This Document Contains Experiments 41 to 44 Name____________________________________________________Section________________Date___________ Experiment 41: The Effect of Abiotic Factors on Habitat Preference Invitation to Inquiry In the workplace there are many kinds of abiotic factors known to affect the productivity of employees. Assume you are a manager of a business. Identify five important abiotic factors that would affect your employees’ performance on the job. If you only had enough money to modify one of these factors, which one would you choose and why would you choose it? Background The individuals within a population are able to detect and respond to certain features of their environment. Many characteristics of a habitat (the space an organism inhabits) are variable from time to time or at different locations within the habitat. Abiotic factors are physical factors such as temperature, quantity of light, gravity, and pH. These often vary in aquatic habitats. When a specific environmental factor varies continuously over a distance, a gradient exists. Light intensities can range from absolute darkness to extreme brightness. A shady spot may be a few degrees cooler than a position in direct sunlight only a few meters away. The pH of a lake or stream may also vary from place to place. When a gradient exists it is possible for an animal to detect when the stimulus is getting stronger and either move toward or away from the stimulus. For example, if you hear a sound and want to go toward the sound, you can walk in a particular direction. If the sound is getting louder, you continue walking in that direction. However, if the sound is getting fainter, you would change your direction until it did get louder. In this manner you could follow a sound gradient to its source. It seems logical to expect that certain abiotic conditions would be more suitable for an organism to thrive and that organisms would migrate to places where the abiotic conditions are most favorable. If we want to determine the significance of a specific variable, we need to isolate it from other variables. Then we can present a population of organisms with a gradient for that environmental factor and allow the organisms to choose where along the gradient they would prefer to be. If the organisms collect at certain positions along the gradient, we can see that the particular variable is significant to the organism. In this exercise you will apply the scientific method. You will test the hypothesis that animals will respond to environmental gradients by congregating at specific positions along the gradient. You will set up an experimental situation and carefully and accurately collect data. You will then analyze the data you collect to determine which environmental variables are significant to the organism and where along the gradient they prefer to be. During this exercise you will work in an assigned group. Each group works with one variable, such as light, pH, gravity, or temperature, and determines how the organism (brine shrimp) responds. Each group 1. places brine shrimp in the test apparatus (plastic tubing or trough). 2. adjusts the apparatus to establish the specific environmental gradient assigned to it. 3. allows the brine shrimp sufficient time to move to their preferred position along the gradient. 4. collects data concerning population density at five positions along the gradient. 5. reports its data to the class. 6. records data collected by other groups. 7. interprets all the data reported. Experimental Design and Data Collection Although it may appear simple to count the organisms present at each point along the gradient, there are several problems that may cause inaccurate counts. Also, the number of organisms will be very large. Therefore, it may be desirable to count a random sample of the organisms from each of the five positions along the gradient. Therefore, your instructor will discuss possible ways to collect the samples and count the number of organisms in each sample. The following items need to be considered. 1. How should the organisms be removed from the apparatus so that one sample is totally isolated from others? 2. Should you count every individual, or should you sample your populations from each section? 3. How do you make sure that you are counting only living organisms? Procedure—Setting Up the Experiment 1. The class will be divided into five groups: group 1 (control), group 2 (pH), group 3 (temperature), group 4 (light), and group 5 (gravity). 2. Each group needs to obtain its test apparatus which will be either a specific piece of tubing or a plastic trough. 3. Fill the test apparatus with brine shrimp from a well-mixed culture. 4. Adjust your specific variable as described below and allow the container to remain undisturbed for 30 minutes. Specific Instructions for Each Group Group 1 (Control) The control group should have no gradients from one end to the other. Other groups will compare their data to yours to see if their data differs from yours. You want to make sure that all regions of the test apparatus have exactly the same conditions. The apparatus should be horizontal, have no access to light, no difference in temperature along its length, and no difference in pH from one end to the other. Leave the container undisturbed for 30 minutes, then collect your data by the method agreed to at the beginning of the lab. Group 2 (pH) You are working with one variable, pH. You want to establish a pH gradient along the length of your test apparatus. Your apparatus should be horizontal, not have access to light, and be the same temperature from one end to the other. To establish the pH gradient use a hypodermic syringe to slowly inject 0.5 ml of 1% HCl into one end of the container. Next, use a different syringe to inject 1 ml of 1% KOH into the other end. Be careful when removing the needle from the tube. A small amount of liquid may spray out. Leave the container undisturbed for 30 minutes, then collect your data by the method agreed to at the beginning of the lab. You will also need to determine the pH of each of the five samples you collect. Group 3 (Temperature) You are working with one variable, temperature. You want to establish a temperature gradient along the length of your test apparatus. Your apparatus should be horizontal, not have access to light, and be the same pH from one end to the other. To establish the temperature gradient, cover the left end of the container with a plastic bag of crushed ice and place an infrared heat lamp 30 cm above the other end. Leave the container undisturbed for 30 minutes, then collect your data by the method agreed to at the beginning of the lab. You will also need to record the temperature of each of the five samples you collect. Group 4 (Light) You are working with one variable, light. You want to establish a light gradient along the length of your test apparatus. Your apparatus should be horizontal and have the same temperature and pH from one end to the other. To establish the light gradient, place a source of light at one end of the apparatus. The apparatus will need to be shielded from the lights of the room so that the only source of light available to the brine shrimp is coming from one end of the apparatus. The source of light should either be a fluorescent lamp or be placed far enough away from the apparatus so that it does not heat up one end of the apparatus and accidently set up a temperature gradient. Leave the container undisturbed for 30 minutes, then collect your data by the method agreed to at the beginning of the lab. You will also need to record the distance each of the five samples is from the source of light. Group 5 (Gravity) You are working with one variable, gravity. You want to establish a gravity gradient along the length of your test apparatus. Your apparatus should not have access to light, and should be the same pH and temperature from one end to the other. To establish the gravity gradient, position the apparatus so that one end is much higher than the other. Leave the apparatus undisturbed for 30 minutes, then collect your data by the method agreed to at the beginning of the lab. You will also need to record the elevation of each of the five samples you collect. Data Gathering After allowing 30 minutes for your brine shrimp to respond to the environmental gradient you established, do the following: 1. Divide the apparatus into five equal sections so that organisms are unable to swim from one section to the next. Section your apparatus as follows. Section 1 Section 2 Section 3 Section 4 Section 5 0 cm 20 cm 40 cm 60 cm 80 cm 100 cm 2. Empty the contents of each section into a separate beaker. 3. Label your beakers so that you can identify which beaker came from each section of the apparatus. 4. Record the pH and temperature of each beaker. 5. Measure the volume of water in each of the beakers. 6. Count the number of individuals in each sample by the method agreed to at the beginning of the lab. 7. Divide the number of brine shrimp in your sample by the number of milliliters of water in that portion of the apparatus. This will give you the number of organisms per mL of water. number of brine shrimp counted in the section Brine shrimp per mL = number of mL of water in the section 8. Report your data and record data from all other groups in Table 41.1. 9. Interpret the data collected. Do brine shrimp respond to light, temperature, pH, or gravity? How do you know? Describe the preferred habitat of brine shrimp. Table 41.1 Data Sheet Section of the Apparatus Team I II III IV V 1. Control Left End Right End pH__________ pH__________ pH__________ pH__________ pH__________ Temp._______ Temp._______ Temp._______ Temp._______ Temp._______ mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 organisms organisms organisms organisms organisms counted_____ counted_____ counted_____ counted_____ counted_____ org/mL______ org/mL______ org/mL______ org/mL______ org/mL______ 2. pH Acid Base pH__________ pH__________ pH__________ pH__________ pH__________ Temp._______ Temp._______ Temp._______ Temp._______ Temp._______ mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 organisms organisms organisms organisms organisms counted_____ counted_____ counted_____ counted_____ counted_____ org/mL______ org/mL______ org/mL______ org/mL______ org/mL______ 3. Temperature Cold Hot pH__________ pH__________ pH__________ pH__________ pH__________ Temp._______ Temp._______ Temp._______ Temp._______ Temp._______ mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 organisms organisms organisms organisms organisms counted_____ counted_____ counted_____ counted_____ counted_____ org/mL______ org/mL______ org/mL______ org/mL______ org/mL______ 4. Light Dark Light pH__________ pH__________ pH__________ pH__________ pH__________ Temp._______ Temp._______ Temp._______ Temp._______ Temp._______ mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 organisms organisms organisms organisms organisms counted_____ counted_____ counted_____ counted_____ counted_____ org/mL______ org/mL______ org/mL______ org/mL______ org/mL______ 5. Gravity Bottom Top pH__________ pH__________ pH__________ pH__________ pH__________ Temp._______ Temp._______ Temp._______ Temp._______ Temp._______ mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 mL H O_____2 organisms organisms organisms organisms organisms counted_____ counted_____ counted_____ counted_____ counted_____ org/mL______ org/mL______ org/mL______ org/mL______ org/mL______ Calculate the number of organisms per milliliter as follows: organisms counted in the sample Organisms / mL = total milliliters in the section of the apparatus The Effect of Abiotic Factors on Habitat Preference Name_____________________________________________ Lab Section ____________________ Your instructor may collect these end-of-exercise questions. If so, please fill in your name and lab section. End-of-Exercise Questions 1. What is the purpose of the control? The control serves as a basis for comparison. 2. Why is it necessary to have large numbers of organisms in your sample? The larger the number of organisms, the less likely that a few aberrant individuals will influence the results. 3. Were the brine shrimp equally distributed in the five sections of control at the completion of theexperiment? Should they have been the same? Explain why or why not. If the brine shrimp have no stimuli to react to, they should swim around at random and should be equally distributed in the tube. If students do not obtain equal distribution, it could be because (1) there was a light leak, (2) the organisms were not well mixed at the beginning, or (3) counting errors (students tend to estimate rather than actually counting.) 4. Use the chi-square test to determine if the number of organisms in the five sections of the control are significantly different. Use the same test of statistical significance to evaluate the other four sets of data. O Observed E Expected (O - E) 2 (O - E) (O - E)2 E Control pH Temperature Light Gravity Chi-square value = ______________ Degrees of freedom = ____________ Probability = ___________________ 5. How would you modify your procedures if you were to repeat this exercise? Answers will vary 6. Using your data, describe how you think brine shrimp respond to: pH The organisms avoided or did not survive in extreme pHs. Temperature High temperature killed some of the organisms. Organisms migrated from hottest to coolest end of the tube. Light If the brine shrimp only have a weak, directional source of light they will swim toward it. They are likely to avoid bright light. Gravity When other environmental clues are absent, brine shrimp move downward in the water column. Name____________________________________________________Section________________Date___________ Experiment 42: Natural Selection Invitation to Inquiry Our species has been around for over 100,000 years. During this period our species has been subjected to natural selection. How might selecting agents be different today from what they were 100,000 years ago? Speculate on how the following things have affected the evolution of humans: glasses and contact lenses antibiotics to control bacterial disease availability of food Introduction The success of an individual within a species is determined by a variety of conditions and events in the life of the organism. The characteristics an individual has may determine whether it will survive and reproduce. The phenotype of an organism consists of the physical, behavioral, and physiological characteristics displayed by the organism. Most of these characteristics are determined by genes which can be passed from one generation to the next. From an evolutionary perspective the most successful individuals are those that reproduce and pass the largest number of copies of their genes on to the next generation. Those that pass on many copies of their genes are selected for and those that do not are selected against. The individual environmental factors that determine if an individual survives and reproduces are known as selecting agents. Natural selection is a term used to describe any natural events that determine which individuals within a species have the opportunity to pass their genes to the next generation. The result of natural selection is a change in the frequency of certain genes found in the species. Evolution is the continuous genetic adaptation of a population of organisms to its environment. Therefore, natural selection results in evolution. In this exercise we will look at three different mechanisms by which natural selection can influence which individuals pass their genes to the next generation; differential survival, differential reproductive rates, and differential mate selection. Differential Survival Background Information Several thousand years ago the survival of any individual human depended on an ability to locate food and avoid predators. Food was often in short supply and individuals were forced to experiment. They would try new kinds of food if they were desperate. Many kinds of plants produce chemicals that taste bad and are toxic to the organisms that eat them. Humans were also preyed upon by other kinds of animals. Good eyesight was useful for avoiding predators and locating food. The ability to obtain adequate food was important for survival and reproduction because poorly nourished individuals had a much lower chance of successfully reproducing. In the following activities we will simulate how the ability to taste, see, and obtain food could influence the number of offspring a particular individual human could produce. Procedure Avoiding Toxic Plants All individuals will be issued a piece of PTC paper to taste. 1. Place the PTC paper in your mouth. You are either a taster or a nontaster. It will be easy for you to determine this. a. Tasters will be able to identify foods that contain certain common kinds of plant toxins. Therefore they will have a greater number of children that survive because they will not feed toxic plants to their children. During their lifetime each taster will have 10 children that will live. b. Nontasters will not be able to identify the toxins, will feed toxic plants to their children, and many of their offspring will die. Thus they will have only five offspring that live. 2. Record the number of offspring you will have in the space provided on the data sheet on page 379 Spotting Danger and Locating Food Because eyesight is important in spotting danger and locating food, the number of offspring produced will be related to how well people can see. 1. To simulate this situation the instructor will hold up a card with a word written on it. Write the word on the data sheet on page 379 a. Those who correctly identify the word will have 10 offspring. b. Those who get part of the word correct will have five offspring. c. Those who cannot identify the word will have zero offspring. 2. Record the number of offspring you will have on the data sheet on page 379 Health and Nutrition Nutritional status is important in determining how many offspring an individual is likely to have survive. 1. To simulate nutritional status write down what you ate for breakfast this morning in the space provided on the data sheet on page 379 a Individuals who had breakfasts that included at least three of the major kinds of food items—(1)cereals, (2)milk products, (3)fruit, (4)vegetables, or (5)meat—will have 10 children. b Individuals who ate breakfast, but had only one or two of the major food groups, will have five children. c Individuals who had no breakfast (coffee, soft drinks, etc., do not qualify as breakfast) will have no offspring. 2. Record the number of offspring you have on the data sheet on page 379 and complete the analysis activities on the data sheet on page 380. Differential Reproductive Rates Background Information The “fitness” of an individual organism is determined by the number of offspring the individual is able to produce. Each offspring produced by sexual reproduction is carrying half its genes from each parent. Therefore, each offspring produced by a parent allows the parent to pass its genes on to the next generation. Those individuals that pass more copies of their genes to the next generation are being selected for. The phenotype of an organism consists of the characteristics that can be observed. The phenotype is determined in part by the genes an organism has and in part by the environment of the organism. Procedure 1. In this exercise you will be given a playing card that will represent your phenotype. The playing card represents an important feature of the organism that will determine the likelihood that the individual will reproduce. 2. Males and females in the class will have an opportunity to select mates and produce offspring. The object of the game is to produce the largest number of offspring in 10 generations. 3. No individual may have more than one mate. Unmated individuals will have no offspring. Any disputes about access to potential mates will be settled by the instructor based on the phenotype (playing card) of the disputing persons. 4. Move around the room and choose your mate based on your phenotype (playing card) and the phenotype of the potential mate. At this point you don’t know what the best combinations are, but some combinations of phenotypes will produce many offspring and others will produce none. 5. Once all individuals have had an opportunity to choose a mate, the instructor will tell each couple how many offspring they produced. The instructor will use a consistent method of determining the number of offspring based on the combination of cards held by the couple. The combination of cards will result in three, two, one, or zero offspring. 6. At the end of each round, record the number of offspring you produced on the data sheet on page 379 7. At the end of each round, all individuals may stay with the same mate or choose new mates. Remember your goal is to produce as many offspring as possible. 8. Continue this process through 10 rounds. 9. After the tenth round the instructor will explain the rules if they have not already been figured out. 10. Complete the analysis activities on the data sheet on page 380. Differential Mate Selection—Lek Mating Systems Background Information In lek mating systems males stake out territories usually in the presence of other males. The females evaluate the characteristics of the various males and choose which male they will mate with from among all the males present. Usually only a small number of the males are chosen and the other males do not mate. Males can have several mates during any mating season. The males that are chosen are selected for and have a greater chance of passing their genes on to the next generation. Procedure 1. In a lek mating system, because females decide which males show the most desirablecharacteristics, the females will have special rules that will be involved in deciding which males will be chosen for mating and how many offspring they will have. a. The instructor will provide the females in the class with special rules that will determine which males are most suitable for mates b. Each male will be issued a meterstick. c. Each person will be issued a playing card to be used in case disputes arise. 2. Males will distribute themselves around the room but must be at least 2 meters apart. 3. Females will choose mates by standing near them. 4. Any disputes about where a male may stand or which females have access to a specific male will be decided by the instructor based on the playing cards held by the individuals who are in dispute. 5. Each female will produce one offspring per year. Each male can produce as many offspring as he has females, but the maximum number of females per male is five. Each individual will record the number of offspring they will have per year. 6. At the end of each year the males may redistribute themselves and females must choose again. 7. Repeat for 10 rounds. 8. After the tenth round the instructor will explain the rules by which the females choose males. 9. Complete the analysis activities on the data sheet on page 381. Natural Selection Name ___________________________________________ Lab section____________________ Your instructor may collect these end-of-exercise questions. If so, please fill in your name and lab section. Data Sheet and End-of-Exercise Questions Differential Reproductive Rates Differential Mate Selection Offspring produced Offspring produced Year 1 Year 1 Year 2 Year 2 Year 3 Year 3 Year 4 Year 4 Year 5 Year 5 Year 6 Year 6 Year 7 Year 7 Year 8 Year 8 Year 9 Year 9 Year 10 Year 10 Total Total Differential Survival Analysis The maximum number of offspring possible from this series of simulations is 30. Complete the following chart. Number of Offspring Number of People in Class That Had This Number of Offspring 30 25 20 15 10 5 0 1. Which individuals in the class had genes that allowed them to be selected for?_____*__________Which individuals were selected against? _________________________________**__________ 2. Could individuals do anything to improve their chances of reproducing? ____No____________ Differential Reproductive Rates Analysis The maximum number of offspring possible is 30. Complete the following chart. Number of Offspring Number of People in Class That Had This Number of Offspring 28-30 25-27 *Th ose with good eyesight that could 22-24 tas te PTC and were able to find food. 19-21 “ ” 16-18 13-15 10-12 **Th ose with poor eyesight that could 7-9 not t aste PTC and could not “find food.” 4-6 1-3 0 3. Based on the cards they held did all of the people in the class have the same opportunity to reproduce? No, some people had superior phenotypes based on the cards (genes) they are dealt. Differential Mate Selection Analysis The maximum number of offspring possible is 50. Complete the following chart. Number of Offspring Number of People in Class That Had This Number of Offspring 46-50 41-45 36-40 31-35 26-30 21-25 16-20 11-15 6-10 1-5 0 4. Were some males more successful than others?____Yes___ 5. How much of their success was determined by genes.______________ Much of their initial success was due to their “genes.” They may have enhanced their success later by moving to a more preferred room location. 6. Describe two human characteristics presumed to be determined by genes that would lower a person’s reproductive success. Many possible answers; hereditary diseases, low mental ability, hereditary deformities. 7. Many eye-sight characteristics are inherited (color blindness, astigmatism, near sightedness). Compared to 1000 years ago do you feel these genes are being selected against more or less strongly. Explain your answer. They are not being selected against as strongly today because technology allows us to repair malfunctioning visual system. 8. In many studies observers consider human individuals with symmetrical facial features to be more beautiful than those who have some degree of asymmetry. How might facial symmetry or lack of symmetry affect a person’s reproductive success? Beauty (attractiveness) may make individuals more successful. Some studies of human sexual behavior suggested that the most beautiful persons have opportunities to mate with more partners. 9. If an organism’s reproductive fitness is determined by the genes it inherited, can all individuals have an equal chance of reproducing. Explain you answer. No, they did not have any choice about which genes they inherited. You are stuck with what you are dealt. 10. If in a lek mating system the genes that determined the behavior of the females mutated so thatthey behaved differently, would the same males be successful? Explain your answer. No, if the females started to look for different characteristics, those males with the original characteristics would be discriminated against. Special directions for specific groups of students Differential Reproductive Rates SPECIAL DIRECTIONS FOR THE INSTRUCTOR Pairs of the same-colored suits have no offspring. Pairs of different-colored suits, numbers ace through 9, have one offspring. Pairs of different-colored suits with only one member having a number of 10 through king produce two offspring. Pairs of different-colored suits with both members having numbers of 10 through king have three offspring. In cases of dispute over mating privileges with particular individuals the individual with the highest value card has priority. Differential Mate Selection -- Lek Mating Systems Special Notes for Females Only Males with caps on are the most desired males. But they can have no more than three mates per year. Males with their caps on backward can not mate. Males without caps can only have one mate per year. Males standing nearest the windows are the most desirable and can have two mates per year. Males with caps on who are standing near the windows can have five mates per year. Potential Problems None 376a Experiment 42: Natural Selection Equipment Pack of playing cards PTC paper 4 x 8 pieces of paper with a word printed on it, such as windmill 10 meter sticks Special directions for specific groups of students Differential Reproductive Rates SPECIAL DIRECTIONS FOR THE INSTRUCTOR Pairs of the same-colored suits have no offspring. Pairs of different-colored suits, numbers ace through 9, have one offspring. Pairs of different-colored suits with only one member having a number of 10 through king produce two offspring. Pairs of different-colored suits with both members having numbers of 10 through king have three offspring. In cases of dispute over mating privileges with particular individuals the individual with the highest value card has priority. Differential Mate Selection -- Lek Mating Systems Special Notes for Females Only Males with caps on are the most desired males. But they can have no more than three mates per year. Males with their caps on backward can not mate. Males without caps can only have one mate per year. Males standing nearest the windows are the most desirable and can have two mates per year. Males with caps on who are standing near the windows can have five mates per year. Potential Problems None Results Differential Survival Rate 1. Which individuals in the class had genes that allowed them to be selected for? Those that had good eyesight, could taste PTC, and were able to “find food.” Which individuals were selected against? Those with poor eyesight, who could not taste PTC and who were not able to “find food.” 2. Could individuals do anything to improve their chances of reproducing? No, all of these items were predetermined by genes or their previous behavior. Differential Reproductive Rates Analysis 3. Based on the cards they held did all of the people in the class have the same opportunity to reproduce? No, some people had superior phenotypes based on the cards (genes) they were dealt. Differential Mate Selection Analysis 4. Were some males more successful than others? Yes, those that had preferred characteristics and chose to stand in the correct place. 5. How much of their success was determined by genes? Much of their initial success was due to their “genes.” They may have enhanced their success later by moving to a more preferred room location. 6. Describe two human characteristics presumed to be determined by genes that would lower a person’s reproductive success. Many possible answers: hereditary diseases, low mental ability, hereditary deformities 7. Many eye-sight characteristics are inherited (color blindness, astigmatism, near sightedness). Compared to 1000 years ago, do you feel these genes are being selected against more or less strongly? Explain your answer. They are not being selected against as strongly today because technology allows us to repair malfunctioning visual systems. 8. In many studies observers consider human individuals with symmetrical facial features to be more beautiful than those who have some degree of asymmetry. How might facial symmetry or lack of symmetry affect a person’s reproductive success? Beauty (attractiveness) may make individuals more successful. Some studies of human sexual behavior suggested that the most beautiful persons have opportunities to mate with more partners. 9. If an organism’s reproductive fitness is determined by the genes it inherited, can all individuals have an equal chance of reproducing? Explain you answer. No, they did not have any choice about which genes they inherited. You are stuck with what you are dealt. 10. If in a lek mating system the genes that determined the behavior of the females mutated so that they behaved differently, would the same males be successful? Explain your answer. No, if the females started to look for different characteristics, those males with the original characteristics would be discriminated against. Name____________________________________________________Section________________Date___________ Experiment 43: Roll Call of the Animals Invitation to Inquiry We often overlook the many kinds of organisms that share our homes with us. Look in the light fixtures of your home or apartment and collect all the organisms you find there. Arrange them on a sheet of white paper. Arrange them into logical categories. You do not need to be able to tell exactly what they are. Just use obvious characteristics to sort them. How many different kinds of animals did you find? Background There is great diversity within the animal kingdom. No one can be expected to recognize all of the different organisms. You already know the differences between cows and dogs, birds and people, and snakes and frogs. You place these animals in categories based on certain differences in the characteristics that each possesses. If you know what critical traits to look for, it is possible to separate any animal into its proper taxonomic category. A taxonomic category is a group of closely related organisms that have evolved along similar lines. Recognizing the important characteristics that differentiate organisms into natural categories is the basis of the science of taxonomy, the classifying and naming of organisms. The ranking order of classification groups (taxons) from the most inclusive through the least inclusive is as follows: Domain Kingdom Phylum Class Order Family Genus Species Organisms in the same kingdom are very broadly similar; those in the same phylum are more similar to each other than those in other phyla. Those organisms in the same genus are quite similar, more so than those in another genus of the same family. Each species of organism has a scientific name that is often descriptive and employ two terms: the genus name followed by a specific epithet. Since two names are used to identify a species it is called a binomial nomenclature. The genus name is always capitalized and the specific epithet is never capitalized, and both the genus and the specific epithet are underlined or set in italics. For example, the leopard frog is scientifically identified as Rana pipiens. You belong to the species Homo sapiens. You can become acquainted with most of the important groups of the animal kingdom through this laboratory experience. By using a dichotomous key you will become familiar with some of the important characteristics used to classify animals. Although it is impossible to demonstrate all of the kinds of animals, you will have an opportunity to see examples of the major phyla and classes of animals. During this lab exercise you will: 1. Use the dichotomous key provided to identify the various specimens. 2. Record the phylum or class to which each animal belongs. Procedure A dichotomous key is a tool used to help determine the taxonomic category to which a specific organism belongs. It consists of a series of pairs of statements that require you to place the organism into one of two categories. Each choice will lead you to another pair of statements until you have identified the animal’s taxonomic category. For each of the organisms on display in the lab, begin at step 1 of the key and proceed through the key until you have identified the specimen. When you have determined the name of the organism, write the underlined name (from the key) opposite the appropriate number on the answer sheet provided at the end of this exercise on page 380. You may begin your work at any station and proceed to any available station thereafter; just be careful to place your answer at the appropriate number on your answer sheet. Dichotomous Key 1. a. Irregular-shaped body; structure with many pores—Phylum Porifera (e.g., sponge) b. Regular-shaped body (with right and left halves or a cylindrical shape) -----------------------2 2. a. Radial symmetry (disk-shaped or barrel-shaped) ------------------------------------------------4 b. Bilateral symmetry (similar right and left body halves) -----------------------------------------3 3. a. Animal has internal skeleton -------------------------------------------------------------------------19 b. Animal has external skeleton or no apparent skeleton ---------------------------------------------6 4. a. Body hard, arms extend from a central disc, or spines present—Phylum Echinodermata 18 b. Soft body; little or no color—Phylum Coelenterata -----------------------------------------------5 5. a. Saucer-shaped transparent body with small tentacles—Class Scyphozoa (e.g., jellyfish) b. Barrel-shaped body; tentacles at one end—Class Anthozoa (e.g., sea anemone) 6. a. Hard outer covering ----------------------------------------------------------------------------------10 b. No hard outer covering --------------------------------------------------------------------------------7 7. a. Body flattened—Phylum Platyhelminthes ----------------------------------------------------------8 b. Body not flattened --------------------------------------------------------------------------------------9 8. a. Smooth, nonsegmented body—Class Trematoda (e.g., liver fluke) b. Apparently segmented, flattened body—Class Cestoda (e.g., tapeworm) 9. a. Nonsegmented -----------------------------------------------------------------------------------------11 b. Segmented body—Phylum Annelida (e.g., earthworm) 10. a. Body has jointed legs—Phylum Arthropoda ---------------------------------------------------------14 b. Body inside of shell is soft, has no jointed legs—Phylum Mollusca ------------------------------13 11. a. Tentacles or other appendages present -----------------------------------------------------------------12 b. Body long and tubular, no appendages—Phylum Nematoda 12. a. Appears as snail without shell—Class Gastropoda (e.g., slug) b. Tentacles and eyes present—Class Cephalopoda (e.g., squid, octopus) 13. a. Bivalved shell (two halves)—Class Bivalvia (e.g., clam) b. Univalved shell (single unit)—Class Gastropoda (e.g., snails) 14. a. Jointed appendages on most body sections -----------------------------------------------------------15 b. Jointed appendages on certain body segments; not all appendages are legs ---------------------16 15. a. One pair of legs per body segment—Class Chilopoda (e.g., centipede) b. Two pairs of legs per body segment—Class Diplopoda (e.g., millipede) 16. a. Two pairs of antennae; large claws often present—Class Crustacea (e.g., crab) b. One pair of antennae or none, no large claws --------------------------------------------------------17 17. a. Four pairs of legs; no antennae or wings—Class Arachnida (e.g., spider) b. Three pairs of legs; wings present—Class Insecta (e.g., insects) 18. a. Arms present; body surface knobby—Class Asteroidea (e.g., sea stars) b. Many-spined animal; resembles a pincushion—Class Echinoidea (e.g., sea urchin) 19. a. Fish-like, flattened body, appendages fin-like not jointed ------------------------------------------20 b. Not fish-like, body not flattened, appendages jointed or absent -----------------------------------21 20. a. Scales on body do not overlap, skeleton of cartilage—Class Chondrichthyes (sharks, stingray) b. Scales on body overlap, skeleton bony—Class Osteichthyes (e.g., bony fishes) 21. a. Body covered by scales, zero or four legs—Class Reptilia (e.g., snake, lizard, turtle) b. Body not covered by scales -----------------------------------------------------------------------------22 22. a. Claws absent—Class Amphibia (e.g., frogs, toads, and salamanders) b. Claws or nails present on toes, skin covered with feathers or hair --------------------------------23 23. a. Feathered; claws present—Class Aves (e.g., birds) b. Hair present—Class Mammalia (e.g., mammals) Results 1. __________________________________________________ 2. __________________________________________________ 3. __________________________________________________ 4. __________________________________________________ 5. __________________________________________________ 6. __________________________________________________ 7. __________________________________________________ 8. __________________________________________________ 9. __________________________________________________ 10. __________________________________________________ 11. __________________________________________________ 12. __________________________________________________ 13. __________________________________________________ 14. __________________________________________________ 15. __________________________________________________ 16. __________________________________________________ 17. __________________________________________________ 18. __________________________________________________ 19. __________________________________________________ 20. __________________________________________________ 21. __________________________________________________ 22. __________________________________________________ 23. __________________________________________________ Name____________________________________________________Section________________Date___________ Experiment 44: Special Project The Special Project (SP) is an independent investigation that is accomplished outside of the classroom and laboratory room, with ordinary and everyday devices. No laboratory equipment will be available for this project since the SP is intended to be an unstructured “kitchen science” investigation. You will need to take this your-stuff-only restriction into consideration when deciding what you are going to investigate as you must use only available equipment to do the investigation. This restriction is an important part of the process. The SP is an opportunity to explore that area of science that interests you most, and in a real-world situation. You are free to pursue any science concept for your experiment, but your project should not simply mimic one of the regular experiments assigned in class or one from the laboratory manual. As best you are able to, you are to play the role of an original, creative thinker during this investigation. Important: A SP proposal must be submitted to your laboratory instructor, and approved before beginning any work. This is necessary for safety considerations, to avoid project duplications, and to ensure that your project satisfies the intent of the assignment. Please read the guidelines below, and also read the evaluation sheet to make sure you understand the intent of the SP. You will be informed of the due date for the proposal, which should briefly include the following: • Name(s) of the person(s) working as an individual or as a team. • A brief statement of the question to be answered. • What equipment will be used in what procedure to find the answer. • How measurements will be made; how data will be collected. You will have about 30 days to conduct the SP outside of class. One lab period has been established as a reporting session, a time when the experimental findings will be presented in both oral and written formats. The oral presentation will not be as detailed as the written one, however, it is the only way the rest of the class will be able to benefit from your efforts. It therefore warrants some thought and creativity. The SP oral presentation should include the following if possible: • Reporting responsibilities should be equally divided among all team members. • Describe the question to be answered and how the investigation was conducted. • The independent and dependent variables should be identified. • Use display boards to show diagrams, data tables, and graphs. • An interpretation of results using graphic analysis (mathematical model). • Explanations for the deviation (if any) of results from what was expected. • Concluding statements. The SP written report should be typed following the outline below. An appropriate title for your project should be in the center of the first page with the names of each team member in the upper right hand corner. Each of the following sections should be included in your report prefaced with the appropriate heading. Purpose: A brief statement of the question that was investigated. Apparatus: A diagram of the equipment with all parts labeled, showing the experimental setup. Procedure: The sequence for conducting the experiment stated in brief sentences. The independent and dependent variables should also be clearly identified, including a short statement of how the independent variables were controlled. Raw Data: The values measured directly from the experiment with data from as many trials as judged necessary (a minimum of three trials is required). Data should be organized into neat tables with the units (m, kg, s, etc.) clearly labeled. This section should be the original handwritten data sheet written at the time of the experiment. Evaluation of Data: Begin with a presentation of findings via graphs and formal data tables. Formal data tables include averaged values of your multiple trials as well as processed data in a spreadsheet format. Processed data refers to calculated values derived at by inserting experimental values into various equations. State what equations were used and identify the symbols used in the equations. If repetitive calculations are performed, show only one example calculation. All other calculated values will appear in your formal data tables. Graphs should be labeled with the variables on the appropriate axes and units indicated clearly. Interpret your graphs with statements of relationships between the variables. These statements need to be complete English sentences. A mathematical model for the graph should be found (if possible) and stated in this section also. An equation for a line with the slope and y-intercept given in the proper units is an example of such a mathematical model. This section should also contain a statement describing the quality of the results. Conclusion: Results are compared to what was expected and plausible explanations offered for any deviation. The meaning of the slope of a graph and any equations derived from graphical analysis are also stated here. You should also state whether the goals of your experiment were accomplished or not. Note: As the due date for the SP proposal and the presentation day approaches, please feel free to contact your laboratory instructor for individual help, advice, or encouragement. SP Evaluation Scorecard Team Members: Proposal (5 points)---------------------------------------------------------------------------------________ Turned in on time and clearly stated. Format of Report (4 points)---------------------------------------------------------------------________ 1. Group names, title. 2. Each section of report clearly labeled, neat, and organized. Purpose of Investigation (2 points)----------------------------------------------------------________ Question to be answered by experiment is clearly identified and stated. Procedure (6 points)------------------------------------------------------------------------------________ 1. Independent and dependent variables are clearly defined and controlled. 2. Clear, brief sequence of steps. 3. Diagram(s) drawn with all components labeled. Raw Data (6 points)-------------------------------------------------------------------------------________ 1. Measurement data organized into neat tables. 2. Values are clearly labeled. 3. Multiple trials. Evaluation of Data (12 points)-----------------------------------------------------------------________ 1. Tables and/or sample calculations. 2. Graphs; variables on appropriate axes, use of units. 3. Interpretation of graphs. a. Written statement of relationship. b. Mathematical model (equation, units on slope). Conclusion (12 points)----------------------------------------------------------------------------________ 1. Written explanation (English sentences) of relationships. 2. Meaning of slope in terms of experimental question. 3. General equation included. 4. Reasonable explanation for divergent results (when applicable). Presentation (3 points)---------------------------------------------------------------------------________ 1. Display clear and understandable. 2. Team functioned well together. 3. Team seemed knowledgeable in their presentation. Total Points-------------------------------------------------------------------------------------------_________ 383 Appendix I: The Simple Line Graph An equation describes a relationship between variables, and a graph helps you “picture” this relationship. A line graph pictures how changes in one variable go with changes in a second variable; that is, how the two variables change together. One variable usually can be easily manipulated; the other variable is caused to change in value by manipulation of the first variable. The manipulated variable is known by various names (independent, input, or cause variable) and the responding variable is known by various related names (dependent, output, or effect variable). The manipulated variable is usually placed on the horizontal or x-axis of the graph, so you can also identify it as the x-variable. The responding variable is placed on the vertical or y-axis. This variable is identified as the y-variable. The graph in Appendix Figure I.1 shows the mass of different volumes of water at room temperature. Volume is placed on the x-axis because the volume of water is easily manipulated and the mass values change as a consequence of changing the values of volume. Note that both variables are named, and the measuring unit for each variable is identified on the graph. The graph also shows a number scale on each axis that represents changes in the values of each variable. The scales are usually, but not always, linear. A linear scale has equal intervals that represent equal increases in the value of the variable. Thus, a certain distance on the x-axis to the right represents a certain increase in the value of the x-variable. Likewise, certain distances up the yaxis represent certain increases in the value of the y-variable. In the example, each mark has a value Unit for of five. Scales are usually chosen in such a way that the graph is large and easy to read. The origin is the only point where both the x- and y-variables have a value of zero at the same time. The example graph has three data points. A data point represents measurements of two related variables that were made at the same time. For example, a volume of 190 cm3 of water was found to have a mass of 175 g. Locate 190 cm3 on the x-axis and imagine a line moving straight up from this point on the scale (each mark on the scale has a value of 5 cm3). Now locate 175 g on the y-axis and imagine a line moving straight out from this point on the scale (again, note that each mark on this scale has a value of 5 g). Where the lines meet is the data point for the 190 cm3 and175 g measurements. A data point is usually indicated with a small dot or an x; a dot is used in the example graph. A “best-fit” smooth, straight line is drawn as close to all the data points as possible. If it is not possible to draw the straight line through all the data points (and it usually never is), then a straight line should be drawn that has the same number of data points on both sides of the line. Such a line will represent a best approximation of the relationship between the two variables. The origin is also used as a data point in the example because a volume of zero will have a mass of zero. In any case, the dots are never connected as in dot-to-dot sketches. For most of the experiments in this lab manual a set of perfect, error-free data would produce a straight line. In such experiments it is not a straight line because of experimental error, and you are trying to eliminate the error by approximating what the relationship should be. The smooth, straight line tells you how the two variables get larger together. If the scales on both the axes are the same, a 45˚ line means that the two variables are increasing in an exact direct proportion. A more flat or more upright line means that one variable is increasing faster than the other. The more you work with graphs, the easier it will become for you to analyze what the slope means. 386 Appendix II: The Slope of a Straight Line Volume (cm )3 Appendix Figure II.1 One way to determine the relationship between two variables that are graphed with a straight line is to calculate the slope. The slope is a ratio between the changes in one variable and the changes in the other. The ratio is between the changes in the value of the x-variable compared to the changes in the value of the y-variable. The symbol ∆ (Greek letter Delta) means “change in,” so the symbol ∆x means “change in x.” The first step in calculating the slope is to find out how much the x-variable is changing (∆x) in relation to how much the y-variable is changing (∆y). You can find this relationship by first drawing a dashed line to the right of the straight line so that the x-variable has increased by some convenient unit as shown in the example in Appendix Figure II.1. Where you start or end this dashed line will not matter since the ratio between the variables will be the same everywhere on the graph line. However, it is very important to remember when finding a slope of a graph to avoid using data points in your calculations. Two points whose coordinates are easy to find should be used instead of data points. One of the main reasons for plotting a graph and drawing a best-fit straight line is to smooth out any measurement errors made. Using data points directly in calculations defeats this purpose. The ∆x is determined by subtracting the final value of the x-variable on the dashed line (xf) from the initial value of the x-variable on the dashed line (xi), or ∆x = xf – xi. In the example graph above, the dashed line has a xf of 200 cm3 and a xi of 100 cm3, so ∆x is 200 cm3 – 100 cm3, or 100 cm3. Note that ∆x has both a number value and a unit. Now you need to find ∆y. The example graph shows a dashed line drawn back up to the graph line from the x-variable dashed line. The value of ∆y is yf – yi. In the example, ∆y = 200 g – 100 g. The slope of a straight graph line is the ratio of ∆y to ∆x, or Slope = ∆∆xy. In the example, Slope = 100 g 3 100 cm or Slope = 1g cm/ 3. Thus the slope is 1 g/cm3 and this tells you how the variables change together. Since g/cm3 is also the definition of density, you have just calculated the density of water from a graph. Note that the slope can be calculated only for two variables that are increasing together (variables that are in direct proportion and have a line that moves upward and to the right). If variables change in any other way, mathematical operations must be performed to change the variables into this relationship. Examples of such necessary changes include taking the inverse of one variable, squaring one variable, taking the inverse square, and so forth. 388 Appendix III: Experimental Error All measurements are subject to some uncertainty, as a wide range of errors can and do happen. Measurements should be made with great accuracy and with careful thought about what you are doing to reduce the possibility of error. Here is a list of some of the possible sources of error to consider and avoid. Improper Measurement Technique. Always use the smallest division or marking on the scale of the measuring instrument, then estimate the next interval between the shown markings. For example, the instrument illustrated in Appendix Figure III.1 shows a measurement of 2.45 units, and the .05 is estimated because the reading is about halfway between the marked divisions of 2.4 and 2.5. If you do not estimate the next smallest division you are losing information that may be important to the experiment you are conducting. Appendix Figure III.1 Incorrect Reading. This is an error in reading (misreading) an instrument scale. Some graduated cylinders, for example, are calibrated with marks that represent 2.0 mL intervals. Believing that the marks represent l.0 mL intervals will result in an incorrect reading. This category of errors also includes the misreading of a scale that often occurs when you are not paying sufficient attention to what you are doing. Incorrect Recording. A personal mistake that occurs when the data are incorrectly recorded; for example, making a reading of 2.54 units and then recording a measurement of 2.45 units. Assumptions About Variables. A personal mistake that occurs when there is a lack of clear, careful thinking about what you are doing. Examples are an assumption that water always boils at a temperature of 212˚F (100˚C), or assuming that the temperature of a container of tap water is the same now as it was 15 minutes ago. Not Controlling Variables. This category of errors is closely related to the assumptions category but in this case means failing to recognize the influence of some variable on the outcome of an experiment. An example is the failure to recognize the role that air resistance might have in influencing the length of time that an object falls through the air. Math Errors. This is a personal error that happens to everyone but penalizes only those who do not check their work and think about the results and what they mean. Math errors include not using significant figures for measurement calculations. Accidental Blunders. Just like math errors, accidents do happen. However, the blunder can come from a poor attitude or frame of mind about the quality of work being done. In the laboratory, an example of a lack of quality work would be spilling a few drops of water during an experiment with an “Oh well, it doesn’t matter” response. Instrument Calibration. Errors can result from an incorrectly calibrated instrument, but these errors can be avoided by a quality work habit of checking the calibration of an instrument against a known standard, then adjusting the instrument as necessary. Inconsistency. Errors from inconsistency are again closely associated with a lack of quality work habits. Such errors could result from a personal bias; that is, trying to “fit” the data to an expected outcome, or using a single measurement when a spread of values is possible. Whatever the source of errors, it is important that you recognize the error, or errors, in an experiment and know the possible consequence and impact on the results. After all, how else will you know if two seemingly different values from the same experiment are acceptable as the “same” answer or which answer is correct? One way to express the impact of errors is to compare the results obtained from an experiment with the true or accepted value. Everyone knows that percent is a ratio that is calculated from Part Whole × 100% of whole = % of part. This percent relationship is the basic form used to calculate a percent error or a percent difference. The percent error is calculated from the absolute difference between the experimental value and the accepted value (the part) divided by the accepted value (the whole). Absolute difference is designated by the use of two vertical lines around the difference, so Experimental value − Accepted value % Error = Accepted value × 100%. Note that the absolute value for the part is obtained when the smaller value is subtracted from the larger. For example, suppose you experimentally determine the frequency of a tuning fork to be 511 Hz but the accepted value stamped on the fork is 522 Hz. Subtracting the smaller value from the larger, the percentage error is 522 Hz − 511Hz 522 Hz × 100% = 2 1. %. You should strive for the lowest percentage error possible, but some experiments will have a higher level of percentage errors than other experiments, depending on the nature of the measurements required. In some experiments the acceptable percentage error might be 5%, but other experiments could require a percentage error of no more than 2%. A true, or accepted, value is not always known so it is sometimes impossible to calculate an actual error. However, it is possible in these situations to express the error in a measured quantity as a percent of the quantity itself. This is called a percent difference, or a percent deviation from the mean. This method is used to compare the accuracy of two or more measurements by seeing how consistent they are with each other. The percent difference is calculated from the absolute difference between one measurement and a second measurement, divided by the average of the two measurements. As before, absolute difference is designated by the use of two vertical lines around the difference, and One value − Another value % Difference = Average of the two values × 100%. Appendix IV: Significant Figures The numerical value of any measurement will always contain some uncertainty. Suppose, for example, that you are measuring one side of a square piece of paper as shown above. You could say that the paper is about 2.5 cm wide and you would be correct. This measurement, however, would be unsatisfactory for many purposes. It does not approach the true value of the length and contains too much uncertainty. It seems clear that the paper width is larger than 2.4 cm but shorter than 2.5 cm. But how much larger than 2.4 cm? You cannot be certain if the paper is 2.44, 2.45, or 2.46 cm wide. As your best estimate, you might say that the paper is 2.45 cm wide. Everyone would agree that you can be certain about the first two numbers (2.4) and they should be recorded. The last number (0.05) has been estimated and is not certain. The two certain numbers, together with one uncertain number, represent the greatest accuracy possible with the ruler being used. The paper is said to be 2.45 cm wide. A significant figure is a number that is believed to be correct with some uncertainty only in the last digit. The value of the width of the paper (2.45 cm) represents three significant figures. As you can see, the number of significant figures can be determined by the degree of accuracy of the measuring instrument being used. But suppose you need to calculate the area of the paper. You would multiply 2.45 cm × 2.45 cm and the product for the area would be 6.0025 cm2. This is a greater accuracy than you were able to obtain with your measuring instrument. The result of a calculation can be no more accurate than the values being treated. Because the measurement had only three significant figures (two certain, one uncertain), then the answer can have only three significant figures. Thus, the area is correctly expressed as 6.00 cm2. There are a few simple rules that will help you determine how many significant figures are contained in a reported measurement. Rule 1. All digits reported as a direct result of a measurement are significant. Rule 2. Zero is significant when it occurs between nonzero digits. For example, 607 has three significant figures and the zero is one of the significant figures. Rule 3. In figures reported as larger than the digit one, the digit zero is not significant when it follows a nonzero digit to indicate place. For example, in a report that “23,000 people attended the rock concert,” the digits 2 and 3 are significant but the zeros are not significant. In this situation the 23 is the measured part of the figure and the three zeros tell you an estimate of how many attended the concert, that is, 23 thousand. If the figure is a measurement rather than an estimate, then it is written with a decimal point after the last zero to indicate that the zeros are significant. Thus 23,000 has two significant figures (2 and 3), but 23,000. has five significant figures. The figure 23,000 means “about 23 thousand” but 23,000. means 23,000. and not 22,999 or 23,001. One way to show the number of significant figures is to use scientific notation, e.g., 2.3 × 103 has two significant figures, 2.30 × 103 has three, and 2.300 × 104 has four significant figures. Another way to show the number of significant figures is to put a bar over the top of a significant zero if it could be mistaken for a placeholder. Rule 4. In figures reported as smaller than the digit one, zeros after a decimal point that come before nonzero digits are not significant and serve only as place holders. For example, 0.0023 has two significant figures, 2 and 3. Zeros alone after a decimal point or zeros after a nonzero digit indicate a measurement, however, so these zeros are significant. The figure 0.00230, for example, has three significant figures since the 230 means 230 and not 229 or 231. Likewise, the figure 3.000 cm has four significant figures because the presence of the three zeros means that the measurement was actually 3.000 and not 2.999 or 3.00l. Multiplication and Division When multiplying or dividing measurement figures, the answer may have no more significant figures than the least number of significant figures in the figures being multiplied or divided. This simply means that an answer can be no more accurate than the least accurate measurement entering into the calculation, and that you cannot improve the accuracy of a measurement by doing a calculation. For example, in multiplying 54.2 mi/hr × 4.0 hours to find out the total distance traveled, the first figure (54.2) has three significant figures but the second (4.0) has only two significant figures. The answer can contain only two significant figures since this is the weakest number of those involved in the calculation. The correct answer is therefore 220 miles, not 216.8 miles. This may seem strange since multiplying the two numbers together gives the answer of 216.8 miles. This answer, however, means a greater accuracy than is possible and the accuracy cannot be improved over the weakest number involved in the calculation. Since the weakest number (4.0) has only two significant figures the answer must also have only two significant figures, which is 220 miles. The result of a calculation is rounded to have the same least number of significant figures as the least number of a measurement involved in the calculation. When rounding numbers, the last significant figure is increased by one if the number after it is five or larger. If the number after the last significant figure is four or less, the nonsignificant figures are simply dropped. Thus, if two significant figures are called for in the answer of the above example, 216.8 is rounded up to 220 because the last number after the two significant figures is 6, a number larger than 5. If the calculation result had been 214.8, the rounded number would be 210 miles. Note that measurement figures are the only figures involved in the number of significant figures in the answer. Numbers that are counted or defined are not included in the determination of significant figures in an answer. For example, when dividing by 2 to find an average property of two objects, the 2 is ignored when considering the number of significant figures. Defined numbers are defined exactly and are not used in significant figures. For example, that a diameter is 2 times the radius is not a measurement. In addition, 1 kilogram is defined to be exactly 1000 grams so such a conversion is not a measurement. Addition and Subtraction Addition and subtraction operations involving measurements, as with multiplication and division, cannot result in an answer that implies greater accuracy than the measurements had before the calculation. Recall that the last digit in a measurement is considered to be uncertain because it is the result of an estimate. The answer to an addition or subtraction calculation can have this uncertain number no farther from the decimal place than it was in the weakest number involved in the calculation. Thus, when 8.4 is added to 4.926, the weakest number is 8.4 and the uncertain number is .4, one place to the right of the decimal. The sum of 13.326 is therefore rounded to 13.3, reflecting the placement of this weakest doubtful figure. Example Problem In Appendix III, “Experimental Error,” an example was given of an experimental result of 511 Hz and an accepted value of 522 Hz, resulting in a calculation of 522 Hz − 511Hz 522 Hz × 100% = 2 1. %. Since 522 – 511 is 11, the least number of significant figures of measurements involved in this calculation is two. Note that the 100 does not enter into the determination since it is not a measurement number. The calculated result (from a calculator) is 2.1072797, which is rounded off to have only two significant figures, so the answer is recorded as 2.1%. Appendix V: Conversion of Units The measurement of most properties results in both a numerical value and a unit. The statement that a glass contains 50 cm3 of a liquid conveys two important concepts — the numerical value of 50, and the reference unit of cubic centimeters. Both the numerical value and the unit are necessary to communicate correctly the volume of the liquid. When working with calculations involving measurement units, both the numerical value and the units are treated mathematically. As in other mathematical operations, there are general rules to follow. Rule 1. Only properties with like units may be added or subtracted. It should be obvious that adding quantities such as 5 dollars and 10 dimes is meaningless. You must first convert to like units before adding or subtracting. Rule 2. Like or unlike units may be multiplied or divided and treated in the same manner as numbers. You have used this rule when dealing with area (length × length = length2, for example, or cm × cm = cm2) and when dealing with volume (length × length × length = length3, for example, or cm × cm × cm = cm3). You can use the above two rules to create a conversion ratio that will help you change one unit to another. Suppose you need to convert 2.3 kilograms to grams. First, write the relationship between kilograms and grams: 1000 grams = 1.000 kg. Next, divide both sides by what you wish to convert from (kilograms in this example): 1000 g 1 000. kg 1 000. kg = 1 000. kg. One kilogram divided by one kilogram equals 1, just as 10 divided by 10 equals 1. Therefore, the right side of the relationship becomes 1: 1000 g 1 000 . kg = 1. The 1 is usually understood—that is, not stated—and the operation is called canceling. Canceling leaves you with the fraction 1000 g/1.000 kg, which is a conversion ratio that can be used to convert from kg to g. You simply multiply the conversion ratio by the numerical value and unit you wish to convert: 2 3. kg × l1000.000 kgg = 2300 g. The kg units cancel. Showing the whole operation with units only, you can see how you end up with the correct unit of g: kg × kgg = kg gkg⋅ = g. Since you did obtain the correct unit, you know that you used the correct conversion ratio. If you had blundered and used an inverted conversion ratio, you would obtain: 1 000. kg kg2 2 3. × 1000 g = 23 g , which yields the meaningless, incorrect units of kg2/g. Carrying out the mathematical operations on the numbers and the units will always tell you if you used the correct conversion ratio or not. Example Problem A distance is reported as 100.0 km and you want to know how far this is in miles. Solution First, you need to obtain a conversion factor from a textbook or reference book, which usually groups similar conversion factors in a table. Such a table will show two conversion factors for kilometers and miles: (a) 1.000 km = 0.621 mi, and (b) 1.000 mi = 1.609 km. You select the factor that is in the same form as your problem. For example, your problem is 100.0 km = ? mi. The conversion factor in this form is 1.000 km = 0.621 mi. Second, you convert this conversion factor into a conversion ratio by dividing the factor by what you want to convert from. Conversion factor: Divide factor by what you want to convert from: Resulting conversion ratio: 1.000 km = 0.621 mi 1.000 km = 0.621 mi 1.000 km 1.000 km 0.621 mi km The conversion ratio is now multiplied by the numerical value and unit you wish to convert. 100 0. km × 100 0. × 0 621. 0 621. mi km km mi⋅ km 62 1. miles. Appendix VI: Scientific Notation Most of the properties of things that you might measure in your everyday world can be expressed with a small range of numerical values together with some standard unit of measure. The range of numerical values for most everyday things can be dealt with by using units (1’s), tens (10’s), hundreds (100’s), or perhaps thousands (1,000’s). But the universe contains some objects of incredibly large size that require some very big numbers to describe. The sun, for example, has a mass of about 1,970,000,000,000,000,000,000,000,000,000 kg. On the other hand, very small numbers are needed to measure the size and parts of an atom. The radius of a hydrogen atom, for example, is about 0.00000000005 m. Such extremely large and small numbers are cumbersome and awkward since there are so many zeros to keep track of, even if you are successful in carefully counting all the zeros. A method does exist to deal with extremely large or small numbers in a more condensed form. The method is called scientific notation, but it is also sometimes called powers of ten or exponential notation since it is based on exponents of 10. Whatever it is called, the method is a compact way of dealing with numbers that not only helps you keep track of zeros but also provides a simplified way to make calculations as well. In algebra you save a lot of time (as well as paper) by writing (a × a × a × a × a) as a5. The small number written to the right and above a letter or number is a superscript called an exponent. The exponent means that the letter or number is to be multiplied by itself that many times. For example, a5 means “a” multiplied by itself five times, or a × a × a × a × a. As you can see, it is much easier to write the exponential form of this operation than it is to write out the long form. Scientific notation uses an exponent to indicate the power of the base 10. The exponent tells how many times the base, 10, is multiplied by itself. For example: 10,000. = 104 1,000. = 103 100. = 102 10. = 101 1. = 100 0.1 = 10-1 0.01 = 10-2 0.001 = 10-3 0.0001 = 10-4 This table could be extended indefinitely, but this somewhat shorter version will give you an idea of how the method works. The symbol 104 is read as “ten to the fourth power” and means 10 × 10 × 10 × 10. Ten times itself four times is 10,000, so 104 is the scientific notation for 10,000. It is also equal to the number of zeros between the 1 and the decimal point. That is, to write the longer form of 104 you simply write 1, then move the decimal point four places to the right; hence ten to the fourth power is 10,000. The powers of ten table also shows that numbers smaller than one have negative exponents. A negative exponent means a reciprocal: 10−1 = = 0 1. 10−2 = = 0 01. 10−3 = = 0 001. To write the longer form of 10-4, you simply write 1 then move the decimal point four places to the left; hence ten to the negative fourth power is 0.000l. Scientific notation usually, but not always, is expressed as the product of two numbers: (1) a number between 1 and 10 that is called the coefficient, and (2) a power of ten that is called the exponential. For example, the mass of the sun that was given in long form earlier is expressed in scientific notation as 1.97 × 1030 kg and the radius of a hydrogen atom is 5.0 × 10-11 m. In these expressions, the coefficients are 1.97 and 5.0 and the power of ten notations are the exponentials. Note that in both of these examples, the exponential tells you where to place the decimal point if you wish to write the number all the way out in the long form. Sometimes scientific notation is written without a coefficient, showing only the exponential. In these cases the coefficient of 1.0 is understood; that is, not stated. If you try to enter a scientific notation in your calculator, however, you will need to enter the understood 1.0 or the calculator will not be able to function correctly. Note also that 1.97 × 1030 kg and the expressions 0.197 × 1031 kg and 19.7 × 1029 kg are all correct expressions of the mass of the sun. By convention, however, you will use the form that has one digit to the left of the decimal. Example Problem What is 26,000,000 in scientific notation? Solution Count how many times you must shift the decimal point until one digit remains to the left of the decimal point. For numbers larger than the digit 1, the number of shifts tells you how much the exponent is increased, so the answer is 2.6 × 107, which means the coefficient 2.6 is multiplied by 10 seven times. Example What is 0.000732 in scientific notation? (Answer: 7.32 × 10-4.) Multiplication and Division It was stated earlier that scientific notation provides a compact way of dealing with very large or very small numbers but provides a simplified way to make calculations as well. There are a few mathematical rules that will describe how the use of scientific notation simplifies these calculations. To multiply two scientific notation numbers, the coefficients are multiplied as usual and the exponents are added algebraically. For example, to multiply (2 × 102) by (3 × 103), first separate the coefficients from the exponentials, (2 × 3) × (102 × 103), then multiply the coefficients and add the exponents, 6 × 10(2+3) = 6 × 105. Adding the exponents is possible because 102 × 103 means the same thing as (10 × 10) × (10 × 10 × 10), which equals (100) × (1,000), or 100,000, which is expressed as 105 in scientific notation. Note that two negative exponents add algebraically, for example, 10-2 × 10-3 = 10[(-2) + (-3)] = 10-5. A negative and a positive exponent also add algebraically, as in 105 × 10-3 = 10[(+5) + (-3)] = 102. If the result of a calculation involving two scientific notation numbers does not have the conventional one digit to the left of the decimal, move the decimal point so it does, changing the exponent according to which way and how much the decimal point is moved. Note that the exponent increases by one number for each decimal point moved to the left. Likewise, the exponent decreases by one number for each decimal point moved to the right. For example, 938. × 103 becomes 9.38 × 105 when the decimal point is moved two places to the left. To divide two scientific notation numbers, the coefficients are divided as usual and the exponents are subtracted. For example, to divide (6 × 106) by (3 × 102), first separate the coefficients from the exponentials, then divide the coefficients and subtract the exponents. Note that when you subtract a negative exponent, for example, 10[(3) – (-2)], you change the sign and add, 10(3+2) = 105. Example Problem Solve the following problem concerning scientific notation: Solution First, separate the coefficients from the exponentials, then multiply and divide the coefficients and add and subtract the exponents as the problem requires. Solving these remaining operations gives 2 × 10-6. Solution Manual Experiment for Integrated Science Bill W. Tillery, Eldon D. Enger , Frederick C. Ross 9780073512259
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