ISP 207L Supplementary Information Scientific Notation Numbers written in Scientific Notation are composed of two numbers. 1) Digit term A number between 1 and 10 2) Exponential term Integer power of 10 Example: 4.7 X 10 8 4.7 is the digit term 10 8 is the exponential term Converting large numbers into scientific notation: 60,000,000,000,000 Put the decimal point to the left of the last zero: 60,000,000,000,000. Move the decimal point to the left until you make a number between 1 and 10, 13 places to the left to get 6.0 X 10 13 Converting small numbers into scientific notation: 0.000,000,000,000,000,8 Move the decimal to the right to make a number between 1 and 10 16 places to the right to get 8 X 10-16 Examples of scientific notation: 10000 = 1 X 10 4 98765 = 9.8765 X 10 4 1000 = 1 X 10 3 9876 = 9.876 X 10 3 100 = 1 X 10 2 987 = 9.87 X 10 2 10 = 1 X 10 1 98 = 9.8 X 10 1 1 = 1X 10 0 any number to the zero power = 1 1/10 = 1 X 10-1 0.98 = 9.8 X 10-1 1/100 = 1 X 10-2 0.098 = 9.8 X 10-2 1/1000 = 1 X 10-3 0.0098 = 9.8 X 10-3 1/10000 = 1 X 10-4 0.00098 = 9.8 X 10-4 A good way to remember what sign the exponent integer should be: If the number being converted to scientific notation is larger than one, the exponent will be positive. If the number being converted to scientific notation is smaller than one, the exponent will be negative. 1
Significant Figures There are errors in all measurements, some to a large degree, some to a lesser degree. Significant figures are important because they represent the limitation in the measurement. Example: A penny minted in 1980 was weighed on a balance. The value was 3.034 g. The limitation in the measured value is to the thousandth place. It is incorrect to write 3.03400000000 or even 3.0340 because the additional digits indicate the measurement was accurate to more decimal places, when in reality the measured value was measured to the thousandth place. Number Number of Significant Figures 716.3648 7 all numbers are significant 0.0000476 3 zeros are located to the right of the number and used to locate the decimal point, are not significant 4.0 2 the zero is located to the left of the decimal point and is significant 0.040 2 zeros located to the right of the number are used to locate the decimal point and thus not significant, the zero on the left of the number is significant 100 1 zeros are left of the number and don t count because there is no decimal point in the number 100. 3 zeros are left of the number and all count as significant because of the decimal point 100.0 4 zeros are left of the number and all count as significant Addition and Subtraction of Significant Figures: When adding or subtracting select the number with the least number of significant figures and that number of significant figures must be used in your answer. Multiplication and Division of Significant Figures: When multiplying or dividing select the number with the least number of significant figures and that number of significant figures must be used in your answer. Rounding Off Significant Figures: The last digit to be retained is increased by one only if the following digit is 5 or greater. 2
Guidelines for Graphing Data Graphs are used to visualize the relationships between an experimental parameter such as time and a series of measured values. Your graph should include the following: title of graph labeled axes with correct units data points clearly indicated by the Excel program data points circled on hand drawn graphs, a best fit line, do not connect the dots the general calculation for the slope of a line y 2 -y 1 /x 2 -x 1 the calculation for determining the slope of YOUR line the general equation of a line, y=mx+b the equation of the best fit line of YOUR graph a legend, if more than one data set is included in the same graph Your graph should fill the entire page of graph paper. The x- and y-axes do not have to start at the origin (0,0). The x-axis is the independent variable, such as an experimental parameter that is controlled, such as time. The y-axis is the dependent variable, and its values depend on the values of the independent variable that is plotted on the x-axis. The equation of a straight line is: y = mx +b Where y is the dependent variable, b is the y-intercept, m is the slope, x is the independent variable. The equation of the line can be calculated by the Point-Slope Method. The slope of a straight line (best fit line) can be calculated by selecting two points that are far apart on the line and using the following equation: y 2- y 1 x 2- x 1 The y-intercept can be found when x = zero on the graph. The y-intercept can be calculated. First calculate the slope and pick a data point that lies on the line. Then calculate b: y = mx + b Substitute the value of the slope for m. Substitute the x value of the point that lies on the line. Substitute the y value of the same point. Solve for b. 3
Knowing the y-intercept and the slope of the straight line, you can write the equation of the best fit line. m = slope = rate (this is important to understand) b = the y-intercept when x equals zero Excel Graphing Program Use Excel, if available. Please follow the above guidelines. Display trendline (best fit line), equation of the line, and r 2 value on the graph. The trendline is the best fit line. The r 2 value is a numeric value of how scattered your data points are from the best fit line. The closer the r 2 value is to one (1), the better the fit of your data points. Experimental Error Experimental error can occur with the material you use, such as glassware, electronic balance, thermometer, contaminated chemicals. Experimental error can occur by the mistakes you make. For example: Glassware and the electronic balance might be incorrectly calibrated. You use two different electronic balances during the experiment. You record data incorrectly. You make a mistake when transferring data from one sheet of paper to another. Your freehand best fit line on a graph, the line might be off a bit. When you weigh out a portion of a dry chemical, you might drop some of the chemical on the weigh pan. When you select a chemical to weigh out and it s the wrong one. When you use a graduated cylinder to measure a liquid then pour the liquid into a second container, some of the liquid stays in the graduated cylinder. When you work with two or more samples and you mislabel them. When you leave out a step in the experiment. (see next page) 4
Your Name: Lab Partner s Name: Other Colaborators Names: ISP 207L Date of Laboratory Title of Laboratory: Heating Water Sample Laboratory Report Objective: The objective of this lab was to determine the rate in which water was heated. Experimental Design: One hundred ml of distilled water was placed into a 250 ml glass beaker. The initial temperature of the water was taken and recorded. The beaker was then placed on the heating plate set at 100 C. The temperature of water was recorded at one minute intervals and ended after 7 minutes had lapsed. Justification for the Experimental Design: One hundred ml of water was chosen because the volume of water was not too large to prolong heating or too small where evaporation would interfere with the experiment. Distilled water was used because it is pure water. Tap water contains ions that might influence the results. A 250 ml glass beaker was chosen because the beaker was only filled to 1/3 its volume. The heating plate was set at 100 C to produce a good rate of heating. One minute intervals were chosen because the rate of heating would not be too high or too low. Seven minutes was chosen to stop the experiment because the laboratory is only one hour long. Calculations used in this experiment: See calculations on graph. (In your lab report, calculations can be written by hand.) Data: Table 1. The temperature increase of 100 ml of water heated on a heating plate set at 100 C. Time (min) Temperature ( C) 0 17.15 1 17.50 2 18.35 3 18.75 4 19.25 5 10.95 6 20.55 7 21.00 Analysis of Data: The rate in which 100 ml of distilled water was heated from 17.15 to 21.00 C was 0.54 C per minute. (see next page) 5
Sources of experimental errors: Experimental errors would occur if the graduated cylinder, thermometer, and watch were not calibrated correctly or not correctly read. Experimental error would also occur if the temperature was recorded incorrectly and if the number of seconds were incorrectly read and/or recorded. A sample graph can be found with your handouts from August 29, 2006. If you have any questions, please ask your instructor or teaching assistant. Final Exam Pointers Final exam will be on December 5, 2006 during your regular section meeting time. You will be asked to develop an experiment. 1) Objectives: Write a brief paragraph stating the objectives of the experiment. 2) Hypothesis: State one hypothesis. 3) Procedure: List the steps you would take to test your hypotheses, in the order you would perform them. 4) State your reasoning for EACH step in the procedure. 5) Controls: State your control. Is it a positive control? Is it a negative control? 6) State your reasoning for your control(s). 7) Materials: List all the things you will need to perform your experiment, such as glassware, instruments, ice, heating plate, thermometer, stop watch etc. 8) Data: List what type of data you might receive from your experiment. 9) Interpretation of hypothetical data: State what your hypothetical data might mean. 10) What type of format would you use to display your data? Example: table, graph. 11) Experimental Error. List all places experimental error might play a part in your experiment. 6