chapter 3 Measurement I. Making Measurements Using the Metric System Introduction

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1 Measurement JJ Introduction If you become a nurse, a physical therapist, a biologist, or just about anything to do with science, you will be asked to measure things. Measuring things may seem trivial, but it is actually very important. Giving a patient the wrong amount of a drug can be fatal! When you need to measure something, the first step is to decide what units to use. Most every measurement you ever make will be according to one of two measuring systems: the metric system or the English system. In the sciences, the metric system is preferred because it is much easier to convert numbers from one metric unit to another than it is to convert numbers in the English system. Conversions in the metric system always involve multiplying or dividing by ten or a multiple of ten. In the English system there is no consistent method for conversion. Consider that there are 12 inches in a foot, 16 ounces in a pound, and 4 quarts in a gallon. Once you have decided which system to use, you need to decide what type of measurement to make. If your instructor asks you how big he or she is, what would you say? What does big mean? Most of you would probably give an answer in units of feet and inches, which are units for measuring length. A few of you might give answers in pounds, which are units of mass. It is doubtful that any of you would try to give an answer in gallons, which are units of volume. Therefore, you must decide whether you are going to measure an object s length, mass, or volume. I. Making Measurements Using the Metric System Objective 1: Measure length, mass, and volume using the metric system. The basic unit for measuring length in the metric system is the meter (m), which is slightly longer than an English yard. A person s height is easily measured in meters, and the average person is somewhat less than two meters tall. However, it is not convenient to measure something tiny, 19

2 like a cell, in units of meters. Nor is it convenient to measure the distance between two cities in units of meters. Thus, the metric system allows easy conversion to smaller or larger units. For example, a micrometer is one millionth of a meter, and a cell can be measured in micrometers. A kilometer is one thousand meters, and a kilometer can be used to measure long distances. You should become familiar with the measures of length given below: 1 kilometer (km) is equal to 1,000 meters 1 km = 1,000 m 1 centimeter (cm) is equal to 1/100 meters 1 cm = 0.01 m 1 millimeter (mm) is equal to 1/1,000 meters 1 mm = m 1 micrometer (µm) is equal to 1/1,000,000 meters 1 µm = m The basic unit for measuring mass in the metric system is the gram (g). A single paper clip has a mass of approximately one gram. It would take a lot of paper clips to equal the mass of a person, and the mass of a person is typically measured in kilograms (kg). Just as a kilometer is equal to 1,000 meters, a kilogram is equal to 1,000 grams. By the way, mass is a measure of the amount of matter in an object, and an object s mass remains constant as long as the object itself does not change. An object s weight depends upon the force of gravity. Thus, a person s mass on Earth is the same as the person s mass in space. However, the person s weight changes when he flies to the moon. We tend to use the words mass and weight interchangeably, but be aware of the subtle difference. You should become familiar with the measures of mass given below: 1 kilogram (kg) is equal to 1,000 grams 1 kg = 1,000 g 1 milligram (mg) is equal to 1/1,000 grams 1 mg = g 1 microgram (µg) is equal to 1/1,000,000 grams 1 µg = g The basic unit for measuring volume in the metric system is the liter (L). If you have ever bought a drink in a two-liter bottle, then you should have a good idea of the volume of one liter. Note that one milliliter (ml) has the same volume as one cubic centimeter (cc). A 10 cc syringe can be used to inject up to 10 ml of fluid. You should become familiar with the measures of volume given below: 1 milliliter (ml) is equal to 1/1,000 liters 1 ml = L 1 microliter (µl) is equal to 1/1,000,000 liters 1 µl = L ACTIVITY 1 Obtain a meter stick and a ruler. Measure the length (height) of your lab partner, measure the length of your index finger, and measure the length of the fingernail on your little finger. Write your data in the following table, and express each measurement in units of meters, centimeters, and millimeters. 20

3 Measurement person Object Meters Centimeters Millimeters index finger fingernail Using a pan balance, measure the masses of the following objects: a glass beaker, a pen or pencil, and a coin. Be sure the balance is correctly zeroed before making your measurements. Write your data in the table below, and express each measurement in units of kilograms, grams, and milligrams. beaker Object Kilograms Grams Milligrams pen or pencil coin Obtain a beaker and a graduated cylinder. Fill each approximately half full with water and bring them both to your table. Record, as accurately as possible, the amount of water in each, then fill in the following table. When reading the volume in the graduated cylinder, you should notice the surface of the water is not perfectly level. There is a curve to the surface, called the meniscus. Your reading of the volume should be taken at the bottom of the meniscus, not where the water creeps up on the sides of the cylinder. Meniscus Read volume here 80 Hayden-McNeil, LLC Figure 3-1. Reading a meniscus. Object Liters Milliliters Microliters beaker graduated cylinder 21

4 Obtain a plastic pipette. If you are not sure how to use the pipette, ask if someone at your table knows how, or ask your instructor. Do not use your mouth to suck fluid into the pipette! Use the water in your beaker or graduated cylinder and practice dispensing fluid with the pipette. Note the smallest and largest amounts that can be dispensed accurately with the pipette. QUESTIONS 1. Put the following units in order from largest to smallest: centimeter, meter, millimeter. 2. Suppose an object is 5 cm in length. If you measure the object in millimeters, does your unit of measure get smaller or larger? If you measure the object in millimeters, what happens to the number? Does it get smaller or larger? 3. What is the difference between mass and weight? 4. Consider a graduated cylinder, a beaker, and a pipette. Which provides the most accurate measure of volume? Which provides the least accurate measure? 22

5 Measurement II. Converting Units Objective 2: Convert measurements from one unit to another unit. You have already been required to make metric metric conversions in the previous activity. In this section you will learn more about conversions and be asked to make conversions between metric and English units. Conversions are always done by either multiplying or dividing. The trick is knowing which operation to perform. Suppose you wish to convert 1.8 meters to centimeters. You should know by now that there are one hundred centimeters in one meter, or 1 m = 100 cm. Because 1 m = 100 cm, the following is also true: 1 m/100 cm = 100 cm/1 m = 1 Multiplying a quantity by 1 does not change the original quantity. Thus, we can perform the following multiplication: 1.8 m 100 cm/1 m = 180 cm Note that the units of meters have cancelled out, and our measurement is now in centimeters. Had we multiplied 1.8 m by 1 m/100 cm (which is the same as dividing by 100 cm), then the units would not have properly cancelled. Also note that when converting to a smaller unit the number gets larger. This is because it takes more of the smaller units to measure a given object. Many of you may know how to convert metric units by simply moving the decimal point to the right or left. Moving a decimal point two places to the right is equivalent to multiplying by 100. Moving a decimal point two places to the left is equivalent to dividing by 100. Figure 3-2 should help you visualize the relationships among the different metric units. Use whatever method works best for you, but be prepared. You will be asked to perform metric metric conversions on your lab exam, and you will be asked to do them without using a calculator! Your instructor should demonstrate conversions for your class by reviewing some examples kilo centi milli micro Figure 3-2. You will also be expected to perform some conversions between metric units and English units. These conversions must be done by multiplying or dividing. Since the conversions are not based on multiples of ten, you cannot simply move the decimal point. As an example, let us convert 12 inches to centimeters. The conversion factor to be used here is that 1 inch is equal to 2.54 cm. Therefore, the following is also true: 1 inch/2.54 cm = 2.54 cm/1 inch = 1 and 12 inches 2.54 cm/1 inch = 30.5 cm 23

6 Note that the units of inches have cancelled out and the measurement is left in units of cm. When you are asked to perform an English metric conversion the appropriate conversion factor will be given and a calculator will be provided. Here are some English metric conversion factors that you may find useful: 1 inch = 2.54 cm 1 lb = 454 g 1 kg = 2.2 lb 1 L = 1.05 qt ACTIVITY 2 Perform the following metric metric conversions. By the time of the exam, you should be able to perform problems like these without the conversion factors being given and without a calculator. For further practice, make up your own problems. Convert 254 cm to meters: Convert 3.62 m to millimeters: Convert m to micrometers: The next two are a bit harder, but you should be able to figure them out. Convert 72 cm to millimeters: Convert 0.11 mm to micrometers: Perform the following English metric conversions. You will be given the conversion factors and a calculator to perform similar problems on your exam. Convert 36 inches to centimeters. 1 inch = 2.54 cm 24

7 Measurement Convert 185 lb to kilograms. 1 kg = 2.2 lb Convert 2.0 L to quarts. 1 L = 1.05 qt QUESTIONS 5. A two-liter bottle of Coke and a two-quart bottle of Coke are both on sale for 99 cents. Which is the better bargain? Briefly explain your answer. 6. Mark is 6'4" tall. This is equivalent to 193 cm tall. Suppose you wish to convert this measurement from centimeters to meters, and suppose you multiply by 100. Does the answer you get make sense? Explain why or why not. How do you properly convert centimeters to meters? What is Mark s actual height in meters? 25

8 CLEAN UP Return meter sticks and rulers to their proper places. Leave pan balances on the tables. Rinse out the beakers and graduated cylinders in the sinks and place them on the drying racks. Return the green pipette suckers to their proper places. Dispose of the pipettes in the cardboard sharps box. Do not throw the pipettes into the regular trash! Throw away all trash. Leave your tables clean (wipe them down if necessary) and push in your stools before leaving. 26

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