Presentation Transcript

1. GenChem/Organic Chemistry Laboratory Department Office Room 303 Planetary Hall MSN 3E2 Phone 703-993-1070 FAX 703-993-1055 Dr. James C. Schornick Office Room 355 Planetary Hall Mailbox Room 303 Planetary Hall Phone 703-993-1091 E-Mail jschorni@gmu.edu Classes (Spring 2013) M – Chem 211 Lab Sec 204 2 :00 pm – 5:50 pm Rm 409 Planetary Hall T – Chem 212Gen ChemSec 004 4:30 pm – 7:10 pm Rm2247Bull Run Hall, PWC W – Chem 318 Org Lab I Sec 211 12.30pm–4:20pm Rm409Planetary Hall Office Hours M, T, R, F 9:00 am – 11:00 am Rm 318 Planetary Hall M, W, R, F 1:00 pm – 4:00 pm Rm 318 Planetary Hall T 2:30 pm – 4:30 pm Rm 410 Occoquan, PWC Course Texts Slayden, S. Chemistry 211, 212, 251 Laboratory Experiments Silberberg, Chemistry, Molecular Nature of Matter and Change Web Sites Genchem http://chem.gmu.edu/results Schornick http://mason.gmu.edu/~jschorni Chem Dept http://chemistry.gmu.edu/
2. General Chemistry Laboratory (211 & 212) Objective The purpose of the Genchem 211/212 laboratory courses is to introduce the student to basic techniques used in the lab to investigate the chemical and physical properties of compounds and their chemical reactions. Experiments
3. Chemistry Laboratory Class Elements: Experiments (12 each semester) Reports – Typed, Formal Quizzes – weekly Final Exam Safety procedures Strictly Enforced Goggles Lab Coats Gloves - Latex Non-latex (Nitrile) alternatives available) Suggest old jeans & shirts (chemical spills & stains inevitable) No Shorts, Flipflops, or Open-Toed shoes Safety Related Conduct
4. Chemistry Laboratory Honor Code GMU operates under a strict Honor Code policy Honor Code violations will be addressed by the instructor, the Department Chair, or the GMU Office of Academic Integrity, depending on the severity of the offense The following policies will be strictly enforced in Organic Laboratory. Quizzes and Final Exams given in the laboratory will be closed book. Instructor will hand out any additional resources required Lab Reports Students may discuss freely among themselves course subject matter from the lab texts, instructors lectures, and instructor’s website notes, but not in the context of specifics regarding lab report preparation or solutions to any homework assignments. All students are encouraged to seek help from the instructor, regarding details of report preparation or solutions to problems.
5. Chemistry Laboratory Honor Code (con’t) Students are encouraged to report suspected violations of the Honor Code to the instructor Suspected violations should be reported orally and in writing to the instructor Students reporting violations should be prepared to participate in a Honor Code Hearing, if applicable Students, who are reluctant to report violations should consider the harm done to themselves and other students by students who cheat, which has a diminishing effect on grade value
6. Chemistry Laboratory Class Elements (Con’t): Missed labs There are very limited provisions for missed lab sessions, especially in the summer sessions. Laboratory setup logistics severely limit provisions for making up missed lab sessions. Students can sometimes make up a lab during the same week of a given experiment (except in summer sessions). It is the student’s responsibility to anticipate and make provisions for missed labs. Missed laboratory sessions will receive a grade of zero for the report unless arrangements are made with the instructor for making up the lab work. Missed Lab Reports Laboratory reports not handed in will receive a grade of “0.” Late Lab Reports Laboratory reports are due the week following the experiment. One Week Late – 10 points deduction Two Weeks Late – 25 points deduction Three Weeks Late – Grade of “0”
7. Chemistry Laboratory Laboratory Process Quizzes - Quizzes are given at the beginning of lab and last about 20 – 25 minutes. Lab Lecture - (30-45 min)) Introduction to the next experiment Review Student Questions Instructor Subjects Detailed instructions for the Experiment Pre-Lab Reports Pre-lab reports containing Purpose, References, Procedure Descriptions, and proposed Data Presentation Templates are prepared using a supplied template. The pre-lab is due at the beginning of lab and will be checked by instructor during the Quiz. Final Lab Report – The pre-lab reports are completed with experimental data, a data summary, and an analysis of the experimental results. The final lab report is submitted the week following the experimental work The Lab Report is prepared according to the detailed guide lines described in this document utilizing a Microsoft Word lab report template obtained from the web site - http://classweb.gmu.edu/jschorni
8. Chemistry Laboratory Grades: Reports, quizzes, exams, and the problem set are graded on basis of 100 points. Instructor defines curve for assigning letter grades. Missed assignments will receive a grade of “0”, if not submitted within 3 weeks of lab. Quizzes – 20% of Grade Quizzes will cover the background and theory of the experiment performed the previous week, to include theory, reaction equations, procedural details, applicable computations. Lab Reports (60% of Grade) The grade for each experiment is based on the laboratory report: Technical content Procedure Descriptions Results & Observations Analysis of Results, Conclusions Completeness Organization / logical structure Presentation / Neatness Final Exam (20% of Grade) Laboratory grades are normalized to a class mean of 80% and incorporated into the lecture grade as 20% of the total grade.
9. Chemistry Laboratory The Laboratory Report: The laboratory report plays the most important role in the presentation of the laboratory course. The primary focus of the Genchem lab course is to enhance the learning of laboratory techniques and evaluation of experimental results through a comprehensive laboratory report process. The report process requires pre-lab planning, focused lab work, and a conscientious effort to effectively communicate the lab results to others in a clear, concise, grammatically and technically correct manner. Continued improvement in neatness, technical content, organization, and readability dictate the grading process as the semester proceeds. Final reports, including any attached tables, excel charts, etc. for a given experiment, will be submitted at the beginning of class the week following the completion of the experimental data collection.
10. Chemistry Laboratory The Laboratory Report (Con’t): During summer sessions there are three (3) lab sessions per week. The lab reports for a summer session week are due no later than Friday of the week following the experiments of the previous week. The Lab Report is graded on the basis of: Detailed adherence to the lab report template logical Organization Completeness Brevity Scientific Knowledge & Correctness Computational Accuracy Neatness Readability Pre-lab Preparation – The student uses a Microsoft Word report template (downloaded from the Instructor’s Website) to prepare a “Pre-lab Report”, which is checked at the beginning of the lab session. The “Pre-lab” report then evolves to the “Final Report”to reflect adjustments to the pre-lab procedure descriptions, inclusion and summary of the experimental results, and the analysis of the results leading to applicable conclusions.
11. Chemistry Laboratory The Laboratory Report (Con’t): Results must be organized logically in the lab report using a student designed data template for each procedure within the report. Note: Each lab report consists of one or more “Procedures. Results must be organized and presented in a logical manner, using tables where appropriate Algorithms, including variables, must be defined The computation of each result must be presented including the data substitution for each variable The “Results Summary” section, following the last experimental procedure, is a paragraph summarizing all of the results obtained in the experiment. Ex: the mass of the methyl benzoate reagent was 3.146 g. The “Analysis & Conclusions” section, following the “Results Summary,” is a logical development of a set of arguments, utilizing selected results from the experiment, to support any conclusions arrived at as a result of the experimental process. Emphasis is placed on correct grammar and brevity. Use as few words as possible, but use complete, grammatically correct, sentences. Do not use “First Person”, i.e., I, me, my, our, etc.
12. Chemistry Laboratory The Pre-lab Report The Pre-Lab is a template for the final report. It is created utilizing a Microsoft Word template down-loaded from the Instructors Website: http://classweb.gmu.edu/jschorni/ Click on: genlabreporttemplate.doc The Pre-lab contains all the elements of the final report except the experimental data, i.e., the results, final computations, summary, analysis, conclusions. The pre-lab report will be checked by the instructor during the lab session. The components of the pre-lab consist of the following: Note: All information in the Pre-Lab Report is assumed known to the student prior to the lab session from the laboratory text resources and the Web Site notes provided by the Instructor. Name, Date, Course & Section No., Drawer No., Partner(s), if any, entered into the Header Page of the report Title of Experiment Purpose Approach – Sequential list of the procedures to be used to conduct the experiment) References – Formal citation format for both text resources & compound resources.
13. Chemistry Laboratory Pre-lab Report – Principal Components Pre-Lab Report Components (Con’t) Procedures: Start each procedure on a new page Materials & Equipment (2 Columns) Procedure Description Equation Setup Templates for presentation of results (observed or computed, utilizing tables when appropriate)
14. Chemistry Laboratory Final Report (The Pre-Lab report is completed) Name (Must be on all pages of report) Title (Must be on all pages of report) Purpose Approach References Procedure #1 – Procedure Name (New Page) Materials & Apparatus (2 Columns) Procedure Description, Equation Setup Populated Data Templates & Tables Final Calculations Procedure #2 – Procedure Name (New Page) Materials & Apparatus (2 Columns) Procedure Description, Equation Setup Populated Data Templates & Tables Final Calculations Procedure #……. Summary Table of Results (optional) Summary paragraph of Results (New Page) Analysis/Conclusions – Logically derived supporting statements to justify conclusions made as to the significance of the experimental results.
15. Chemistry Laboratory Report Elements Name, Date, Drawer, Experiment No., Partners, etc. on each Header page of the report Note: Instructions for entering information into the Header fields are given in the report template. Title: Short statement about the experiment, e.g., Nitration of Methyl Benzoate. Purpose: Short, concise statement of what the experiment will accomplish. The statement should include: The principle reaction involved A new technique being introduced The principal instrument(s) that will be used. Ex: The purpose of this experiment is to determine the amount of acid present from the titration with a standard base. Ex: The purpose of this experiment is to synthesize the analgesic Aspirin (Acetylsalicylic Acid)in an Esterification reaction between Acetic Anhydride and Salicylic Acid. Ex. The purpose of this experiment is to identify an organic compound using Boiling Point, Refractive Index, and Infrared Spectroscopy
16. Organic Chemistry Laboratory (I & ll) Report Elements (Con’t): Approach: The Approach is a logical order listing, in paragraph form, of the procedures, including major steps within a procedure, that you will use to conduct the experiment. The task here is to determine what constitutes a procedure. A procedure is a logical group of steps to produce a particular result An element in the Approach would be a simple descriptive statement of the procedure to be used. ex. Determine the Mass of Benzoic Acid by Weighing. ex. Separate crude product from reaction solution by vacuum filtration. Note: Care must be taken not to include procedural details. Note: Calculations are considered to be procedures, and thus, would be elements in the Approach. ex. Adjust the Refractive Index value to the standard temperature value of 20oC.
17. Chemistry Laboratory Report Elements (Con’t) Approach (Con’t): Example: Determine the Mass of the Ethanol from its volume and density. Compute the Moles of the Reagents. Setup the Stoichiometric Balanced reaction equation. Determine the Molar Ratios. Determine the Limiting Reagent. Compute the Theoretical Yield. Extract (wash) the product with Distilled Water followed by 5% Sodium Bicarbonate. Dry the product with Anhydrous Sodium Sulfate. Determine the yield. Compute the % yield of the product. Determine the Refractive Index corrected for room temperature. Obtain an IR Spectra. Example: Determine the Mass of Formic Acid by weighing. Determine the Mass of Isobutyl Alcohol from its volume and density. Compute the Moles of the two reagents. Setup the Stoichiometric equation. Determine the Molar ratios. Determine the Limiting Reagent. Calculate the Theoretical Yield. Mix the reagents together with the Sulfuric Acid catalyst. Wash/Extract the organic layer with Sodium Bicarbonate. Separate the Organic layer from the Aqueous layer in a separatory funnel. Dry the product with Anhydrous Sodium Sulfate. Purify and determine the Boiling Point of the product using Simple Distillation. Determine the Mass of the purified product. Compute the Percent Yield of the product. Determine the Melting Point of the product.
18. Chemistry Laboratory Report Elements (Con't) Reference Citations – Text A formal citation of the principal resources used to provide background information and procedural details for the experiment. The following text is normally cited in each GenchemLab report: Slayden, S., Chemistry 211, 212, 251 Laboratory Experiments: 192 p.
19. Organic Chemistry Laboratory (I & ll) Report Elements (Con’t): Procedures: In general, start each new procedure on a NEW page. Exceptions can be made when two (2) or more procedures and associated results can be placed on one page in their entirety without crowding. The procedure description is placed in the left column of the procedure table in the template. Applicable results for a given procedure go in the column just to the right of the Procedure description. Each procedure is setup as an individual numbered and named entity. It includes: Procedure No. & Title Materials, and Equipment (M & E) Use two (2) columns in list (bullet) format, one for Materials and one for Equipment. The Materials column includes, disposable items (capillary tubes, etc.), principal reagents and amounts used Apparatus setups need to include a detailed list of the major components (distillation head, condenser, Meltemp apparatus, Filter Flask, etc.)
20. Chemistry Laboratory Report Elements (Con’t): Procedures (Con’t): Procedure Setup (Con’t): Procedure Description A short, concise, but complete, description of the experimental steps used to obtain a particular experiment result. The procedure descriptions should be an abbreviated form of the detailed instructions from the lab text, lab manual, or Web Site Notes. The student will develop original text in describing purpose the procedures, and the templates for presenting results. DO NOT COPY THE BOOK. The Procedure steps should be complete sentences put in list (bullet) format. If the procedure involves a computation, the algorithm is setup as part of the procedure description. Variables must be defined. The equation (derived as necessary) must be setup to represent the computational form of the algorithm.
21. Chemistry Laboratory Report Elements (Con’t) Results The results obtained from the experiment are reported on the “Right” side of a procedure page opposite the procedure description. The format of each “Results” section must be a carefully designed original that presents the data / observations / calculations in a logical and clearly readable manner, i.e., NEAT. The results are tabulated, but not discussed in a table or other designed format. Excel tables can be imported.
22. Chemistry Laboratory Download the Lab Report Template from the Web Site http://classweb.gmu.edu/jschorni/Chem 211Lab http://classweb.gmu.edu/jschorni/Chem 212Lab Make a copy of original template for each experiment Information is typed in the shaded blocks of the tables. Procedure Descriptions, Materials, Equipment are “Bulletized” Enter Information into “Header” table at top of page as follows:Word 2003 - Click on “View” in Menu Bar; select “Header & Footer.”Enter required information. Text will flow to to the Header at the top of each page. .When finished, click on “View” again and select “Print Layout” to return to normal data entry. Word 2007/2010 – Right click in Header box. “Edit Header” box appears. Left click in “Edit Header” box. Enter required information. Text will flow to the Header at the top of each page. When finished, click on “view” in Menu bar. Click on “Print Layout” to return to normal data entry Or, double click on “Header” box in lower left corner of “Header” table
23. Chemistry Laboratory Typical Header Table Typical Procedure Table NOTE: Each Shaded Block Will Expand As Necessary To Accommodate Additional Lines Of Information.
24. Procedure Examples
25. Procedure Examples
26. Procedure Examples
27. Procedure Examples
28. Chemistry Laboratory Summary Discussion After all the data collection procedures have been completed, the results are summarized in the Summary Results section in “Paragraph” format, i.e., ALL RESULTS. The results are not to be embellished or interpreted in any way. It is simply a summary listing of each result you obtained. Analysis/Conclusions A step by step presentation of arguments, utilizing selected results as applicable, to make a statement in support of any conclusions you have reached regarding the results of the experiment. What sequence of results lead to your selection of the year in which the composition of a penny changed?
29. Procedure Examples
30. Sec Chemistry Laboratory Report Grading Form Experiment: Name:
31. Laboratory Report Grading Codes Lab Report (Pre-Lab & Final) Code Comment a Report – not done, late, incomplete b Report Template – not used, not typed c Header Info – missing, incomplete d References – missing, incomplete e Purpose/Approach – missing, incomplete, weak f Procedure Descrip – missing, incomplete, weak g Procedure Setup – disorganized, ambiguous h Procedure Setup – crowded, start on new page i Result Templates – missing, incomplete Purpose Code Comment a Text – format, grammar, sentence structure b Text – wordy, overstated, superfluous c Text – originality, use your own words d Elements – omit background. approach items e Elements – principal reaction/equipment missing f Elements – missing, incomplete g Elements – technically weak, incorrect h Elements – disorganized, ambiguous Approach Code Comment a Text – format, grammar, sentence structure b Text – wordy, overstated, superfluous c Text – not in paragraph form d Text – originality, use your own words e Elements – each element in a separate sentence f Elements – omit background, procedural details g Elements – missing, incomplete h Elements – technically weak, incorrect i Elements – disorganized, ambiguous Reference Citations Code Comment a Reference Citation – missing, incomplete b Reference Citation – incorrect c URL Citation – missing, incomplete d Compound Citation – missing, incomplete e Compound Citation – incorrect f Compound Citation – page no., item no., missing g Citation Source – not citable (website, catalog) Materials & Equipment (M&E) Code Comment a Format – not in 2-column “bullet” format b M&E items – missing, incomplete c M&E items – mislabeled, incorrect Procedures Code Comment a Procedure No. – missing, incorrect b Procedure Title – missing, incomplete, incorrect c Procedure Title – wordy, overstated d Procedures – missing e Procedures – not used, not applicable f Procedures – disorganized, ambiguous g Procedures – need to be separated h Procedures – need to be combined i Procedure Desc – not in “Bullet” format j Procedure Desc – missing, incomplete k Procedure Desc – disorganized, ambiguous l Procedure Desc – technically weak, incorrect m Procedure Desc – originality, use your own words n Procedure Text – grammar, sentence structure o Procedure Text – wordy, overstated, superfluous p Extraneous Info – omit analysis & conclusions Results (Includes Tables, Charts & IR/NMR spectra) CodeComment a Template – weak design, disorganized b Presentation – messy, not typed c Results – missing, incomplete d Results – incorrect, ambiguous e Results – redundant, misplaced f Tables, Charts – missing, incomplete, incorrect g Spectra – missing, incomplete, incorrect h spectra Labels – missing, incomplete, incorrect i Extraneous Info – omit background, procedure items j Conclusions – out of place, move to analysis Computations CodeComment a Equation Setup ` – missing, incomplete, incorrect b Variables – undefined, ambiguous c Data Substitution – missing, incomplete, incorrect d Units – missing, incomplete e Units – incorrect, ambiguous, incorrect f Computation ` – missing, incomplete, incorrect g Precision, Sig Fig – incorrect Summary of Results CodeComment a Results – missing, incomplete b Results – incorrect, don’t match report c Results – disorganized, ambiguous d Results – each result in a separate sentence e Text – not in paragraph format f Text – grammar, sentence structure g Text – wordy, overstated, superfluous h Extraneous Info – omit background, procedural details i Conclusions – out of place, move to analysis Analysis, Significance of Results, Conclusions CodeComment a Analysis – weak, incorrect b Analysis – disorganized, ambiguous c Analysis – arguments incomplete, missing d Analysis – arguments lack support data e Analysis – weak theory connection f Results – repeat of summary of results g Text – grammar, sentence structure h Text – wordy, overstated, superfluous i Extraneous Info – omit, purpose, procedural details
32. Chemistry Lab Report - Computations There is NO separate “Calculations” section. Each computation is placed in the report as a NEW PROCEDURE A Computation Procedure is created as soon as all pertinent information needed for the calculation becomes available through prior experimental results and/or other computed results. Each computation is to be setup as a separate procedure. The equation is setup along with variable definitions in the procedure description. The data substitution and final calculations are presented in the results section across from the description section. Appropriate units must be presented and the calculations must be carried out with correct precision. The student must plan and design the results section to accommodate all of the anticipated results – measured, observed, or computed - for a given procedure. New procedures should not be started until the previous procedure and associated results are completed. Computations using results from two or more procedures should be grouped and presented in a separately titled procedure as soon as all of the pertinent data for the new computation is available.
33. Chemistry Lab Report - Computations Computation Setup In the “Description” box of the Procedure section provide a brief description of the equation and what it does. Set up the equation in the “Equation Setup” box of the Procedure Section. The equation setup should define the variables used in the equation and their logical relationship. In the “Results” box of the Procedure section show the values of the variables used in the equation and then substitute the values in the equation and make the final calculation. Show appropriate units. Report results to appropriate accuracy, i.e. correct number of decimal places and significant figures. Note: When multiple computations are done using the same “Equation” only “ONE” procedure is needed. If the equation changes then a “NEW” procedure is required.
34. Chemistry Lab Report - Computations Organic Chem Lab AlgorithmsMany of the Organic Laboratory Reports require the student to make computations for selected results.These include: Mass of a reagent from the weight of the vial containing the reagent and the mass of the vial empty. Mass Vial + Compound = 9.234g Mass Vial = 6.528g Mass Compound = 2.706g Mass of a liquid reagent (generally inorganic acids or bases) from the volume, density, and% composition. Mass (g) = Vol(mL) x Den(g/mL) x % comp/100 Moles of reagents from the Mass and Molecular Weight. moles = mass / mol wgt. The Moles of a reagent can also be computed directly from the Volume and Molarity of the reagent, e.g. the Molarity of concentrated HCL is 12 moles/L moles = Vol(L) x Molarity (moles/L)
35. Chemistry Lab Report - Computations Limiting Reagent The “Limiting Reagent” is that reactant whose mass (on a molar equivalent basis) actually consumed in the reaction is less than the amount of the other reactant, i.e., the reactant in excess. From the Stoichiometric balanced reaction equation determine the molar ratio among the reactants and products, i.e., how many moles of reagent A react with how many moles of reagent B to yield how many moles of product C, D, etc. If the ratio of moles of A to moles of B actually used is greater than the Stoichiometric molar ratio of A to B, then the A reagent is in “Excess” and the B reagent is “Limiting.” If, however, the actual molar ratio of A to B used is less than the Stoichiometric molar ratio, then B is in excess and A is “Limiting.” Example 1 A + B  C Molar Ratio A:B = 1 Moles actually used: A = 0.345 B = 0.698 Ratio of moles actually used (A/B): 0.345/0.698 = 0.498 0.498 < 1.0  B is in excess) & A is Limiting The theoretical yield of product will be the same as the “limiting Reagent” on a molar equivalent basis (A/C=1), i.e., 0.0345 moles.
36. Chemistry Lab Report - Computations Limiting Reagent Example 2 A + B  C Stoichiometric Molar ratio A:B = 1 : 1 = 1.0 Moles actually used: A = 0.20 B = 0.12 Ratio of Moles actually used (A/B): 0.20 / 0.12 = 1.67 The ratio of A:B is greater than 1.00 A is in excess and B is limiting. Only 0.12 moles of the 0.2 moles of A would be required to react with the 0.12 moles of B. The reaction would have a theoretical yield of 0.12 moles of C (Molar Ratio of B:C = 1). Example 3 – Molar Ratio 1:2:1 A + 2B  C Stoichiometric Molar ratio A:B = 1 : 2 = 0.5 Moles actually used: A = 0.0069; B = 0.023 Ratio of Moles actually used (A/B): 0.0069 / 0.023 = 0.30 < 0.5  A is limiting Only 0.0069  2 = 0.0138 moles of the 0.023 moles of B are required to react with 0.0069 moles of A. Since 0.0138 < 0.023: B is in excess, A is limiting. The reaction would have a theoretical yield of 0.0069 moles of C (Molar Ratio of A:C = 1).
37. Chemistry Lab Report - Computations Limiting Reagent (Con’t) Limiting Reagent Procedure Setup Alternative Limiting Reagent Determination 4 NH3(g) + 5 O2(g)  4NO(g) + 6 H2O(g) 2.00 g NH3 is mixed with 4.00 g Oxygen The limiting reactant that produces the lesser amount of product (NO) is Oxygen: (3.00g vs. 3.54g)
38. Chemistry Lab Report - Computations The Theoretical Yield Table (Con’t) The Theoretical Yield, in grams, is computed from the number of moles of the “Limiting Reagent”, the Stoichiometric Molar Ratio, and the Molecular Weight of the product. Yield = moles (Lim) x Molar Ratio x Mol Wgt The Percent Yield of a product obtained in a “Synthesis” experiment is computed from the amount of product actually obtained in the experiment and the Theoretical Yield. % Yield = Actual Yield / Theoretical Yield x 100 Note: The yield values can be expressed in either grams or moles Lab Report: Limiting Reagent Procedure setup
39. IR /NMR Problem Set Notes Partial Elemental Analysis of the Compound (Con’t) Where: nx = No. of Atoms of elements X in compound RMM = Relative Molecular Mass (Mol Wgt) RAM = Relative Atomic Mass of Element X Example Molecular Weight (RMM) = 58.0800 g/mol % Carbon – 62.0% Mol Wgt C (RAM) – 12.01 % Hydrogen – 10.4% Mol Wgt H (RAM) – 1.01  Now compute the remaining mass of the molecule after accounting for Mass of Carbon and Hydrogen 58.08 – (36.01 + 6.04) = 16.03 ~ 16  1 (Oxygen)  Molecular Formula – C3H6O
40. Approximate Numbers and Significant Digits Some numbers are “Exact” or “Pure”, i.e., having been defined or counted. Examples: 3 Cherries, 125 People, 50 Measurements, 16 oz in a pound Most numbers involved in technical and scientific work are obtained through some process of measurement. All measurement processes are imprecise, i.e., only approximations of the true values. The precision of an instrument dictates the relative accuracy of the values that can be reported, i.e., the number of significant digits. The precision of a number refers directly to the position of the last significant digit relative to the decimal point. All none zero digits are significant. Zeros other than those used as placeholders for proper positioning of the decimal point, are also significant. There is uncertainty in the last significant digit. For example: A person records his weight on a scale to be 160 lbs. The last “zero” is a placeholder and is not significant. Thus, the “6” has uncertainty. His true weight could be 158 lbs, 161 lbs, 159.4 lbs, 160.0 lbs. etc. When multiplying or dividing groups of measured values the answer will have the same number of significant digits as the least accurately known number. When adding or subtracting numbers, the answer is significant only to the fewest number of decimal places contained in any of the numbers being added or subtracted, i.e. significant to the least precise number. NumberSignificant Digits 9600 2 No decimal point; therefore last two zeros are not significant, i.e., placeholders. The uncertainty is in the last significant digit, i.e. the “6” 20004 5 Five significant figures; the 3 zeros are significant; the “4” has uncertainty. 4.0006 5 5 significant figures; precision is defined to the fourth decimal 0.0709 3 3 significant figures; the zero after the decimal is a placeholder 6.000 4 Precision is defined to the third decimal, thus all zeros here are significant. The uncertainty is in the last zero 0.0005 1 Zeros to the right of the decimal are used as placeholders for decimal point Precision is defined to the fourth decimal. 1.07 3 Precision defined to the second decimal; thus all digits significant 1.070 4 Precision is defined to the third decimal; thus all 4 digits are significant. The uncertainty is in the last “zero” 700.00 5 Precision is defined to the second decimal, thus all five digits are significant 25 x 11.7 = 290 not 292.5 16.5 / 3.780 = 4.37 not 4.3651 4.65 + 3.8906 = 8.54 not 8.5406 7.71 x 0.001 + 180.5 + 2000 = 2000 (0.008 + 180.5 + 2000) = (180.5 + 2000) = 2000 7.71 x 0.001 x (1/180.5) x 2000 = 0.1 (0.008 x 0.006 x 2000) = (0.00005 x 2000) = 0.1 (0.066 x 39.82) / ( 1.43 x 8.61) = 0.21 (2.6 / 12.3) = 0.21