Table One. Mass of a small package using three different measurement methods

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1 MS20 Laboratory Scientific Measurements and the Metric System Objectives To understand how to make measurements utilizing various instruments To learn how to use the metric system To convert between the metric system and the English (American) System of length, volume, mass and temperature for measurements To apply metric measurements in future laboratories To express calculations and measurements to an appropriate level significance To be able to create and label bar and line graphs of collected data Introduction For scientists to communicate their results to other scientists around the world, there must be some uniformity in units of which their data are expressed. In this week s lab, you will practice making precise quantitative measurements; you will learn to interpret and to convert those measurements in a uniform way; and you will learn to express the precision of your measurement. A. MEASUREMENT PRECISION AND SIGNIFICANT FIGURES In science it is important to be honest when reporting values. A measurement cannot be more precise than the equipment used to make the measurement. In making a calculation, we must report the final value with no more precision than the least precise value used in the calculation. We achieve this by controlling the number of significant figures used to report the measurement. (Please read Appendix One for an important discussion of the difference between accuracy and precision.) The number of significant figures in a measurement, such as , is equal to the number of digits that are confidently known (9,1,5,6,4 in this example) plus the last digit (7 in this example), which is an estimate or approximation. As we improve the sensitivity of the equipment used to make a measurement, the number of significant figures increases. For example, you might use a bathroom scale, a postal scale and one of the lab balances to weigh a small package. Each of these devices has a different level of precision. A table of possible values is shown in Table One. Table One. Mass of a small package using three different measurement methods Measurement Device Mass (kg) Precision Significant Figures Bathroom scale 2 kg ± 1 kg 1 Postal Scale 2.10 kg ± 0.01 kg 3 Lab Balance kg ± kg 4 MS20 Measurements Lab Page 1 of 8

2 In our example in Table One, each of the masses is reported to the correct number of significant figures based upon the precision of the device. Here are some rules for counting significant figures: Zeros within a number are always significant. In Table One, has four significant figures. The number 4,005 has four significant figures. Zeros that do nothing but set the decimal point are not significant. The number 4,000 has one significant figure. The number 23,000,000 has two significant figures. Zeros to the right of the decimal point are significant. The number has five significant figures. In Table One, the number 2.10 has three significant figures Mathematical Operations and Significant Figures When combining measurements having different degrees of precision, the precision of the final answer can be no greater than the least precise measurement. Thus, when measurements are added or subtracted the result can have no more decimal places than the least precise measurement. When measurements are multiplied or divided, the result can have no more significant figures than the least precise measurement. For example, suppose you were to use your calculator to add the weights of several components of a sea water sample, as shown in Table Two. Table Two. Weight of NaCl, MgSO 4 and H 2 0 in a seawater sample. Note: Correct total weight cannot have more decimal places than the least precise measurement (water). Component Weight (g) Comments NaCl (salt) decimal places MgSO 4 (magnesium sulfate) decimal places H 2 O (water) decimal place Total Weight (incorrect answer) As seen on calculator Total Weight (correct answer) decimal place The total weight of g has four decimal places, but one of the measurements has only one decimal place (the water). So the correct answer to this problem is g. MS20 Measurements Lab Page 2 of 8

3 Here s an example using division. If a boat travels nautical miles (nm) in 2 hours, what is the average speed over that time? The speed of the boat is nm / 2 hours = nm/h However, since 2 hours only has one significant figure, the correct answer is 50 nm/h B. THE METRIC SYSTEM The metric system (International System or SI) is used worldwide, with the exception of the United States. This system is very easy to understand and use. There are three basic metric measurements upon which the system is based, length, volume and mass. The specific base units of measure are: the meter (m) for length, the liter (L) for volume and the gram (g) for mass. To these base units, prefixes can be added to express smaller or larger units. Since the metric system is based on powers of ten, these prefixes reflect changes that are in multiples of ten. This makes converting within the metric system quite easy by simply moving the decimal point. Prefix Power Decimal Fraction of 10 kilo (K) ,000 one thousand hecta (H) one hundred deca (D) ten BASE UNIT one deci (d) one tenth centi (c) one hundredth milli (m) one thousandth micro (µ) one millionth nano (ç) one billionth Another method for converting within the metric system is to use algebraic unit conversion. To make an algebraic conversion, you must first know the units from which you are converting and the unit to which you are converting. For example, suppose you were asked how many meters are there in 34.5 centimeters. In this example you are converting from centimeters (cm) to meters (m). The conversion equation would look like this: 34.5 cm x 1 m / 100 cm = 34.5 m / 100 = m Where 34.5 cm is the value to be converted and 1m / 100 cm is the unit conversion. You can also see that the unit you want (meters) is in the numerator, while the original unit (centimeters) is in the denominator. Thus the unit cm cancels and we are left with simple arithmetic and the desired unit, meters. If you were to convert a larger unit to a smaller unit, you would multiply or move the MS20 Measurements Lab Page 3 of 8

4 decimal to the right. If you wanted to know how many milligrams (mg) are in 5.5 grams (g), you would set up your conversion equation like this: 5.5 g x 1000 mg / 1 g = 5500 mg / 1 = 5500 mg Again, 5.5 g is the value to be converted, there are 1000 mg in one gram, and the unit gram cancels leaving us with the desired number of mg. C. CONVERSION BETWEEN THE METRIC AND ENGLISH SYSTEMS The United States seems to be the last user of the so-called English system of measurements. In June 1992, the United States Department of Commerce issued the final report of its study on the metrification of our country, A Metric America: A Decision Whose Time Has Come. This report concluded that the U.S. would eventually join the rest of the world in the use of the metric system of measurement. The study found that measurement in the United States was already based on metric units in many areas and that it was becoming more so every day. It was clearly stated that conversion to the metric system was in the best interests of the nation, particularly in view of the importance of foreign trade and the increasing influence of technology in American life. Unfortunately, many individuals living in the United States are not familiar with the metric system, so conversion from one system to the other is often necessary. You are not required to memorize the conversions between the metric and English systems, but it is important that you be familiar with how to use them when converting between the two systems. A table of Metric and English conversions is shown in Table Three (page 8). Converting between the two systems is easily done with the algebraic conversion method shown above. Let s say you were watching the evening news last night and the reporter said that a blue whale can consume as much as 510 kg of krill a day. How many pounds is 512 kg? To make this conversion you need to find the appropriate conversion factor (see Table Three). Then set up the equation as we did in the examples above: 510 kg x 2.2 lbs / 1 kg = 1122 lbs Once again, 510 kg is the measurement to be converted, and there are 2.2 lbs in one kg. As before, the kg cancels and we are left with simple arithmetic and the unit lbs (pounds). Now since both numbers have only two significant figures, the correct answer is 1100 lbs (we can be no more precise than that). Your friend wants to teach you how to ski and said that he has a pair of 205 s that you can use (ski and snowboard lengths are measured in centimeters). How many feet is 205 cm? 205 cm x 1 in / 2.54 cm x 1 ft / 12 in = 6.72 ft MS20 Measurements Lab Page 4 of 8

5 D. LINEAR MEASUREMENTS On the counter, you will find various sizes and shapes of numbered blocks composed of different types of hardwoods and softwoods. These blocks have different dimensions, masses and densities. Procedure: 1. Select three blocks that are NOT the same general size and shape. There are not enough blocks for everyone to have three blocks, so please only obtain the blocks when you are ready for them. 2. Measure the length, width, and height for each of the three blocks and record them on the answer sheet at the end of the lab (to be turned in). Do not forget to use the appropriate metric units. Area Calculation: In some aspects of science, it is important to calculate the area, a two dimensional measurement expressed in squared units. Since most biological structures are not simple rectangular, circular or cylindrical in shape, scientists may have to devise other means in estimating its area. Calculating the area of one side of a rectangular solid is simple. Take the length of the side and multiply it by its width The units are squared since the length and the width both have the same units of measure. Volume Calculation: Volume measurements are also an important measurement to many scientists. To calculate volume, multiple the length, width and height of the object resulting in cubic units of measure (i.e. cubic centimeters or cubic inches; expressed cm 3 and in 3 respectively). E. MASS MEASUREMENTS AND DENSITY Mass Measurements The mass of an object is a measure of its matter. Mass is not affected by gravity and therefore a more appropriate measure to use than weight, which is affected by gravitational force. If you were to travel from earth to the moon, you would weigh less; however, your mass would remain unchanged. Precise measurements in the laboratory require accurate instruments. Numerous types of balances are used in the laboratory. These can be manually adjusted mechanical balances or complex electronic analytical balances. In this section, you will learn how to use a balance to obtain the mass of various objects to the nearest 0.1 gram. Your laboratory instructor will demonstrate the proper use of the balance. Record the mass for the three blocks on your worksheet. Do not forget the units! Density Calculations A combination of different measurements may be important when expressed as a single relationship. Mass and volume are often combined for certain objects in determining whether the object will have a tendency to sink or float. The ratio of MS20 Measurements Lab Page 5 of 8

6 mass to unit volume is an object s density, represented by: Density (D) = Mass (M) / Volume (V) To determine the density of an object, take its mass and divide by its volume. Density is expressed as mass per unit volume (i.e. g/cm 3 or lbs/in 3 ). Procedure: 1. Determine the density of the three blocks from your linear and mass measurements. Record your results on your worksheet. 2. Remember: D = M/V. Do not forget the appropriate units! F. LIQUID VOLUME MEASUREMENTS The base unit of measure for a liquid volume is the liter (L). The liter can be subdivided into milliliters (ml), which is one thousandth of a liter (1 L = 1000 ml). In this section, you will utilize a glass graduated cylinder to make volumetric measurements of fluids. The graduated cylinders that you may use throughout the semester are: 10 ml, 25 ml and 100 ml. Before making any liquid measurements, be sure to check the total volume the graduated cylinder can accommodate. Always use the smallest graduated cylinder that will accommodate your measurement. For example, use a 10 ml graduated cylinder to measure 5 ml of a liquid as opposed to a 25 ml graduated cylinder. Be sure you understand how to read the graduation markings. Each cylinder is marked differently. Look at all three sizes of graduated cylinders and determine now to read the markings. NOTE: For pure water, there is an equivalency between the three base units. 1 milliliter (ml) = 1 gram (g) = 1 cubic centimeter (cc or cm 3 ) Procedure: 1. Obtain a 10 ml graduated cylinder and an eyedropper. Fill a small beaker with deionized (DI) water. 2. Weigh the empty graduated cylinder to the nearest 0.1 gram and record the mass on your worksheet. 3. Place 5.0 ml of DI water into the graduated cylinder. NOTE: Read the bottom of the meniscus to get the proper volume reading. Be sure to look at eye level and not at an angle to the meniscus. 4. Reweigh the graduated cylinder with the 5.0 ml of DI water and record your results on your worksheet. 5. Take an eyedropper and count the number of drops it takes to change the volume 1 ml. Record the number of drops. 6. Repeat the procedure again by counting the number drops it takes to change the volume another 1 ml. Record the number of drops on your worksheet. 7. Reweigh the graduated cylinder with the two additional milliliters of water. Record the weight of the cylinder with 7 ml. MS20 Measurements Lab Page 6 of 8

7 8. Take an eyedropper and count the number of drops it takes to add another 1 ml. Record the number of drops G. COMBINING MEASUREMENTS H. TEMPERATURE MEASUREMENTS Most of you are familiar with the Fahrenheit scale for temperature measurement. In science, the Celsius (or centigrade) and Kelvin scales are used. Scientific temperature readings in biology are often measured in degrees Celsius as opposed to Kelvin. Countries other than the United States also use the Celsius scale for temperature measurement. Conversions between the Celsius and Fahrenheit scales are done with the following formulas: F = (9/5 C) + 32 or C = 5/9 ( F 32) For example, to convert 22 C to F, use the first formula: F = (9/5 C) + 32 = (9/5 x 22) + 32 = = 72 F Procedure: 1. Obtain a glass thermometer and determine the temperature of the lab classroom. Please be careful when removing the thermometer from the plastic sleeve. 2. Determine the outside temperature in a shady area and a sunny area. Allow the thermometer to remain in a particular area for 3-5 minutes to obtain a more accurate reading. 3. Do not let the thermometer touch any surfaces as that could affect the temperature reading due to conductive heat gain/loss. Record your results on your worksheet. I. GRAPHIC PRESENTATION An easy way to analyze and present quantitative data is to construct a graph. Graphs can show general trends or relationships between two or more variables and allow for easy data interpretation. Two basic types of graphs are commonly used by scientists: line and bar. Line graphs are used when the variable (data) is continuous; data with unlimited values between points. Time (seconds, minutes, days, etc.) is an example of a continuous variable. Bar graphs are used when there are only discrete points between the variables. When constructing line or bar graphs, there are some basic rules to follow. These are: 1. The dependent variable is plotted on the Y-axis (vertical) and the independent variable is plotted on the X-axis (horizontal). For example, in MS20 Measurements Lab Page 7 of 8

8 graphing your growth rate (height) versus developmental years (age), your height would be plotted on the Y-axis and age on the X-axis. Your height is dependent upon your age. Your age is independent of your height. 2. The X and Y axes both need to have a label and units in which the measurements were taken. If we refer back to the example above, height is the axis label for dependent variable and age is the axis label for the independent variable. Units would be years and cm for each, respectively. 3. The increments need to be consistent and should span most of the axis for each variable. 4. For a line graph, a smooth line should be drawn after the data points have been plotted. For a bar graph, the bar should extend from the data points to the X-axis. If there are more than two sets of data being plotted on the same graph, make sure to include a legend to identify each line or bar. 5. All graphs must have a figure caption that describes the measurements shown in the graph. Procedure 1 1. Using the data from the block density calculation create a bar graph showing density of each type of wood. 2. Create an appropriate figure caption. Procedure 2 1. Each student will determine their height and weight. Record these in the table on the board. Your instructor will show you how to use the vertical meter stick to make this measurement. 2. Using Excel covert the weights (in pounds) into the metric value, kilograms. 3. Using Excel, create a line graph of height versus weight for the class. Length Volume (Liquids): 1 cm = inches (in) 1 ounce (oz) = 29.6 ml 1 L = 10 dl 1 m = 39.4 inches 1 quart (qt) = L 1 L = 1000 ml 1 km = miles 1 gallon (gal) = L 1 ml = 1000 µl 1 in = 2.54 cm 1 pint (pt) = 16 fluid oz 1 yard = m 1 qt = 2 pt 1 mile = 1.61 km 1 gal = 4 qt 1 mile = 5280 ft Mass: 1 foot = 12 in 1 g = oz Area: 1 kg = oz (2.2 lbs) 1 sq. cm (cm 2 ) = in 2 1 metric ton = 1000 kg 1 m 2 = 1.2 yd 2 1 pound (lb) = 454 g 1 km 2 = mile 2 1 lb = 16 oz 1 ft 2 = 929 cm 2 1 oz = g 1 mile 2 = 2.59 km 2 Volume (Solids): Temperature: 1 cubic foot (ft 3 ) = 28,320 cm 3 F = (9/5 C) + 32 C = 5/9 ( F 32) 1 yd 3 = m 3 Table Three. Metric and English (American) Conversion Factors MS20 Measurements Lab Page 8 of 8