Chem Lab 2
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CHEM 1111 v.0116 Page 1 Uncertainty in Measurement and Significant Figures Why? /\Emm'& \WWONVRN G The number of digits, the significant figures, reported for a numerical quantity conveys the quality of the measurement of analysis to the reader. In any business involving numerical values, the precision of these values, which is represented by the number of digits, is vital information. In this course and others, you will have to use a meaningful number of digits in reporting your results. Learning Objectives e Appreciate the difference between precision and accuracy e Understand the relationship between precision and the number of significant figures in a number Success Criteria e Report numerical values to the correct number of significant figures o Identify the accuracy and precision of a numerical value Resources e Textbook e Instructor Model Accuracy refers to the agreement between a measurement and a standard or true value. (In archery, this would be how close one comes to striking the bullseye.) Precision is the smallest repeatable digit of a measurement. (In archery, this would be how close a group of arrows strikes relative to each other, regardless of how close they are to the bullseye.) 1. How could you word a statement that would explain the concept of accuracy to a child? QACELACY 1D VoW TAIOR. SOMRINNY 19 4o RING exocryy (1t WK ANowing a ball ard v \ards Xty Wwhnee you aimed — Thnor \S ocuiotR 2. How could you word a statement that would explain the concept of precision to a child? PreciSi00 S doind) 20MRTVING tng SOme wWaY EVerArime, even wvieh w3 aor agwnt, like 4vnowiney a boll in o comer ove« ondd OVe( but You asSsed 4w centes — tViotS PreCise
CHEM 1111 v.0116 Page 2 Model — Measuring with Rulers 3. Measure the shaded box below with the top ruler as accurately and precisely as possible. Which digit did you estimate? 2 o 4, Measure the shaded box with the lower ruler as accurately and precisely as possible. Which digit did you 7.0 estimate? The following is a zoomed-in view of the end of the shaded box and the area circled on the lower ruler. Each mark represents 0.1 mm or 0.01cm. »1.2.% 20 21 5. Using this information, what would be the length of the shaded box? 2.3‘ of¢ e A oA 0.23% Now using an actual ruler (from around your house or dorm), measure the shaded box’s length in cm. 5 2¢cn of 27 6. Which of the rulers (choosing between a real ruler and the rulers printed above on this activity) used was the most accurate? Why do you believe this? T onene W (VR( pum"e,c\ WOS MOR accuittt. conoasind T couldd et an andwer CLOBRI -t L eXaet valvk 7. Which of the rulers used was the most precise? Why do you believe this? W It T was usind o+ LomL gave muie Pftfi‘%‘?- meoaturements qround TWL exack yalve ofF e Syiuded LOR | vibwRveLs TULIE D L opPottuniFy For Muman errac Wi Wl (VR gt e ooy T S\ aed preCI¥e valoes
CHEM 1111 v.0116 Page 3 Model - Significant Figures Significant figures are all of the digits of a number that can easily be repeatedly measured using some sort of device (a ruler, a scale, a thermometer, etc.) and the last digit of the number that is subject to interpretation by the person reading the device. Measuring with a ruler you can accurately obtain the number of centimeters and tenths of centimeters from the markings on the ruler but you have to guess the value of the hundredths of centimeters between the tenths markings - the guessed number is the first uncertain digit. 8. Look back at the measurements that you took of the shaded box with each ruler. How many significant digits were in each measurement? for vy Fier maguement T got 0on€, 4o 2 3 oQawn twah 5. 2cm wnicht wovld be 2 Ronge cetuxra =3 Information - Zeros in Numbers Zeros used in numbers are one of the most confusing aspects of significant figure determination. The use of and location of a decimal point relative to a given zero determines if the zero is significant or not. Examples Significant Figures Why? 50.0r 5.0 x 10! Two The placement of the decimal means the person recording the data felt that the measurement of the zero was correctly estimated only to the second digit. 200 or 2 x 102 One The lack of the decimal means the person recording the data felt that the measurement was correctly estimated to only one digit. In the number 200 the zeros are only place holders. 430.3 or 4.303 x 10? Four A zero between two other nonzero numbers is always 80.07 or 8.007 x 10! significant. 0.006 or 6 x 1073 " One Preceding zeros are not significant as they are only place 0.00000005 or 5 x 108 holders. 200.0 or 2.000 x 10? Four Zeros after the decimal point are significant if i)receded by 0.07700 or 7.700 x 102 another significant number or significant zero. Key Questions 9. Consider your most precise measurement for the shaded box that you found using the printed rulers. How many significant figures were in that measurement? Were there any significant zeroes in your measurement? oY) NSy PrECITR meateMent Wit ¢ cumof rolec was 2 0% amd W Wats D 1Y F1933 gand oS O vWYMhcont O 55 10. What is the difference in the numbers: 100, 100. and 100.0? SO AVRY (BRI 4AVL 2omE VoloR numerically | Howrver oo by 1rselt Suymoo\Vies 1T s\9mfican Fioyore , \OD, wvn decimol ynt MOKe eNei nvmver before WL decimol SqaiFeany, 2o betnd 2 sygmificant Fuies, Logrly 100,0 oo all NUMBERS bend Syvambtant anol bLING M g €\g3, LR\
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CHEM 1111 v.0116 Page 4 Key Questions 1. If each member of your group was sent an identical pencil and your grade on this laboratory depended on how well each member of your group measured the length of the pencil, what would be some of your concerns about your group’s measurement? (Imagine you are working with a group if you are in fact, working individually.) MONY concesn would be orouve et U?/ Nowewer(, Y Mo\ conclin wouid bE ViuMAN Extal, condIHtency, Rrecyion o€ ovl meawue MM ond tun maye communicatio 2. How would you determine which measurement would be the one you report on your ]')%gsr? aut LVLORS MOSt CONS\RIEMT anNBwWel & (eprese coper. FurtuLemore, probably enaluoré ever4ones measuie memts andd chelt aadd acld eSS Crrers before ConcluSion Error is the difference between the measurements and the true value. Many people think that error refers to the mistakes made during a laboratory procedure, but this is not what error means to scientists! Every measurement has some error associated with it due to the limits of the measuring device. 5. What are at least two sources of error in measuring the length of a pencil? Homan Judgement, Feading ecrofs, maybe some deformi+ies wtwn ouc renc . 6. Why is it wise to take several measurements and report an average value? : By O\O\(\?) AN\S Wk Can feduce Rontom [ Human ecors, WWiCW (ovid Gueroo our b efFects andl WAP provid US withh O OCCUIOR” (P RIELATATION oF our volue , furtnesmex 1(\9,(&0\3\(\(3 p(e,c\S\O(\ , snmvaomnm Wl Wm\cee,;(o;%' eanunc< GUC QCCUTACY) , BN RN WRYIAR ap cuc Syandardd ag peess,
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