Laboratory Exercises in Microbiology - part 10 pps

Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes A. Dilutions with Sample Problems © The McGraw−Hill Companies, 2002 Problem 6 C 1 ϭ 70% C 2 ϭ 50% V 2 ϭ 45 ml V 1 ϭ X Thus, 32.1 ml of 70% alcohol ϩ 12.9 ml of H 2 O ϭ 45 ml of a 50% alcohol solution. Problem 7 C 1 ϭ 20% C 2 ϭ 1% V 2 ϭ 150 ml V 1 ϭ X Thus, 12.5 ml of a 20% solution ϩ 237.5 ml of broth ϭ 250 ml of a 1% dextrose broth solution. Problem 8 C 1 ϭ 5% C 2 ϭ 2% V 2 ϭ 45 ml V 1 ϭ X Thus, 18 ml of 5% ϩ 27 ml of saline ϭ 45 ml of a 2% red blood cell suspension. Problem 9 C 1 ϭ 0.1% C 2 ϭ 0.02% V 2 ϭ X V 1 ϭ 25 ml Thus, prepare a total volume of 125 of a 0.02% solution from 25 ml of 0.01% solution by adding 100 ml of diluent to the latter. Problem 10 C 1 ϭ 95% C 2 ϭ X V 2 ϭ 38 ml V 1 ϭ 10 ml Problem 11 C 1 ϭ 10% C 2 ϭ X V 2 ϭ 15 ml V 1 ϭ 3 ml Problem 12 In order to make all units equal, you have to convert 10 grams to milligrams. stock solution ϭ 10,000 mg/ml final concentration ϭ 2 mg/ml IC 10,000 mg/ml ___ ϭ _____________ ϭ 5,000 FC 2 mg/ml Thus, the dilution factor is 5,000. To perform a 1:5000 dilution: Step #1 1 ml of 10,000 mg/ml stock solution protein ϩ 49 ml of diluent ϭ 1:50 dilution ϭ 200 mg/ml Step #2 1 ml of 200 mg/ml ϩ 9 ml of diluent ϭ 1:10 dilution ϭ 20 mg/ml Step #3 1 ml of 20 mg/ml ϩ 9 ml of diluent ϭ 1:10 dilution ϭ 2 mg/ml To check to make sure the correct dilution was made: 50 ϫ 10 ϫ 10 ϭ 5,000 424 Appendix A Dilutions with Sample Problems 70% 45 50 ϫ 45 ____ ϭ ___ X ϭ ________ X ϭ 32.1 ml 50% X 70 20% 250 ____ ϭ ___ 20X ϭ 250 X ϭ 12.5 ml 1% X 5% 45 ml 90 ___ ϭ _________ X ϭ ___ X ϭ 18 ml 2% X 5 0.1% X ______ ϭ _____ 0.02X ϭ 2.5 X ϭ 125 ml 0.02% 25 ml 95% 38 ml ____ ϭ _____ 38X ϭ 950 X ϭ 25% X 10 ml 10% 15 ml* ____ ϭ ______ 15X ϭ 30 X ϭ 2% X 3 ml *3 ϩ 12 ϭ 15 ml (total volume) Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes A. Dilutions with Sample Problems © The McGraw−Hill Companies, 2002 Problem 13 Make all units the same. 10 mg ϫ 1,000 ␮g/mg ϭ 10,000 ␮g stock solution ϭ 10,000 ␮g/ml final concentration ϭ 0.5 ␮g/ml IC 10,000 ␮g/ml ___ ϭ DF ϭ _____________ ϭ 20,000 FC 0.5 ␮g/ml Thus, the dilution factor is 20,000. Step #1 1 ml of 10,000 ␮g/ml ϩ 19 ml of diluent ϭ 1:20 dilution ϭ 500 ␮g/ml (10,000/20 ϭ 500) Step #2 1 ml of 500 ␮g/ml ϩ 99 ml of diluent ϭ 1:100 dilution ϭ 5 ␮g/ml (500/100 ϭ 5) Step #3 1 ml of 5 ␮g/ml ϩ 9 ml of diluent ϭ 1:10 dilution ϭ 0.5 ␮g/ml (5/10 ϭ 0.5) To check to make sure the correct dilution was made: 20 ϫ 100 ϫ 10 ϭ 20,000 To help you with these types of problems, always remember that volumes may change depending on the protocol, but the di- lution factor will always remain the same. For example: 1 ϩ 99 10 ϩ 990 1:100 dilution 0.1 ϩ 9.9 1 ϩ 4 10 ϩ 40 1:5 dilution 0.1 ϩ 0.4 1 ϩ 19 10 ϩ 190 1:20 dilution 0.1 ϩ 1.9 1 ϩ 249 10 ϩ 2,490 1:250 dilution 0.1 ϩ 24.9 1 ϩ 9 10 ϩ 90 1:10 dilution 0.5 ϩ 4.5 1 ϩ 7 5 ϩ 35 1:8 dilution 0.5 ϩ 3.5 1 ϩ 14 5 ϩ 70 1:15 dilution 0.5 ϩ 7.0 Problem 14 The first step is to establish the initial dilution as follows: 128 ____ ϭ 32 4 1:32 is the first step dilution, the second is 1:4. 1 ml of serum ϩ 31 ml of diluent ϭ 1:32 (individual dilution) 1 ml of the 1:32 dilution ϭ 3 ml of diluent ϭ 1:4 (individual dilution) To check to make sure the dilution was correctly made: 32 ϫ 4 ϭ 128 Appendix A Dilutions with Sample Problems 425 Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes A. Dilutions with Sample Problems © The McGraw−Hill Companies, 2002 Problem 15 We can obtain a 1:3000 dilution in 3 steps by using 1:30 and 1:10 dilutions. 3,000 _____ ϭ 1,500 2 1 ml of serum ϩ 29 ml of diluent ϭ 1:30 (individual dilution) 1 ml of 1:30 dilution ϩ 9 ml of diluent ϭ 1:10 (individual dilution) 1 ml of 1:10 ϩ 9 ml of diluent ϭ 1:10 (individual dilution) To check to make sure the dilution was correctly made: 30 ϫ 10 ϫ 10 ϭ 3,000 Problem 16 D 1 V 1 _____ ϭ ___ D 2 V 2 D 1 ϭ 1 D 2 ϭ 5 V 1 ϭ X V 2 ϭ 1 Thus, 0.2 ml (undiluted sera) ϩ 0.08 ml of saline ϭ 1.0. Problem 17 D 1 ϭ 1 D 2 ϭ 20 V 1 ϭ X V 2 ϭ 8 Thus, 0.4 ml of undiluted sera ϩ 7.6 ml of saline ϭ 1:20. Problem 18 2.01 ϫ 10 6 Problem 19 2.8 ϫ 10 6 Problem 20 3.8 ϫ 10 8 Problem 21 2.6 ϫ 10 9 Problem 22 4.6 ϫ 10 8 Problem 23 8.4 ϫ 10 10 426 Appendix A Dilutions with Sample Problems 1X __ ϭ __ 5X ϭ 1X ϭ 0.2 ml 51 1X __ ϭ __ 20X ϭ 8X ϭ 0.4 ml 20 8 Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes B. Metric and English Measurement Equivalents © The McGraw−Hill Companies, 2002 427 APPENDIX B Metric and English Measurement Equivalents The Metric System The metric system comprises three basic units of measure- ment: distance measured in meters, volume measured in liters, and mass measured in grams. In order to designate larger and smaller measures, a system of prefixes based on multiples of ten is used in conjunction with the basic unit of measurement. The most common prefixes are kilo = 10 3 = 1,000 centi = 10 –2 = 0.01 = 1/100 milli = 10 –3 = 0.001 = 1/1,000 micro = 10 –6 = 0.000001 = 1/1,000,000 nano = 10 –9 = 0.000000001 = 1/1,000,000,000 The English System The measurements of the English system used in the United States unfortunately are not systematically related. For ex- ample, there are 12 inches in a foot and 3 feet in a yard. Quick conversion tables for the metric and English systems are listed below. Units of Length Metric to English 1 centimeter (cm) or 10 mm = 0.394 in or 0.0328 ft 1 meter (m) = 100 cm or 1,000 mm = 39.4 in or 3.28 ft or 1.09 yd 1 kilometer (km) = 1,000 m = 3,281 ft or 0.621 mile (mi) The Number of: Multiplied by: Equals: millimeters 0.04 inches centimeters 0.4 inches meters 3.3 feet meters 1.1 yards kilometers 0.6 miles English to Metric 1 in = 2.54 cm 1 ft or 12 in = 30.48 cm 1 yd or 3 ft or 36 in = 91.44 cm or 0.9144 m 1 mi or 5,280 ft or 1,760 yd = 1,609 m or 1.609 km The Number of: Multiplied by: Equals: inches 2.5 centimeters feet 30.5 centimeters yards 0.9 meters miles 1.6 kilometers Units of Area Metric to English 1 square centimeter (cm 2 ) or 100 mm 2 = 0.155 in 2 1 square meter (m 2 ) = 1,550 in 2 or 1.196 yd 2 1 hectare (ha) or 10,000 m 2 = 107,600 ft 2 or 2.471 acres (A) 1 square kilometer (km 2 ) or 1,000,000 m 2 or 100 ha = 247 A or 0.3861 mi 2 The Number of: Multiplied by: Equals: square centimeters 0.16 square inches square meters 1.2 square yards square kilometers 0.4 square miles English to Metric 1 square foot (ft 2 ) or 144 in 2 = 929 cm 2 1 square yard (yd 2 ) or 9 ft 2 = 8,361 cm 2 or 0.836 m 2 1 acre or 43,560 ft 2 or 4,840 yd 2 = 4,047 m 2 = 0.405 ha 1 square mile (mi 2 ) or 27,878 ft 2 or 640 A = 259 ha or 2.59 km 2 The Number of: Multiplied by: Equals: square inches 6.5 square centimeters square feet 0.09 square meters square yards 0.8 square meters square miles 2.6 square kilometers acres 0.4 hectares Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes B. Metric and English Measurement Equivalents © The McGraw−Hill Companies, 2002 Units of Volume Metric to English 1 cubic centimeter (cm 3 or cc) or 1,000 mm 3 = 0.061 in 3 1 cubic meter (m 3 ) or 1,000,000 cm 3 = 61,024 in 3 or 35.31 ft 3 or 1.308 yd 3 The Number of: Multiplied by: Equals: cubic meters 35 cubic feet cubic meters 1.3 cubic yards English to Metric 1 cubic ft (ft 3 ) or 1,728 in 3 = 28,317 cm 3 or 0.02832 m 3 1 cubic yard (yd 3 ) or 27 ft 3 = 0.7646 m 3 The Number of: Multiplied by: Equals: cubic feet 0.03 cubic meters cubic yards 0.76 cubic meters Units of Liquid Capacity Metric to English 1 milliliter (ml) or 1 cm 3 = 0.06125 in 3 or 0.03 fl oz 1 liter or 1,000 ml = 2.113 pt or 1.06 qt or 0.264 U.S. gal The Number of: Multiplied by: Equals: milliliters 0.03 fluid ounces liters 2.10 pints liters 1.06 quarts English to Metric 1 fluid ounce or 1.81 in 3 = 29.57 ml 1 pint or 16 fl oz = 473.2 ml 1 qt or 32 fl oz or 2 pt = 946.4 ml 1 gal or 128 fl oz or 4 qt or 8 pt = 3,785 ml or 3.785 liters The Number of: Multiplied by: Equals: teaspoons 5 milliliters tablespoons 15 milliliters fluid ounces a 30 milliliters cups 0.24 liters pints 0.47 liters quarts 0.95 liters gallons 3.8 liters Units of Mass Metric to English 1 gram (g) or 1,000 mg = 0.0353 oz 1 kilogram (kg) or 1,000 g = 35.2802 oz or 2.205 lb 1 metric or long ton or 1,000 kg = 2,205 lb or 1.102 short tons The Number of: Multiplied by: Equals: grams 0.035 ounces kilograms 2.2 pounds English to Metric 1 ounce (oz) or 437.5 grains (gr) = 28.35 g 1 pound (1b) or 16 ounces = 453.6 g or 0.454 kg 1 ton (short ton) or 2,000 lb = 907.2 kg or 0.9072 metric ton The Number of: Multiplied by: Equals: ounces 28 grams pounds 0.45 kilograms tons 0.9 metric ton 428 Appendix B Metric and English Measurement Equivalents a 1 British fluid ounce = 0.961 U.S. fluid ounces or, conversely, 1 U.S. fluid ounce = 1.041 British fluid ounces. The British pint, quart, and gallon = 1.2 U.S. pints, quarts, and gallons, respectively. To convert these U.S. fluid measures, multiply by 0.8327. Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes C. Transmission−Absorbance Table for Spectrophotometry © The McGraw−Hill Companies, 2002 429 APPENDIX C Transmission-Absorbance Table for Spectrophotometry %TA %TA %TA %TA 1.0 2.000 26.0 0.585 51.0 0.292 76.0 0.119 1.5 1.824 26.5 0.577 51.5 0.288 76.5 0.116 2.0 1.699 27.0 0.569 52.0 0.284 77.0 0.114 2.5 1.602 27.5 0.561 52.5 0.280 77.5 0.111 3.0 1.523 28.0 0.553 53.0 0.276 78.0 0.108 3.5 1.456 28.5 0.545 53.5 0.272 78.5 0.105 4.0 1.398 29.0 0.538 54.0 0.268 79.0 0.102 4.5 1.347 29.5 0.530 54.5 0.264 79.5 0.100 5.0 1.301 30.0 0.523 55.0 0.260 80.0 0.097 5.5 1.260 30.5 0.516 55.5 0.256 80.5 0.094 6.0 1.222 31.0 0.509 56.0 0.252 81.0 0.092 6.5 1.187 31.5 0.502 56.5 0.248 81.5 0.089 7.0 1.155 32.0 0.495 57.0 0.244 82.0 0.086 7.5 1.126 32.5 0.488 57.5 0.240 82.5 0.084 8.0 1.097 33.0 0.482 58.0 0.237 83.0 0.081 8.5 1.071 33.5 0.475 58.5 0.233 83.5 0.078 9.0 1.046 34.0 0.469 59.0 0.229 84.0 0.076 9.5 1.022 34.5 0.462 59.5 0.226 84.5 0.073 10.0 1.000 35.0 0.456 60.0 0.222 85.0 0.071 10.5 0.979 35.5 0.450 60.5 0.218 85.5 0.068 11.0 0.959 36.0 0.444 61.0 0.215 86.0 0.066 11.5 0.939 36.5 0.438 61.5 0.211 86.5 0.063 12.0 0.921 37.0 0.432 62.0 0.208 87.0 0.061 12.5 0.903 37.5 0.426 62.5 0.204 87.5 0.058 13.0 0.886 38.0 0.420 63.0 0.201 88.0 0.056 13.5 0.870 38.5 0.414 63.5 0.197 88.5 0.053 14.0 0.854 39.0 0.409 64.0 0.194 89.0 0.051 14.5 0.838 39.5 0.403 64.5 0.191 89.5 0.048 15.0 0.824 40.0 0.398 65.0 0.187 90.0 0.046 15.5 0.810 40.5 0.392 65.5 0.184 90.5 0.043 16.0 0.796 41.0 0.387 66.0 0.181 91.0 0.041 16.5 0.782 41.5 0.382 66.5 0.177 91.5 0.039 17.0 0.770 42.0 0.377 67.0 0.174 92.0 0.036 17.5 0.757 42.5 0.372 67.5 0.171 92.5 0.034 18.0 0.745 43.0 0.367 68.0 0.168 93.0 0.032 18.5 0.733 43.5 0.362 68.5 0.164 93.5 0.029 19.0 0.721 44.0 0.357 69.0 0.161 94.0 0.027 19.5 0.710 44.5 0.352 69.5 0.158 94.5 0.025 20.0 0.699 45.0 0.347 70.0 0.155 95.0 0.022 20.5 0.688 45.5 0.342 70.5 0.152 95.5 0.020 21.0 0.678 46.0 0.337 71.0 0.149 96.0 0.018 21.5 0.668 46.5 0.332 71.5 0.146 96.5 0.016 22.0 0.658 47.0 0.328 72.0 0.143 97.0 0.013 22.5 0.648 47.5 0.323 72.5 0.140 97.5 0.011 23.0 0.638 48.0 0.319 73.0 0.137 98.0 0.009 23.5 0.629 48.5 0.314 73.5 0.134 98.5 0.007 24.0 0.620 49.0 0.310 74.0 0.131 99.0 0.004 24.5 0.611 49.5 0.305 74.5 0.128 99.5 0.002 25.0 0.602 50.0 0.301 75.0 0.125 100.0 0.000 25.5 0.594 50.5 0.297 75.5 0.122 Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes D. Logarithms © The McGraw−Hill Companies, 2002 A logarithm is the exponent of 10, indicating the power to which 10 must be raised to produce a given number. Since 1 is 10 0 and 10 is 10 1 , it is evident that the numbers be- tween 1 and 10 must be greater than 10 0 . Likewise, num- bers between 10 and 100 must be greater than 10 1 but less than 10 2 . These numbers will then have fractional expo- nents expressed as mixed fractions. If they are in fractional forms, they present difficulties in addition or subtraction, so it is best to express them as a decimal; for example, 10 0.3010 . A number written in the form b n is said to be in expo- nential form where b is the base and n is a logarithm. For example, in the following equation, N = b n the number N is equal to the base b to the exponent n . Let us say that b is equal to 2 and n is equal to 4. Written in ex- ponential form, we would have 2 4 . Two to the fourth power equals 16. In logarithmic form, we would write the log of N to the base b is n (log b N = n). So if we take 2 4 = 16 and place it in logarithmic form, we would have log 2 16 = 4. In the following tables, the logarithms are located in the body of the table, and the numbers from 1.0 to 9.9 are given in the left-hand column and the top row. For example, to lo- cate the logarithm of 4.7, read down the left-hand column to 47 and across the column to 0 to find 0.6721 (in the table, the zero and the decimal point are omitted for convenience). Finally, the following relationships should be remem- bered when working with logarithms: log 1 = log 10 0 =0 log 10 = log 10 1 =1 log 100 = log 10 2 =2 log 1,000 = log 10 3 =3 log 10,000 = log 10 4 =4 log 0.1 = log 10 –1 =–1 log 0.01 = log 10 –2 =–2 log 0.001 = log 10 –3 =–3 log 0.0001 = log 10 –4 =–4 Logarithms are particularly useful in graphical rela- tions that extend over a wide range of values since they have the property of giving equal relative weight to all parts of the scale. This is valuable in “spreading out’’ the values that would otherwise be concentrated at the lower end of the scale; for example, in graphing the growth of microbial populations in a culture versus time. Logarithms are also used in pH calculations. 430 APPENDIX D Logarithms Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes E. pH and pH Indicators © The McGraw−Hill Companies, 2002 431 APPENDIX E pH and pH Indicators pH is a measure of hydrogen ion (H + ) activity. In dilute so- lutions, the H + activity is essentially equal to the concentra- tion. In such instances, pH = –log [H + ]. The pH scale ranges from 0 ([H + ] = 1.0 0 M) to 14 ([H + ] = 10 –14 M). A pH meter should be used for accurate pH determina- tions, observing the following precautions: 1. Adjust the temperature of the buffer used for pH meter standardization to the same temperature as the sample. Buffer pH changes with temperature; for ex- ample, the pH of standard phosphate buffer is 6.98 at 0°C, 6.88 at 20°C, and 6.85 at 37°C. 2. It is important to stir solutions while measuring their pH. If the sample is to be stirred with a magnetic mixer, stir the calibrating buffer in the same way. 3. Be sure that the electrodes used with tris buffers are recommended for such use by the manufacturer. This is necessary because some pH electrodes do not give accurate readings with tris (hydroxymethyl) aminomethane buffers. In instances where precision is not required, such as in the preparation of routine media, the pH may be checked by the use of pH indicator solutions. By the proper selection, the pH can be estimated within ± 0.2 pH units. Some common pH indicators and their useful pH ranges are listed in the following table. All of the below indicators can be made by (1) dissolving 0.04 g of indica- tor in 500 ml of 95% ethanol, (2) adding 500 ml of dis- tilled water, and (3) filtering through Whatman No. 1 fil- ter paper. Indicators should be stored in a dark, tightly closed bottle. pH Indicator pH Range Full Acidic Color Full Basic Color Brilliant green 0.0–2.6 Yellow Green Bromcresol green 3.8–5.4 Yellow Blue-green Bromcresol purple 5.2–6.8 Yellow Purple Bromophenol blue 3.0–4.6 Yellow Blue Bromothymol blue 6.0–7.6 Yellow Blue Congo red 3.0–5.0 Blue-violet Red Cresol red 2.3–8.8 Orange Red Cresolphthalein 8.2–9.8 Colorless Red 2,4-dinitrophenol 2.8–4.0 Colorless Red Ethyl violet 0.0–2.4 Yellow Blue Litmus 4.5–8.3 Red Blue Malachite green 0.2–1.8 Yellow Blue-green Methyl green 0.2–1.8 Yellow Blue Methyl red 4.4–6.4 Red Yellow Neutral red 6.8–8.0 Red Amber Phenolphthalein 8.2–10.0 Colorless Pink Phenol red 6.8–8.4 Yellow Red Resazurin 3.8–6.4 Orange Violet Thymol blue 8.0–9.6 Yellow Blue All of the above indicators can be made by (1) dissolving 0.04 g of indicator in 500 ml of 95% ethanol, (2) adding 500 ml of distilled water, and (3) filtering through Whatman No. 1 filter paper. Indicators should be stored in a dark, tightly closed bottle. Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes F. Scientific Notation © The McGraw−Hill Companies, 2002 432 APPENDIX F Scientific Notation Microbiologists often have to deal with either very large or very small numbers, such as 5,550,000,000 or 0.00000082. The mere manipulation of these numbers is cumbersome. As a result, it is more convenient to express such numbers in scientific notation (standard exponential notation). Sci- entific notation is a set of rules involving a shorthand method for writing these numbers and performing simple manipulations with them. Scientific notation uses the fact that every number can be expressed as the product of two numbers—one of which is a power of the number of ten. Numbers greater than one can be expressed as follows: 1=10 0 100,000 = 10 5 10 = 10 1 1,000,000 = 10 6 100 = 10 2 10,000,000 = 10 7 1,000 = 10 3 100,000,000 = 10 8 10,000 = 10 4 1,000,000,000 = 10 9 In the above notations, the exponent to which the ten is raised is equal to the number of zeroes following the one. Numbers less than one can be expressed as follows: 0.1 = 10 –1 0.000001 = 10 –6 0.01 = 10 –2 0.0000001 = 10 –7 0.001 = 10 –3 0.00000001 = 10 –8 0.0001 = 10 –4 0.000000001 = 10 –9 0.00001 = 10 –5 In the above notations, the number of the negative exponent to which ten is raised is equal to the number of digits to the right of the decimal point. Numbers that are not an exact power of ten can also be dealt with in scientific notation. For example, a number such as 1234, which is greater than one, can be expressed in the following ways: 123.4 × 10 0.1234 × 10,000 12.34 × 100 0.01234 × 100,000 1.234 × 1,000 The same numbers can be expressed in scientific notation as follows: 123.4 × 10 1 0.1234 × 10 4 12.34 × 10 2 0.01234 × 10 5 1.234 × 10 3 The same reasoning is followed for numbers less than one. Consider the number 0.1234; it can be expressed in the fol- lowing ways: 1.234 × 0.1 1,234 × 0.0001 12.34 × 0.01 12,340 × 0.00001 123.4 × 0.001 The same numbers can be expressed in scientific notation as follows: 1.234 × 10 –1 1,234 × 10 –4 12.34 × 10 –2 12,340 × 10 –5 123.4 × 10 –3 Multiplication can also be done in scientific notation. Consider the following multiplication: 50 × 250 First, rewriting each number in scientific notation: (5.0 × 10 1 ) × (2.5 × 10 2 ) To multiply, multiply the first two numbers: 5.0 × 2.5 = 12.5 To multiply the second part, add the exponents: 10 1 + 10 2 = 10 3 The answer is written as 12.5 × 10 3 . It can also be written as 1.25 × 10 4 . These same two steps are done in every case of multiplication, even with numbers less than one. For ex- ample, to multiply 0.5 × 0.25: (5 × 10 –1 ) × (2.5 × 10 –1 ) = 12.5 × 10 –2 = 1.25 × 10 –1 = 0.125 When multiplying numbers greater than one by numbers less than one, express the numbers in convenient form, multiply the first part, add the exponents of the second part, and then express the answer in scientific notation. For ex- ample, multiply 0.125 × 5,000: (1.25 × 10 –1 ) = (5 × 10 3 ) = 6.25 × 10 2 Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes F. Scientific Notation © The McGraw−Hill Companies, 2002 Appendix F Scientific Notation 433 When adding a negative number to a positive number, al- ways subtract the negative number from the positive number. Dividing in scientific notation is similar to multiplying. Consider dividing 2,500/500. First, rewriting in scientific notation gives 2.5 × 10 3 5 × 10 2 Second, divide the first two numbers as follows: 2.5 = 0.5 5 Third, subtract the bottom exponent from the top exponent: 10 3 – 10 2 = 10 1 The answer in scientific notation is expressed as 0.5 × 10 1 . Always remember that when you subtract one negative number from another negative number, you add the num- bers and express the answer as a negative number. When subtracting a negative number from a positive number, it is the same as adding a positive number to a positive number. To subtract a positive number from a negative number, add the positive number to the negative number and express the answer as a negative number. Microbiologists use scientific notation continuously. For example, in this laboratory manual, it is used to de- scribe the number of bacteria in a population and to express concentrations of chemicals in solution, of disinfectants, and of antibiotics. [...]... Klebsiella ozaenae rhinoschieromatis Yersiniae Ga s Vo Pr O od Gl ac Ly rnit uc uc tio hin tio sin os ns n e e e Re enterocolitica Yersinia pseudotuberculosis + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 + 100 .0 +J 92.0 –A 2.1... 0 0 0 0 0 0 1.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 GEL 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 GLU 96.0 99.0 99.0 99.0 99.0 99.0 99.0 99.0 69.0 99.0 98.0 97.0 97.0 98.0 99.0 99.0 99.0 98.7 0 99.0 60.0 94.7 0.1 98.4 1.0 1.0 4.0 1.0 1.0 1.0 28.0 1.0 1.0 29.0 30.0 0.1 14.5 1.0 0 0 0 4.6 0 0 0 0 0 0.1 MAN INO 97.0 99.0 8.5 8.3 80.0 92.0 90.0 86.0 76.0 92.0... Becton Dickinson Company 1 Becton Drive Franklin Lakes, NJ 07417 1-2 0 2-8 4 7-6 800 FAX 1-4 1 0-5 8 4-7 121 www.bd.com /microbiology ICN Pharmaceuticals Inc 1263 South Chillicothe Aura, Ohio 44202 1-8 0 0-8 5 4-0 530 FAX 1-8 0 0-3 3 4-6 999 www.biomark@icnbiomed.com Thomas Scientific PO Box 99 Swedesboro, NJ 08085 1-8 0 0-3 4 5-2 100 FAX 1-8 0 0-3 4 5-5 232 www.thomassci.com 450 VWR Scientific Products Educational Division 1 310 Goshen... 1-4 1 0-5 8 4-7 121 www.bd.com /microbiology ICN Pharmaceuticals Inc 1263 South Chillicothe Aura, Ohio 44202 1-8 0 0-8 5 4-0 530 FAX 1-8 0 0-3 3 4-6 999 www.biomark@icnbiomed.com Thomas Scientific PO Box 99 Swedesboro, NJ 08085 1-8 0 0-3 4 5-2 100 FAX 1-8 0 0-3 4 5-5 232 www.thomassci.com EM Science 480 Democrat Road Gibbstown, NJ 08027 1-8 0 0-2 2 2-0 342 FAX 1-8 5 6-4 2 3-4 389 www.emscience.com In addition to making media from commercially... Educational Division 1 310 Goshen Parkway West Chester, PA 19380 –5985 1-8 0 0-9 3 2-5 000 FAX 1-6 1 0-4 3 6-1 761 www.vwrsp.com Becton Dickinson Microbiological Systems PO Box 243 Cockeysville, MD 2103 0 –0248 1-2 0 1-8 1 8-8 900 FAX 41 0-5 8 4-7 121 www.bd.com Maintenance of Microbiological Stock Cultures In microbiology, a stock culture is a standard strain that conforms to typical morphological, biochemical, physiological,... houses such as Carolina, Fisher, and Wards, the following organizations also supply microbiological cultures: American Type Culture Collection 12301 Parklawn Drive Rockville, MD 20852–1776 USA/Canada 1-8 0 0-6 3 8-6 597 Outside USA/Canada 1-3 0 1-8 8 1-2 600 FAX 1-3 0 1-2 3 1-5 826 www.atcc.org REMEL PO Box 14428 12076 Santa Fe Drive Lenexa, KA 66215–3594 1-8 0 0-2 5 5-6 730 FAX 1-8 0 0-4 4 7-3 643 www.remelinc.org Difco Laboratories... paper before use Store in a dark, stoppered bottle Harley−Prescott: Laboratory Exercises in Microbiology, Fifth Edition Appendixes H Reagents, Solutions, Stains, and Tests Nigrosin Solution (Dorner’s, for negative staining) Water-soluble nigrosin 10. 0 g Distilled water 100 .0 ml Formalin (40% formaldehyde) 0.5 ml Gently boil the nigrosin and water approximately 30 minutes Add 0.5 ml of 40%... Solution B: Dissolve 6 ml of N, N,-dimethyl1-naphthylamine in 1 L of 5 N acetic acid DO NOT MIX SOLUTIONS Oxidase Test Reagent Mix 1 g of dimethyl-p-phenylenediamine hydrochloride in 100 ml of distilled water This reagent should be made fresh daily and stored in a dark bottle in the refrigerator O-nitrophenyl-β-D-Galactoside (ONPG) 0.1 M sodium phosphate buffer 50.0 ml ONPG (8 10 4 M) 12.5 mg Phosphate... 0 IND 1.0 1.0 0.1 1.0 0 1.0 0 0 0 1.0 0 0.4 0 0 0 0 0 0 0 25.0 80.0 63.0 70.0 VP 0.1 1.3 0 0.1 0 46.0 50.0 0 0 0 0 0 0 0 0 0 0 93.0 75.3 0 78.0 62.0 75.6 GEL 4.5 33.0 0 85.0 0.5 33.0 0.5 100 100 93.0 100 100 98.0 100 100 100 100 100 100 99.0 100 100 100 GLU 0 0 0 0 0 1.0 0 99.0 99.0 87.0 94.0 99.0 0 85.0 15.0 0 0 0 0 99.0 99.0 99.0 99.0 1.0 1.0 0 0 0 0 0 0 0 0 0 1.0 0 1.0 5.0 8.0 0 0 0.1 0 10. 0 10. 0... much as 10 times (B) Gram’s Iodine Solution (mordant) Iodine crystals 1g Potassium iodide 2g Distilled water 300 ml Store in an amber bottle; discard when the color begins to fade (C) Safranin (counterstain) Solution Safranin 2.5 g 95% ethyl alcohol 100 .0 ml For a working solution, dilute stock solution 1 /10 (10ml of stock safranin to 90 ml of distilled water) India Ink (for . expressed as follows: 1 =10 0 100 ,000 = 10 5 10 = 10 1 1,000,000 = 10 6 100 = 10 2 10, 000,000 = 10 7 1,000 = 10 3 100 ,000,000 = 10 8 10, 000 = 10 4 1,000,000,000 = 10 9 In the above notations,. NJ 08085 1-8 0 0-3 4 5-2 100 FAX 1-8 0 0-3 4 5-5 232 www.thomassci.com EM Science 480 Democrat Road Gibbstown, NJ 08027 1-8 0 0-2 2 2-0 342 FAX 1-8 5 6-4 2 3-4 389 www.emscience.com In addition to making media from. exponent of 10, indicating the power to which 10 must be raised to produce a given number. Since 1 is 10 0 and 10 is 10 1 , it is evident that the numbers be- tween 1 and 10 must be greater than 10 0 .