Scientific Notation Problems (key)



Scientific Notation Problems (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 108 persons)

- The U.S. Federal Debt in 1960 was about $290,000,000,000. Express this number in scientific notation. (2.9 x 1011 dollars)

- Calculate the Federal Debt per person in 1960, express your answer in scientific notation. (1.62 x 103 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 108 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 1012 dollars)

- Calculate the Federal Debt per person in Dec. 2009. (3.93 x 104 dollars per person)

2) Molecules

Avogadro’s number 6.02 x 1023 (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 1023 molecules/mole = 3.35 x 1025 molecules/liter)

3) Bacteria

A tank used for waste water treatment holds 3.95 x 105 liters. The concentration of bacteria in the water is 5.6 x 106 cells per ml. What is the number of bacteria in the tank?

Remember: 1 liter = 1 x 103 ml.

(3.95 x 105 liters) x (1.000 x 103 ml/liter) x (5.6 x 106 cells/ml) = 2.2 x 1015 cells

MCB 101 Introductory Microbiology Lab

Dilution Problems (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 μl with 9.9 ml of sterile saline.

What is the dilution? ___________________

(HINT: 1 ml = 1000 μl)

(1/100 or 0.01)

If the bacterial culture initially had a concentration of 1 x 107 cells per ml, how many bacteria would be found in 10 μl of the diluted culture?

______________________

(1000 or 1 x 103)

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.)

Serial Dilution Problems (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 104 cells per ml from a stock culture that has a concentration of 4.0 x 108 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 108 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 102 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 103 cells per ml from a stock culture that has a concentration of 1.2 x 109 cells per ml you need to use a dilution of:

_______________________.

(2.5 x 10-6)

6) Assume an overnight culture of a bacterium has a concentration of 6.0 x 108 cells/ml.

The culture is diluted as follows:

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 102 cells/ml)

Viable Plate Count Problems (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 107

(0.1 ml) x (10-6)

The concentration of

Staphylococcus epidermidis 5.9 x 108 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 108

(0.1 ml) x (10-7)

The concentration of

Escherichia coli 4.8 x 109

in the overnight culture is: _____________________________________

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