ࡱ> <>; T bjbj 46T$4P,FF[@r%q0$FF J:   Chemistry: Significant Digits In an attempt to get away from the mathematical burden of uncertainties, scientists have gone to the use of established rules for significant digits that have greatly simplified calculations. These rules are: 1. Significant numbers are always measurements and thus should always be accompanied by the measurement's unit. For simplicity, units are not included in the following examples. 2. Any numbers (that are measurements) other than zero are significant. (Many times the zeros are also significant as you will see below.) Thus 123.45 contains five significant digits. 3. Any zeros between numbers are significant, thus 1002.05 contains six significant digits. 4. Unless told differently, all zeros to the left of an understood decimal point (a decimal that is not printed) but to the right of the last number are not significant. The number 921000 contains three significant digits. 5. Any zeros to the left of a number but to the right of a decimal point are not significant. 921000. has six significant digits. 6. These zeros are present merely to indicate the presence of a decimal point (they are used as place holders), (these zeros are not part of the measurement). The number 0.00123 has three significant digits. The reason that these zeros are not significant is that the measurement 0.00123 grams is equal in magnitude to the measurement 1.23 milligrams. 1.23 has three significant digits, thus 0.0123 must also have three significant digits. 7. Any zeros to the right of a number and the right of a decimal point are significant. The value 0.012300 and 25.000 both contain five significant digits. The reason for this is that significant figures indicate to what place a measurement is made. Thus the measurement 25.0 grams tells us that the measurement was made to the tenths place. (The accuracy of the scale is to the tenths place.) Give the number of significant digits in each of the following measurements: 1. 1278.50 __________ 7. 8.002 __________ 13. 43.050 __________ 2. 120000 __________ 8. 823.012 __________ 14. 0.147 __________ 3. 90027.00 __________ 9. 0.005789 __________ 15. 6271.91 __________ 4. 0.0053567 __________ 10. 2.60 __________ 16. 6 __________ 5. 670 __________ 11. 542000. __________ 17. 3.47 __________ 6. 0.00730 __________ 12. 2653008.0 __________ 18. 387465 __________ Round off the following numbers to three significant digits: 19. 120000 _______________ 22. 4.53619 _______________ 20. 5.457 _______________ 23. 43.659 _______________ 21. 0.0008769 _______________ 24. 876493 _______________ Chemistry: Significant Digits (continued) Significant figures in derived quantities (Calculations) In all calculations, the answer must be governed by the least significant figure employed. ADDITION AND SUBTRACTION: The answer should be rounded off so as to contain the same number of decimal places as the number with the least number of decimal places. In other words, an answer can be only as accurate as the number with the least accuracy. Thus: 11.31 + 33.264 + 4.1 = 48.674 Rounded off to 48.7 MULTIPLICATION AND DIVISION: The answer should be rounded off to contain the same number of digits as found in the LEAST accurate of the values. Thus: 5.282 x 3.42 = 18.06444 Rounded off to 18.1 Perform the following operations giving the proper number of significant figures in the answer: 25. 23.4 x 14 _______________ 26. 7.895 + 3.4 _______________ 27. 0.0945 x 1.47 _______________ 28. 0.005 - 0.0007 _______________ 29. 7.895 / 34 _______________ 30. 0.2 / 0.0005 _______________ 31. 350.0 - 200 _______________ 32. 27.68 - 14.369 _______________ 33. 3.08 x 5.2 _______________ 34. 0.0036 x 0.02 _______________ 35. 4.35 x 2.74 x 3.008 _______________ 36. 35.7 x 0.78 x 2.3 _______________ 37. 3.76 / 1.62 _______________ 38. 0.075 / 0.030 _______________ 39. 65 000(0.08 x 200 x 0.004) / (800 x 300) _______________ 40. [(11.34 ( 9.63) / 11.34] ( 100.00 _______________ 41. [( 2.0265 ( 2.02) / 2.0265] ( 100.00 _______________ Answers to Significant Digit Worksheet: Give the number of significant digits in each of the following measurements: 1. 1 278.50 6 7. 8.002 4 13. 43.050 5 2. 120 000 2 8. 823.012 6 14. 0.147 3 3. 90 027.00 7 9. 0.005789 4 15. 6271.91 6 4. 0.0053567 5 10. 2.60 3 16. 6 1 5. 670 2 11. 542 000. 6 17. 3.47 3 6. 0.00730 3 12. 2 653 008.0 8 18. 387 465 6 Round off the following numbers to three significant digits: 19. 120 000 = 1.20 x 105 22. 4.53619 = 4.54 20. 5.457 = 5.46 23. 43.659 = 43.7 21. 0.0008769 = 0.000877 or 8.77 x 10-4 24. 876 493 = 876 000 or 8.76 x 105 Perform the following operations giving the proper number of significant figures in the answer. 25. 23.4 x 14 327.6 = 330 or 3.3 x 102 26. 7.895 + 3.4 11.295 = 11.3 27. 0.0945 x 1.47 0.138 915 = 0.139 28. 0.005 - 0.0007 0.0043 = 0.004 29. 7.895 / 34 0.232 205 882 = 0.23 30. 0.2 / 0.0005 400 = 400 31. 350.0 - 200 150 = 200 32. 27.68 - 14.369 13.311 = 13.31 33. 3.08 x 5.2 16.016 = 16 34. 0.0036 x 0.02 0.000072 = 0.00007 35. 4.35 x 2.74 x 3.008 35.852352 = 35.9 36. 35.7 x 0.78 x 2.3 64.0458 = 64 37. 3.76 / 1.62 2.320987654 = 2.32 38. 0.075 / 0.030 2.5 = 2.5 39. 65 000(0.08 x 200 x 0.004) / (800 x 300) 0.01666666667 = 0.02 40. [(11.34 ( 9.63) / 11.34] ( 100.00 15.079365079 = 15.1 41. [( 2.0265 ( 2.02) / 2.0265] ( 100.00 0.3207500617 = 0.5 Converting between two sets of units never changes the number of significant figures in a measurement. Remember, data are only as good as the original measurement, and no later manipulations can clean them up.  "$G M  $ h u w 'bDbu v{·««« jh}hv5OJQJ j-h}hv5OJQJh}hv5OJQJhv5>*OJQJhv5OJQJhv6OJQJhvOJQJhv5CJOJQJhv56CJOJQJhv5CJOJQJ7#$T  p q @  A B  z -s$&$d%d&d'd/NOPQP^Pgdvz RUVSTA~dh()b/0Ty5[~dhgdv~>}  23gdvdhgdv3")*+5:;<QU[\deghnpstĶĶĶĶĶĶĶĶĶĶĶĶĶĶĶhv5B*OJQJphhvOJQJhv5OJQJ jh}hv5OJQJ j-h}hv5OJQJh}hv5OJQJH3,i*+g_`Jq dh`gdvdh(?HIbfgy}]EIlopq굠ᕵh}hvOJQJ(h}hv5B*CJEHOJQJph h}hv5B*OJQJph"hv5B*CJEHOJQJphhv>*OJQJhv5OJQJhvOJQJhv5B*OJQJph4&)24568X]_37JK^_z}S T ԾԾ嚉hv5OJQJ hR)hv5B*OJQJphhvOJQJ jh}hvOJQJ j-h}hvOJQJh/5B*OJQJphh/OJQJ h}hv5B*OJQJphh}hvOJQJh}hvB*OJQJph0 8a:S T $a$$a$gdv dh^gdv dh`gdv 2P/ =!"#$% Dp666666666vvvvvvvvv666666>6666666666666666666666666666666666666666666666666hH6666666666666666666666666666666666666666666666666666666666666666666666666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH P`P Normal5$7$8$9DH$OJQJ_HmH sH tH DA D Default Paragraph FontViV  Table Normal :V 44 la (k (No List PK!pO[Content_Types].xmlj0Eжr(΢]yl#!MB;.n̨̽\A1&ҫ QWKvUbOX#&1`RT9<l#$>r `С-;c=1g~'}xPiB$IO1Êk9IcLHY<;*v7'aE\h>=^,*8q;^*4?Wq{nԉogAߤ>8f2*<")QHxK |]Zz)ӁMSm@\&>!7;wP3[EBU`1OC5VD Xa?p S4[NS28;Y[꫙,T1|n;+/ʕj\\,E:! t4.T̡ e1 }; [z^pl@ok0e g@GGHPXNT,مde|*YdT\Y䀰+(T7$ow2缂#G֛ʥ?q NK-/M,WgxFV/FQⷶO&ecx\QLW@H!+{[|{!KAi `cm2iU|Y+ ި [[vxrNE3pmR =Y04,!&0+WC܃@oOS2'Sٮ05$ɤ]pm3Ft GɄ-!y"ӉV . `עv,O.%вKasSƭvMz`3{9+e@eՔLy7W_XtlPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-!pO[Content_Types].xmlPK-!֧6 -_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!!Z!theme/theme/theme1.xmlPK-! ѐ'( theme/theme/_rels/themeManager.xml.relsPK]# T&6T z ~3T VXe(NVDG%(~Va,@} ) - A g y } 6=ag# ,N;C^fu}})/V`/6Z_@HV:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::vL[_/TV@hjT0@UnknownG*Ax Times New Roman5Symbol3 *Cx ArialWMTms RmnTimes New RomanA$BCambria Math"Vhggg& , ,!Vxx24HH ?QVHP)?T22!xx ,Significant Digits Chemsitry'significant digits, significant figures%John Bergmann and Jeff Christopherson Etown Admin Oh+'00<P dp    'Significant Digits Chemsitry(John Bergmann and Jeff Christopherson(significant digits, significant figures Normal.dotm Etown Admin2Microsoft Macintosh Word@@w@\%@\% ՜.+,0( px  'Introduction to Chemistry , H Significant Digits Title  !"#$%&'()*,-./012456789:=Root Entry FJWr%?1TableWordDocument46SummaryInformation(+DocumentSummaryInformation83CompObj` F Microsoft Word 97-2004 DocumentNB6WWord.Document.8