer.)
Dilution: 10 -4 10 -5 10 -6 10 -7 10 -8
Number of colonies: too many too many ~ 450 48 4
Show your calculations here. cfu/ml = ____48_______ = 48 x 10 8
(0.1 ml) x (10 -7 )
The concentration of
Escherichia coli 4.8 x 10 9 in the overnight culture is: _____________________________________