LABORATORY EXERCISE I METRIC SYSTEM OF MEASUREMENT

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1 LABORATORY EXERCISE I METRIC SYSTEM OF MEASUREMENT The metric system of measurement is used for all measurement in most countries of the world. The scientific community of the entire world expresses data using the metric system. Therefore, it is necessary for us to know and to be able to effectively use this measurement system. It is also necessary to be able to convert English units into metric units. The problems at the end of this unit will test your ability to do so. The metric system units are related to each other by a factor of ten, so interconversions are done by simply moving the decimal point to the left or right. The standard unit of length is the meter (m). This distance is equal to 1,653, times the wavelength of the orange-red line in the spectrum of Krypton 86. (As you can see, the standard measurements are very precise.) The standard unit of mass is the gram (g). The standard unit of volume is the liter (l). For measuring time, the second, minute and hour are units that are used. Names of multiples or fractions of Metric units are formed by adding a prefix to meter, gram or liter. Memorize the following prefixes & their numerical equivalents: (fill in the blanks in this column) Prefix Example of relationship NAME SYMBOL NUMERICAL EQUIVALENT between prefix and 1 meter kilo (k) = or 1x10 3 (1 x 10 3 = 10 x 10 x 10) kilometer (km) = 1 meter deci (d) = 0.1 or 1x decimeters (dm) = 1 meter centi (c) = 0.01 or 1x10-2 (1 x 10-2 = 0.1 x 0.1) = 1 meter milli (m) = or 1x10-3 = 1meter micro (u) = or 1x10-6 = 1 meter nano (n) = or 1x10-9 = 1 meter femto (f) = or 1x10-15 = 1 meter Note in the table above, that it becomes tedious to include all the zeroes needed to write the number of nanometers per meter or femtometers per meter. Exponential notation (also referred to as scientific notation ) is an easy way to write a number without including all those zero "placeholders". The prefix names simply indicate multiples of ten or fractions of tens (tenths). For example kilo means one thousand, which is also =10 x 10 x 10 or expressed in exponential notation 1x10 3. However, milli means one one-thousandth, which is 1/10 x 1/10 x 1/10 (=.1 x.1 x.1=.001) or 1x10-3 in exponential notation. How would you write 5,000 in exponential notation? All you need to do is move the decimal point, so that there is only one significant number to the left of it. In the case of 5,000, the decimal point follows immediately after the last zero (5,000.). Therefore, we move the decimal 3 places to the left and now must indicate how many places we moved the decimal; so it becomes 5 x 10 3 when written in scientific notation. This method of writing numbers saves scientists & mathematicians time when they are dealing with very large numbers or very tiny fractions that have a lot of zeroes behind or before the significant numbers. How would you write 5/10,000 (0.0005) in exponential notation? In the case of a number that is less than 1, the exponent takes on a negative prefix, indicating 1

2 that is the number of place holders to the right of the decimal point at which the significant numbers start. So, for , you should have answered 5 x 10-4 in the blank above. Here is another example: meters is more convenient to work with when it is written in exponential notation, which would be = meters. We could also express meters (m) in micrometers (um). How many micrometers (um) are in m?. Since a micrometer is one one-millionth (1 x 10-6 ) of a meter, the answer should be 2 um. As you see in the example above, metric prefixes are used in front of other units of measurement, like -meters, -grams, -liters, -seconds and -volts. We will see this usage, especially with the prefix milli- [millimeters (mm), milliseconds (ms), millivolts (mv)]. In Physiology, you will mostly be required to convert metric units into other metric units (simply move a decimal point - left for converting larger units into smaller, right for small to large). ENGLISH : METRIC CONVERSIONS Sometimes we need to convert English units into metric. The following list provides some standard conversion factors to change units from the English to the Metric system or vice versa: (Do not memorize these) 1 yard = meters 1 mile = 1609 meters 1 inch = cm 1 kilogram = 2.2 lbs 1 liter = quarts 1 ounce (wt.) = 28.4 g 1 gallon = liters 1 fluid ounce (volume) = ml 1 kilometer = miles 1 foot = meters OTHER USEFUL CONVERSIONS: VOLUME:WEIGHT CORRELATION: A milliliter is 1/1000 of a liter. This is approximately equal to 1 cubic centimeter (1 cc or 1 cm 3 ). You should memorize this equivalence: 1 ml = 1 cm 3. Furthermore, 1 ml of pure water weighs 1 gram at standard temperature and atmospheric pressure. This is a very convenient conversion (volume : weight) that you should also memorize (i.e. 1 ml water = 1 gram water and therefore 1 ul water=1 mg water). You must memorize this equivlence. TEMPERATURE: The metric system of temperature measurement is in degrees Celsius or Centigrade (C). Below are the conversion formulae. Simply plug the known temperature into the formula. (Do not memorize these) If you know the Farenheit temperature and want to determine the Centigrade temp o C = x ( o F - 32) If you know the Centigrade temperature and want to convert to Farenheit temp o F = (1.8 x o C) + 32 WAVELENGTH OF LIGHT: Another common unit of linear measurement used in science is the Angstrom (A o ). An A o is meters (1 x m or 0.1 nanometers). This, of course, is a very small distance and is used for cellular, intermolecular and light wavelength measurements. (Do not memorize this conversion). ENERGY UNITS: Energy is measured in calories. A calorie is the amount of energy required to raise the temperature of 1 gm of water by 1 degree C. You must memorize the preceeding definintion of calorie. To calculate the number of calories required to warm some water, you would multiply the number of grams of water by the desired increase in temp (#g x T = calories; where T is the change in temp in o C. Terminology note: delta or triangle indicates a change ). Nutritional calories which are printed on food packages are actually Calories with a capital "C" (1 Calorie = 1,000 calories or 1 kilocalorie). 2

3 I. CONVERSION PROBLEMS DIRECTIONS: The following questions represent types of calculations that you will encounter in physiology this semester. Answer the questions in the space provided. In all cases SHOW YOUR WORK!! Remember to ALWAYS use proper units or their abbreviations in your answers. Note: You should not have to spend more than 1 hour on questions If you are having difficulty understanding these conversions, go to the Open Math Lab in the Library at either campus. Request a self tutorial exercise on METRICS(Math 820)and EXPONENTIAL NOTATION (Math 100). Be sure to sign in and out at the entrance to the Math lab and you will earn 5 pts. Extra credit. 1. Convert 1 ul (1 microliter) into ml (milliliters): a. express as a fraction or decimal : b. express as a number using exponential notation : 2. How many micrograms (ug) does 1 ul of water weigh? 3. How many ml are there in 5.5 liters? (a) Expressed as a whole number: (b) expressed in scientific notation: 4. How many ml are there in 5.5 quarts? 5. Convert the following numbers : a) cm = mm b) 46.8 ul = dl c) ug = kg 6. If your blood contain 15 gm of hemoglobin per dl of blood, how much hemoglobin would be contained in 1 liter of blood? 3

4 7. In the space below, draw a rectangle which measures 2.1 cm x 3.0 cm. (a) How many cm 2 does the rectangle measure (i.e. what is the area of the rectangle in cm 2 )? (b) How many mm 2 does the rectangle measure? (Use your metric ruler to confirm this) 8. (a) How many squares, each measuring 1 mm x 1mm (or 1mm 2 ), will fit into a larger square that measures 1 cm 2 (1cm x 1cm)? (hint: a diagram may help you to envision this) (b) How many cubes, each measuring 1 mm x 1 mm x 1 mm (=1mm 3 ) will fill a cube that measures 1 cm 3 (1 cm x 1 cm x 1 cm)? (hint: my diagram may help you to envision this not to scale) example: 1cm 1cm 1cm (c) There are approximately 5 million (5 x 10 6 ) red blood cells in 1 mm 3 of blood. How many RBC s are found in 1 cm 3? In 1 ml? (use 4a & b to help you figure this out if you have trouble) 9. The left ventricle of the human heart is capable of ejecting approximately 70.0 ml per beat (stroke volume). Given this volume, how many times must the heart beat to eject a total of 6.3 liters of blood? (hint:, you must have both volumes in the same units - ml or l) 10. (a) A drug is given at a dosage of 25 mg / kg body weight. Convert this dosage to ug per kg (ug/kg). 4

5 (b) How many ug of the drug in question #10a should be administered to a person who weighs 77 kg? 11. A physiograph chart recorder is an instrument that is used to make a printout of an electrocardiogram (ECG). If it moves paper through it at a speed of 12.7 mm / sec, (a) how many cm per second is this? (b) How many inches per second is this? 12. Compute the arithmetic mean (average) of the following body weights: a. 80 kg d. 58 kg b. 63 kg e. 59 kg c. 89 kg f. 72 kg 13. At rest the left ventricle of the heart pumps 5.0 liters of blood per minute (this is known as the cardiac output). Blood flow to the kidneys is approximately 1,220 ml per min at rest. (a) What percent (%) of the cardiac output do the kidneys receive at rest? (b) Assume that the kidneys will receive the same percent of the cardiac output that was calculated above, regardless of whether you are resting or exercising. If the heart pumps 7.0 liters / min during exercise, how many milliliters of blood will enter the kidneys per min? 5

6 c. What is the change in volume of blood received by kidneys between rest and exercise (difference between the 2 volumes)? Questions 14 & 15 rely on the following information: CALCULATING PERCENT (%) CHANGES/DIFFERENCE IN DATA: Frequently it is more significant to express changes in data by percentages, rather than raw differences. This helps to reduce the inherent fluctuations in the data obtained from different people. If you are asked to determine the % change between an initial piece of data and a final data point you can use the following formula: last data point - first data point X 100 = % change first data point (Final note: % change will be negative if your first data point is higher than the last data point that you recorded) 14. Use the data and answers that you calculated in question #13 to answer this question: Calculate the % change ( %) in blood flow through the kidneys between rest (1 st point) and exercise (last point). 15. The digestive tract & liver receive 1350 ml of blood/minute when you are at rest. During moderate exercise that volume decreases to 550ml/min. Calculate the percent change. 16. (note : this problem takes quite a bit of work; it will be reviewed in lab and does not need to be done prior to lab; you should refer to page 2 for help;). Let s say you were to drink one quart (32 fluid ounces) of water at refrigerator temperature of 40 degrees F. How much energy (calories) would it take to bring the water up to body temperature (37 C)? Express your answer in exponential notation in both calories and kilocaries. 6

7 Preparation for analysis of metric data II. COLLECTION OF DATA USING METRIC VALUES II A. Body composition Analysis 1. Body Mass Index. Body composition can be estimated using a variety of techniques. One estimate of body fat is a height-to-weight ratio called the body mass index (BMI). BMI is body weight in kilograms divided by height in meters squared (kg / m 2 ). Your assignment is to measure your height and weight, then convert them into meters and kg, respectively. Next, plug the values into the formula to calculate the BMI. A ratio of approximately <23 indicates that you are lean, is considered acceptable and > 30 is considered overweight. Record your height & weight to 2 significant numbers beyond the decimal point: Ht. = m Wt. = kg Calculate your BMI = Kg / (m 2 ) = (don t forget to square the meters before dividing into the kg) 2. Waist-to-Hip ratio Being overweight is a greater health risk if you carry most of your fat around your waist. Procedure: - Stand and measure your waist at the navel. Record this value (using 1 significant number beyond the decimal point: cm - Next, measure your hips at the greatest circumference (buttocks). Record this value (using 1 significant number beyond the decimal point: cm - Now divide the waist circumference by the hip circumference to get the waist-to-hip ratio. Your Waist-to-Hip ratio = A waist-to-hip ratio above 1.0 for men and above 0.8 for women is associated with an increased risk of cardiovascular disease, according to the American Heart Association. 3. Recording Data in a Table. The easiest way of recording various raw data points is in a table with labeled columns and rows. (Note: tables should always be titled and numbered in a scientific report) Record your data (height, wt, waist & hip metric measurements in a Table on the blackboard on in a computer program (as directed by your instructor). You will receive a copy of the class data to be used in an upcoming lab exercise on Graphing. In order to maintain anonymity during the semester, you will record all of your personal measurements using the last 4 digits of your social security number (SSN). Sample table: Table I. Physical Measurements taken from Physiology students Student i.d. Height (m) Wt. (kg) Waist (cm) Hips (cm) Sex m/f Age (yrs) M 28 7

8 II B. Comparing Weight & Volume of Water In this exercise you will learn how to use micro-pipettors, instruments that are extremely accurate in measuring small volumes (microliters) of liquid. You will also demonstrate that the volume of water, in milliliters, is equal to its weight in grams at standard temperature. Therefore, 1 ml of water = 1 gram weight. We have the following micropipettors available to us this semester: P100 - the top of the plunger will read 100 (or the largest number on the top of the plunger will read 100. This indicates that the largest volume of liquid that can be taken up by this pipettor is 100microliters (ul); P200 - the top of the plunger will read 200 (or the largest number will be 200); P the top of the plunger will read 1000 (or largest number will be 1000). Look at each of the 3 pipettors before using them. Note the following features and refer to Figures 1 & 2 in Lab exercise 1(if you download this lab exercise from my website you will have to separately download the figure from the physiology website; look for a link entitled P100 pipettor ). If there is only one number on the top of the plunger, that indicates the maximum volume that can be picked up by that pipettor (ul). If there are 2 numbers on the top of the plunger, the largest number indicates the maximum volume that can be taken up by that pipettor and the smallest number indicates the smallest volume that can be accurately measured by that pipettor. Idendity the Volume adjustment knob (Fig. 1A) on each of the pipettors. You turn this between your thumb and forefinger to adjust the volume to be picked up. The volume that you dial is visible in the "volume indicator window" on the side of the pipettor (Fig. 1B). Never adjust the volume above the max volumes of each pipettor (e.g. from top to bottom in volume indicator window: "100" for P100, "200" for P200 and "100" for P1000; note that the P1000 only has 3 numbers - you have to estimate the last digit by looking at the small grid below the bottom number.get it? If not, ask your instructor for a demonstration). Before using your pipettor, ALWAYS INSTALL A DISPOSABLE TIP ON THE END OF THE PIPETTOR; this is the reservoir that will contain the liquid. The pipettor is NEVER TO BE DIPPED INTO A LIQUID WITHOUT A TIP INSTALLED!! The tip should fit snuggly on the end of the pipettor to give a good seal against the barrel of the pipettor. On a P1000 (large) pipettor, never dial below "0-1-0" (read top to bottom) or above "1-0-0". Answer the following questions: On a P1000 pipettor what is the pick-up volume when the pipettor is adjusted to "0-1-0"? ; when adjusted to "1-0-0"? Micropipettors are expensive instruments. Become familiar with their use so as not to damage them. Learn the parts of the pipettor and how to use them. Refer to figure 1A,B and fig. 2 in lab exercise #1). If any liquid enters the barrel of the pipettor, report this to your isntructor immediately and discontinue the use of the pipettor. It needs to be cleaned so as not to damage the internal components. Thanks!!. You will be weighing 100 ul of water in this exercise. Answer the following questions before proceeding with the exercise: Q. How many ml are in 100 ul? ml Q. What is the expected weight of 100 ul of water? g = mg Procedure - Each person should perform the following steps. You may want to work in groups of three. If you have experience working with micropipettors, you may forego the entire procedure and take the practical quiz immediately. Students with experience in micropipetting will be expected to assist other students who are unfamiliar with the instruments. 8

9 1. Water Weight-Volume Comparison: Take your pipettors over to a top-loading balance. Using a Pipetman P-200 (or P-100), install a disposable yellow tip (see Figure 1A). Use the volume adjustment knob to set your pipettor to 100 ul (see Fig. 1B). NEVER DIAL A VALUE BELOW 0 OR ABOVE THE LARGEST NUMBER THAT IS FOUND ON THE TOP OF THE PLUNGER! 2. Obtain a small plastic weighing boat. 3. Tare (zero) the weighing boat on a top loading balance (located in prep room). 4. Use the Pipetman to pick up 100 ul of distilled water from a beaker. To do this, push the pipet plunger down to the first stop to expel air. Hold it there. Insert the tip into the water. Allow the pushbutton to return slowly to the up position (Fig. 2A). Never let it snap up! Pause briefly to ensure that the full volume of sample is drawn into the tip. 5. Withdraw the tip from the sample liquid, making sure that no liquid sticks to the outside of the tip. 6. Dispense the 100ul sample into the weighing boat which is on the zeroed balance. To dispense the liquid, slowly depress the pushbutton of the pipettor all the way down to the second stop point of the Pipetman (Fig. 2B). 7. Record the actual weight of the water: g 8. Now use a P-1000 pipettor to weigh 500ul of water. This time you will install a large blue disposable tip on the end of this pipettor before performing the exercise. Dial the volume adjustment ring so that the window reads 050 (=500ul). Pick up 500 ul of water and weigh it as in steps 2-6 above. 9. Record the actual weight of the water: g FOLLOW-UP: Practice: Take your pipettors back to your station in the lab and practice if your technique needs work. Fill a small beaker half way with water. Obtain a P100 or P200 pipettor, attach the proper disposable tip, and pipet 27 ul or 79 ul of water by taking from the beaker and dispensing it back into the beaker. Have your partner(s) observe and critique your technique. Then practice with a P1,000 pipettor (by pipeting 478 ul or 935 ul). Have your partner(s) observe and critique your technique. Your instructor will assist and observe you also. Practical Quiz: Before leaving Lab tonight,each students must be tested: When you feel confident in your pipetting technique, obtain a Quiz card from the front table and a pre-numbered micro-centrifuge tube. Fill out the card according to instructions. Then measure and dispense the indicated volume of water into the tube. When done, close the tube and leave it in the "Completed Quiz" rack for your instructor to check. Leave the quiz card on the table next to the rack. It is not necessary to weigh the tube. (10 pts. Possible) Review Questions (discuss these questions with your classmates and answer before leaving tonight, but do not turn this in): 1a. When you weighed the water samples that you pipetted, did the actual weight of the water agree with the expected weight in both cases? 1b. If not, what may have contributed to the difference? 9

10 2. Using a P200 pipettor (200ul = maximum volume), describe the procedure for picking up 175 ul of liquid and dispensing it. 3. Using a P1000 pipettor (which holds a max vol. of 1,000 ul), describe the procedure for picking up 645 ul of liquid and dispensing it. 4. If you wanted to measure 100 ul of liquid with a P1000 pipettor, what would the reading be in the volume indicator window of the pipettor (from top to bottom)? 5. If you wanted to measure 235 ul of liquid with a P1000 pipettor, what would the reading be in the volume indicator window of the pipettor (from top to bottom)? 6. In reference to a P1000 pipettor, what does the "P1000" designate or indicate to you? 7. What does the prefix "micro" mean? 8. How many microliters are there in one milliliter? 10