' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]L L}BBL]$$8HI ,նh, ,`, ,`, , ,:/8` 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"_]` L/浍굺L  !"#$%&'()*+,-./0123456789:;<=>?  1#"""  (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0EB H  @H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`HIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   vLDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^L iõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmxӜ ( Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈m浍浭m䵍䵐`"L ŵ8ŵH ~(` d ֠z# u`NX2S,Y:XX2X1S:NXS,Y:MXSS2,Y:15XSS25,Y4:I1150:B MXSS2,Y:15XSS25,Y4:NXSS,Y:I1150:::BXX0:YYYY10:5:B2L(1)L(2)R(1)R(2)T(1)T(2)B(1)B(2)0ı#C6I1:L(1)R(1)T(1)B(1)0I2:L(2)R(2)T(2 working in lab.":YYYY20:15:300j5*WD$"It's time to return to the menu.":YY100:15:100:BACK10800t5*1000ll, that's all there is to ''DIMENSIONAL ANALYSIS.''":YY10:15:WD$"You will find that it can be a great time (and brain) saver when w0:15::WD$"5.0 / 6.4516 = 0.7750015 --> 0.78":XX20:YYYY20:5:WD$"0.78":XX215:YY90:5:100:BACK10680#5*:WD$"Well, that's all there is to ''DIMENSIONAL ANALYSIS.''":YY10:15:WD$"You will find that it can be a great time (and brain) saver when3,3:2:233,3:2:0:2125,77:2141,973*WD$"2.54 x 2.54 = 6.4516":XX70:YY130:5:WD$"We keep all the digits since 2.54 is exact.":YYYY10:15:100:BACK10680l4*127,109145,96:180,99198,81:T120:B160:200:WD$"See how the units cancel?":YY113:2:2155,26:100:BACK1068042b*T100:B160:2002l*WD$"5.0 cm = in":XX160:YY90:5:2195,88:2251,88:215,100237,1002v*233,22:0:1:1148,75:32:185,113:85,93150,93'3*WD$"6.4516 cm":XX88:YY100:5:WD$"1 in":XX107:YY82:5:23D$"We know there are 2.54 cm per inch, but what about square cm and square inches?":YY90:15:300:WD$"Just fill-in the fraction and square the whole thing!":YYYY20:15:100:BACK106802X*WD$"2.54 cm":XX108:YY48:5:WD$"1 in":XX122:YY32:5:233,uation to examine. How many square inches are there in 5.0 cm ?":YY10:15:233,3:2:2260,9:3000:*WD$"5.0 cm = in":XX160:YY40:5:2:2195,38:2251,37:215,50237,500D*300:233,22:0:1:1148,25:32:1110,63:110,43150,43:3001N*Wx 3.451 = 105.18648 --> 105.2":XX20:YY90:5:WD$"105.2":XX223:YY60:5:WD$"The only units left are cm, which is what we want!":YY110:15:300/&*WD$"Also note that 2.54 and 12 are exact numbers.":15:100:BACK10620e00*:WD$"Here is one final sitentimeters. Watch...":YYYY20:15:300:WD$"12 in":XX120:YY50:5:0:190,44:32:150,82.*50,6290,62:WD$"1 in":XX65:YY70:5:300:71,7883,69:134,59145,49:300:WD$"2.54 cm":XX50:YY50:5:100:BACK10620/*T90:B160:200:WD$"2.54 x 12 128,80141,68:192,68204,57:100:BACK10620-)T110:B160:200:WD$"Now we know that there are 2.54 cm in 1 in, but we don't have the conversion from cm to feet. So what do we do?":YY80:15:300].*WD$"First convert feet to inches, and then go to c"CM"A$"cm"A$"CENTIMETERS"A$"centimeters"ĺ(7);(7):10710,)A$"FT"A$"ft"A$"FEET"A$"feet"WD$"Wrong!":10740,)WD$"Of course!"--):YY130:15:WD$"We have to get rid of the original units!":15:WD$"1 ft":XX120:YY70:5:300:WD$"3.451 ft = cm":XX160:YY60:5:221,70251,70:300+)0:1150,44:32:1110,82:110,64150,64:WD$"What units should go in the denominator of this fraction?":YY100:15C,):21:"FT OR CM? ";A$:A$"FT"A$"ft"A$"FEET"A$"feet"A$YY100:5:159,98163,98:WD$"720":XX193:YY50:5G*)100:BACK10540*):WD$"You can also have the units in one fraction cancel out the units in another fraction. For example, if we were converting 3.451 feet to centimeters....":YY10:15>+)300:":XX50:YY44:5:WD$"1 min 2.54 cm":XX50:YY56:5:45,5376,53:95,53137,53:32:145,73:195,73:0:178,34:1136,35))100:BACK10540))122,64136,56:164,52177,44:400:67,5175,44:167,65174,562*)300:WD$"(60/2.54) x 30 = 720":XX80: doing both fractions at once.":YY8:15:213,0217,0:300()WD$"30 =":XX150:YY50:5:157,48161,48:WD$" cm in":XX150:YY44:5:WD$" s min":XX148:YY56:5:165,54177,54:218,54236,54:192,60212,60}))WD$"60 s 1 in 12 = 720":XX70:YY90:5:WD$"720":XX193:YY50:5'r)WD$"Note that there are exactly 60 seconds in a minute so we use both significant digits from the 12.":YY110:15:100:BACK10470;(|):WD$"We could have gone directly from 30 cm/s to 720 in/min byBACK10470&h)T80:B140:200:WD$"This might be easier to see if we rewrite these units.":YY110:15:0:Y4960:145,Y171,Y::3:WD$"in s":L3:XX150:YY45:5:L45:148,54159,54:300&m)148,63157,56:100:BACK104703'o)T100:B140:200:WD$"60 x15N%J)233,22:32:180,72:0:1119,34:80,53120,53:WD$"s":XX110:YY41:5%T)108,50117,41:160,59170,49:300:WD$"min":XX102:YY57:5:300 &^)WD$"There are 60 seconds in 1 minute.":YY120:15:WD$"1":XX90:YY57:5:WD$"60":XX92:YY41:5:100:ing, not inches per second?":YY10:15:300a$6)WD$"12 in/s = in/min":XX130:YYYY30:5%@)190,60215,60:300:WD$"The fraction must replace seconds with minutes. Also notice that the seconds are in the denominator of the given value.":YY70:1,108:WD$"12":XX203:YY40:5:300#")WD$"The time unit of seconds never entered the problem since we wanted it left in the result.":YY120:15:100:BACK10430,$,):WD$"What if we really wanted to know how many inches per minute the object was travelY31:5:300")WD$"And since 2.54 cm = 1 inch....":YY120:15:WD$"1":XX93:YY31:5:WD$"2.54":XX85:YY47:5:100:BACK10430##)T70:B140:200:WD$"So our calculation becomes:":YY80:15:WD$"30 / 2.54 = 11.8110236 --> 12":XX50:YY110:5:57,1086er set of units. (In this case, cm.)":YY60:15!(233,22:32:180,62:0:1119,24:80,43120,43:WD$"cm":XX110:YY47:5:300 ")108,57121,48:148,49160,39:300:WD$"Next put in the units we need in the result, inches.":YY90:15:WD$"in":XX101:Y":YY110:15:100:BACK10410 (:WD$"Write down what we are given and set it equal to what we want.":YY10:15:WD$"30 cm/s = in/s":XX130:YYYY30:5:137,38141,380!(190,50223,50:300:WD$"Put in a fraction, making sure we cancel the prophow fast is that in inches per second?":YYYY20:15:162,48166,48:300(40,91220,91:Y180:Y290:YY1Y2:50,Y60,Y::X50200:0:X,Y1X,Y2:3:X11,Y1X11,Y2::300 (WD$"Even though the units are more complicated, we treat them the same way.:WD$"Let's try another one.":YY100:15:100:BACK10180(:WD$"An inch is defined to be exactly 2.54 cm. (That means our conversion factor can have as many significant digits as we want.)":YY10:15:300H(WD$"If an object slides by at 30 cm/s, 0:15:100:BACK10160(:WD$"That's easy! All you do is cancel the units. You can't impress your friends by telling them you ''know how to cancel.'' So...we give it a fancy name. We call what you just did DIMENSIONAL ANALYSIS!":YY10:159(300K10160(T110:TY150:200:WD$"So this time we multiply by the conversion factor.":YY80:15:WD$"1.61 x 6.0 = 9.66 --> 9.7":XX70:YYYY20:5:WD$"9.7":XX200:YY50:5(WD$"It looks like you might be able to handle that 10 km run after all!":YY13ood! That also means that a '1' should go on bottom (denominator).":10370x(WD$"That is not correct! The numbers must go with their cooresponding units!"(:T100:B150:200:YY100:15:WD$"1.61":XX68:YY43:5:WD$"1":XX70:YY59:5(100:BAClt.":YYYY10:15:WD$"km":XX91:YY43:5>P(100:BACK10160Z(T110:B150:200:WD$"We know that there are 1.61 km in 1 mile. What number goes in the numerator?":YY100:15d(:21:"1.61 OR 1? ";A:A1.61A1ĺ(7);(7):10340Kn(A1.61WD$"Gkm"A$"KILOMETERS"A$"kilometers"ĺ(7);(7):102802(A$"KM"A$"km"A$"KILOMETERS"A$"kilometers"WD$"That's how it's done!":10310<(WD$"That is not correct!")F(:T100:B150:200:YY100:15:WD$"We want to have the same units as the resuXX80:YY59:5E(300:79,68107,58:140,60170,50:100:BACK10160(T110:B150:200:WD$"What units should go on top of the fraction (the numerator)?":YY100:157((:21:"MILES OR KM? ";A$:A$"MI"A$"mi"A$"MILES"A$"miles"A$"KM"A$"A$"KILOMETERS"A$"kilometers"ĺ(7);(7):10220z'A$"mi"A$"MI"A$"miles"A$"MILES"WD$"That's right!":10250(WD$"No!" (:T100:B120:200:YY100:15:WD$"We have to cancel out the units on the original data.":YYYY10:15:WD$"miles":X180:YY50:5:190,60220,60:300n'WD$"Now put in the fraction. Which units go on the bottom?":YY90:15'233,22:1:32:160,72:0:1105,34:60,53105,534':21:"MILES OR KM? ";A$:A$"mi"A$"MI"A$"MILES"A$"miles"A$"KM"A$"km" greater or less than 10 km.":YYYY20:15:100:BACK10070':WD$"Just like before, write down the data you are given:":YY10:15:WD$"6.0 miles":XX120:YY50:5:300"'WD$"Then set it equal to what you want to find.":YY10:15:WD$"= km":XCK10040':WD$"Let's try another one. That seemed too simple!":YY10:15:WD$"If you can run 6.0 miles with no problem, could you manage a 10 km race?":YYYY40:15:300;'WD$"What we have to do is convert 6.0 miles to kilometers and see if it ison factor.":YY70:15:WD$"5.0 / 1.61 = 3.10559 --> 3.1":XX50:YYYY20:5:WD$"3.1":XX180:YY50:5'300:WD$"The only thing we had to think about were the significant digits. Whether to multiply or divide came out automatically.":YY120:15:100:BA:WD$"1 mile = 1.61 km":XX100:YYYY20:5:300'WD$"Put the corresponding numbers into the fraction.":YYYY10:15:300:WD$"1":XX66:YY43:5:WD$"1.61":XX65:YY59:5:100:BACK10040d'T80:B160:200:WD$"This says that we DIVIDE by the conversiK10040~'90,70103,57:140,60155,48:T90:B140:200:WD$"Next put units in the fraction that match those that you want to have in your answer.":YY70:15:300:WD$"miles":XX76:YY43:5/'300:WD$"Now look at your conversion information:":YY90:15$"Now comes the sneaky part! Multiply the given data by a fraction. Set up the fraction so that it will have units which cancel out the given units.":YY90:15:300t'233,22:1:32:160,72:0:1105,34:60,53105,53:WD$"km":XX91:YY59:5:100:BAC:YYYY30:15:100:BACK10000V':WD$"First write down the data you are given:":YY10:15:WD$"5.0 km":XX120:YY50:5:300`'WD$"Then set it equal to what you want to find.":YY10:15:WD$"= miles":XX160:YY50:5:170,60200,60:300j'WD0:15B'300:WD$"For example, knowing that there are 1.61 km in a mile, how many miles have you gone if you went 5.0 km?":YYYY20:15:300L'WD$"Should we multiply or divide by 1.61? Turn the page to see the steps involved in solving this problem."hod that allows you to handle unit conversions with almost NO THINKING!":YYYY20:15:100:BACK10008':WD$"The hardest part of doing a unit conversion problem is remembering whether you should multiply or divide by the given conversion factor.":YY1ormation. You are even expected to understand some of it!":YY10:15:300 $'WD$"Keeping the units straight seems to be one of the most difficult challenges for the novice physicist.":YYYY10:15e .'300:WD$"Well, help is on the way! There is a met279,Q::3: ,ZZ12000::3 ZZ11000:: ::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":" " 1023,7:"RUN MAIN MENU" 'K ':WD$"As a new physics student you are being bombarded with tremendous amounts of infRIGHT ARROW OR ESC >>>";::1:A$:24:1:" ";m hA$""ĺ" "::1000 jA$""BACK1:" ": kA$""ĺ" ": m21:1:958:(7);(7):102 n 0:Y0LAST10:0,Y279,Y::3: 0:QTB:0,QLTRL11:X$(WD$,LTR,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6 XX0:YYYY10:5: d eBACK0T f49168,0:24:958:24::4:"<<< LEFT OR u-)1002:A(X)((X.0005)1000)1000C:0:2:232,0:233,3X3:L45::10000F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXX100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:1                w  (0 ѕнй`)JJ & & f)`ɀ`I `ayLqHɵrims`aiȱȄ詷 ,詷 `iHhLꢩLҦ&$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::V$(V$,(V$)LTR):99:XXXZ:YYYY10:6A Q3(249):Q4(231):Q2(233):Q1(232):1:48:232,0:233,8:100XX,YY:Q1(V$):((V$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:HB N72:M82:ultiplication/Division Rule:":YYYY30:Y110116:5,Y10,Y::15RWD$"Perform calculation and round to the number of significant digits in the limiting measurement.":YYYY10:15R100:BACK21020R1000 first estimated digit.":YYYY10:15K20930~R:WD$"Summary":XX130:YY0:5:130,10178,10:Y3036:5,Y10,Y::WD$" Addition/Subtraction Rule:":YYYY20:15~RWD$"Convert to the same units, perform the calculation, and round to the first estimated digit.":YYYY10:15ARWD$" Mhe brackets would round to 347.8 with 4 significant digits.":YYYY5:15}bRWD$"Since that is the limiting value, the division rule says that the final result of the whole calculation should be rounded to 4 significant digits.":YYYY10:15~lR100:BAC/ 4.5762)":XX30:YY45:5y|NRWD$"= 76.010117":YYYY10:5:WD$"Which can be rounded to....":YY100:15:100:BACK20930|SR0:YY100:15:3:XX30:YY55H}XRWD$"= 76.01":YYYY10:5:WD$"The addition rule says that the result of the calculation inside t1:"HOW MANY DIGITS IN RESULT ? ";N:N4WD$"WOW! You got it right!":YY100:15:21050{0RWD$"The secret is to do the whole calculation and then figure out the digits.":YY100:15{:R100:BACK20930|DR0:Y110130:0,Y279,Y::3:WD$"= (347.8375 or = 3.1416.)":YY110:15XzRTX127:TY136:505:TX118:TY156:505:100:BACK20860^zRzR:WD$"Try this problem. How many significant digits should be in the result?":YY10:15:WD$"(12.2 + 23.45 + 0.0875 + 312.1) / 4.5762":YYYY10:15X{&R2s absolutely correct!":YYYY10:15cyQ:WD$"= 944.60 mm":XX180:YY90:5:WD$"2":XX250:YY85:5zQWD$"The only measurement is 17.340 mm which has 5 significant digits. has as many digits as needed. (Just be sure you punch in at least 5 digits flculating the area of a circle of radius 17.340 mm?":YYYY10:15:WD$"The formula to consider is:":YYYY10:15:WD$"Area = r":XX100:YYYY20:5xQTX150:TY96:505:WD$"2":XX168:YY86:5#yQ21:"NUMBER OF SIGNIFICANT DIGITS = ";N:N5WD$"That' The ''5'' is exact ( = 5.0000...).":YY120:15:100:BACK20820GwQwQ:WD$"Another place where this comes up is when you calculate with the number .":YY10:15:TX190:TY16:505:300xQWD$"For example, how many digits are significant when ca6 + 13.5 + 13.7":YY90:15:0,110178,110:WD$"5":XX85:YY115:5vQWD$"=":XX187:YY107:5:WD$"67.8":XX200:YY100:5:WD$"5":XX210:YY115:5:200,110220,110:WD$"= 13.56":XX227:YY107:5AwQWD$"This rounds to 13.6, with three significant digits.WD$" 13.4 13.6 13.6 13.5 13.7":YYYY10:15:300uQWD$"To find the average, you add up the measure-ments and divide by the number of measurements.":YYYY10:15:100:BACK20820AvQ0:Y100130:0,Y279,Y::3:WD$"13.4 + 13.6 + 13.e where you have to be careful. You must always distinguish between those numbers which are measure-ments and those numbers which are not.":YY10:15:300CuQL45:WD$"Consider the calculation of the average of the following measurements:":YYYY10:15:is 0.09, which has only one significant digit.":YY80:15:WD$"By the way, the solution to the problem is gotten by rounding off 29890.888 to one significant digit. The answer is 30000.":YYYY10srQ15:100:BACK20790s|QtQ:WD$"There is one plac calculate the answer, look at the limiting measurement!)":15:WD$" 216.95 x 12.4 / 0.09 = ?":YYYY10:15r^Q21:"NUMBER OF SIGNIFICANT DIGITS = ";N:N1WD$"Thats right! You are doing well.":YYYY10:15rcQshQWD$"The limiting measurement cant digits (since the time measurement has only two digits).":YYYY10qJQ15:300:WD$"The correct answer is 15 meters/second.":YYYY10:15:100:BACK20760prTQL45::WD$"How many significant digits are there in the answer to:":YY10:15:WD$"(Don't10:15:300:WD$"A calculator gives the answer as 14.648648.":YYYY20:15p@QL47:300:WD$"Not only does the calculator lose track of significant digits, but it also forgets units!":YYYY10:15GqEQWD$"The correct answer is limited to only two signifi$"digits as the measurement with the "o,QYYYY10:5:WD$"fewest significant digits.":YYYY10:5:10,40245,40245,9610,9610,40:100:BACK20590Jp6Q:WD$"Consider the following problem:":YY10:15:WD$" 54.2 meters / 3.7 seconds = ?":YYYYbers have three significant digits.":YYYY30:15FnQ100:BACK20560LnQ'o"QL45::WD$"In general, the rule works like this:":YY10:15:WD$"When multiplying or dividing measure-":XX20:YY50:5:WD$"ments the result has only as many":YYYY10:5:WD.":YY90:15rmPWD$"We round the result down to 28.1 cm.":YYYY10:15:WD$"2":XX215:YY132:5:100:BACK205601nQ0:Y100150:0,Y279,Y::3:WD$"So 3.47 cm x 8.11 cm = 28.1 cm":YY90:15:WD$"2":XX171:YY94:5:300:WD$"Notice that all of the numYY90:15:1250,68^lPTX198:TY56:510:TX205:540:TX210:510:TX218:570:100:BACK20560 mP1250,68:0:Y90140:0,Y279,Y::3:WD$"All digits past the decimal point in 28.1417 are estimates. However, we can only keep the first estimated digit since the product of 8 x 7 is a two digit number.)":15jkPTX199:TY43:570:TX206:560:100:BACK20560lP1238,55:0:Y90150:0,Y279,Y::3:WD$"The estimated digits in the intermediate products make these digits in the final product estimated.":1238,45:100:BACK20560jP1238,45:0:Y90140:0,Y279,Y::3:WD$"Finally, multiplying the ''8'' in 8.11 by the estimated digit in the original 3.47 measurement makes these digits estimates.":YY90:15:1238,557kPWD$"(Both digits are affected :570:1245,35$iP100:BACK20560OiP1245,35:0:Y90120:0,Y279,Y::3jPWD$"Multiplying by the next ''1'' in 8.11 results in this digit being an estimate (since the ''7'' is estimated in the original measurement).":YY90:15:TX213:TY33:570:YY90:15:TX221:TY0:570:TX219:TY10:510:233,21:32:1250,17:100:BACK20560iP1250,17:0:Y90120:0,Y279,Y::3:WD$"Multiplying by the estimated ''1'' in 8.11 makes all these digits estimates.":YY90:15:TX206:TY23:530:TX212:540:TX22021,19:400:WD$"347":XX202:YYYY13:5gPXX195:YYYY10:400:5:WD$"2776":XX181:YYYY10:400:5:178,52222,52:400:YYYY13:XXXX1:WD$"28.1417":5gP100:BACK20560ShPWD$"These ''dotted'' digits are estimates in the original measurements.": track of the estimated digits.":15:100:BACK20450;fnPfxP:10,010,2054,2054,010,0:WD$"3.47 cm":XX60:YY6:5:WD$"8.11 cm":XX16:YY25:5'gPWD$"3.47":XX200:YY0:5:WD$"x 8.":YYYY10:XX188:5:WD$"1":XX211:5:WD$"1":XX218:5:198,192et's find the area of a rectangle that is measured to be 3.47 cm by 8.11 cm.":YY10:15:110,55110,75154,75154,55110,55:300:YY1005fdPWD$"To help us develop the rule for multip-lication of significant digits let's write out the calculation and keep35 m has too many digits. We have not found the distance around the track to the nearest 1/100,000 meter!":YY80:15:300dFPWD$"The answer gets rounded off to 105 meters. Turn the page to find out why.":YYYY10:15:100:BACK20442dPPeZP:WD$"L:15:TX227:TY106:505:WD$"is":XX238:5:WD$"equal to 3.1415927, so":15c(PWD$"C =":XX15:YYYY20:5:TX42:TY136:505:WD$"x D = 3.1415927 x 33.5 m = 105.24335 m":XX50:5:100:BACK20442c2P0:Y90136:0,Y279,Y::3zdNWD$"Electronic calculators are the real villains! They will happily give you an eight digit answer whether that corresart of this lesson you learned that significant digits are those digits from a measurement that are reasonably trustworthy. Now you will learn how to include the significance of numbers in calculations."G4NYY10:15:300:WD$"A difficulty arises from t0:TX1,TY:TX3,TY1:TX4,TY3:TX2,TY3:TX2,TY6:3:zE:0:TX1,TY:TX3,TY:TX3,TY5:TX2,TY3:TX,TY1:3:E1023,2:::10:10:"STAND BY.... ....GETTING THE MENU!":"RUN MAIN MENU"E NF*NL46::WD$"In the first pDTX2,TYTX2,TY4TX2,TY3TX2,TY:TX4,TY3:TX3,TY3:TX3,TY5:qD0:TX,TY2:TX,TY4:TX,TY6:3:D0:TX1,TY:TX3,TY:TX1,TY2:TX2,TY6:TX,TY4:3:D0:YTY1TY102:TX,Y::TX3,TY3:TX2,TY4:TX1,TY1:TX,TY4:3:=E00188:10,Y263,Y::0:WD$"<<< LEFT OR RIGHT ARROW OR ESC >>>":XX20:YY180:5:A$:Y180188:10,Y263,Y::3C(A$)8BACK1:" ":CA$""BACK0:" ":CA$""ĺ" ":"RUN MENU":C(7);(7):200C,ZZ12000::CZZ11000::JOW OR ESC >>>";::1:A$:24:1:" ";dBhA$""ĺ" "::1000~BjA$""BACK1:" ":BkA$""ĺ" ":Bm21:1:958:(7);(7):102BnBB0:Y0LAST10:0,Y279,Y::3:BoC49168,0:3:Y1811:X$(WD$,LTR,1):X$(32)X$"-"ĂAW$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XX0:YYYY10:6AXX0:YYYY10:5:AdAeBACK0KBf49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARR?'@1002:A(X)(X.00051000)1000D@3::0:3:232,0:233,3V@L45::20000@F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1@100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:)ALTRL                               -7@1002:X(40),Y(40):::L45:3:(1023)20050000B@10000`@PSTRING$"":216,0:10000@F(0):232,0:233,8:0:1:XZXX@100XX,YY:(V$)LāQ1(V$):((V$,Q,1))31:99::@LTRL11:X$(V$,LTR,1):X$(32)X$"-"ĂiAW$(VY10:153 WD$"You should now go back to the menu and learn how to do arithmetic with significant digits. It can be tricky sometimes!":YY60:15:100:BACK27203 1000"You should now go back to the menu and learn how to do arithmetic with sign12:X,140X,145::WD$"PLACE HOLDING ZEROS ARE NOT significant. A number like 170000 has 2 significant digits.":XX20:YYYY14:52 100:BACK25903 :WD$"Don't worry, it gets easier with practice. (And you will be getting lots of that in lab!)":YR over it IS significant. This means that 230 has 3 significant digits.":XX20:YYYY14:5:113,100117,1001 300:X712:X,116X,121::WD$"LEADING ZEROS ARE NOT significant. The number 0.009 has 1 significant digit.":XX20:YYYY14:52 300:X7 significant. 108 has 3 significant digits.":XX20:YYYY14:50 300:X712:X,68X,73::WD$"TRAILING ZEROS after a decimal point ARE significant. 7.400 has 4 significant digits.":XX20:YYYY14:5l1 300:X712:X,92X,97::WD$"A ZERO WITH A BA46::WD$"SUMMARY":XX120:YY0:5:120,8166,8:WD$"A digit is significant if it is reasonably trustworthy (directly from a measuring device or the first estimated digit.)":15?0 300:X712:X,44X,49::WD$"A ZERO SURROUNDED by significant digits ISRD ONE!";:868:2710. YY80:WD$"There are two digits that are significant this time. The leading zeros don't count. The zero to the right of the 5 does however, otherwise it wouldn't have been put there!":YYYY10:15. 100:BACK2570. / L zero doesn't because it is just a place holder.":YYYY10:15R-n 100:BACK2570-x :WD$"How many significant digits are there in the number 0.050 ?":YY30:15. :21:"NUMBER OF SIGNIFICANT DIGITS = ";N::N2Ģ21:"GREAT! I THOUGHT THIS WAS A HAgits are there in the number 2900 ?":YY30:15:60,4964,49,Z :21:"NUMBER OF SIGNIFICANT DIGITS = ";N::N3Ģ21:"THAT IS CORRECT!";:868:2670>-d YY80:WD$"There are three digits that are significant here. The zero with the bar counts, the otherOF SIGNIFICANT DIGITS = ";N::N4Ģ21:"GREAT!";:868:2630+< YY80:WD$"There are four digits that are significant in the number 57.04. The zero is surrounded by significant digits.":YYYY10:15+F 100:BACK2570;,P :WD$"How many significant di35:YY22:5* 300:WD$"That's about all there is to it! Let's try a few numbers to see if you have it figured out.":YY50:15:100:BACK2560* L45*( :WD$"How many significant digits are there in the number 57.04 ?":YY30:15=+2 :21:"NUMBER significant we must indicate that specifically, with a bar over it.":YYYY10:15:100:BACK2520 * :WD$"A way to avoid the problem is to use scientific notation.":YY10:15:WD$"Writing 650 as 6.5 x 10 leaves no ambiguity.":YYYY10:15:WD$"2":XX1must be there for a reason--it is significant!":YY10:15( 300:WD$"We had to put the zero on 650--otherwise we would have a different number. In other words, the zero is there whether it is significant or not!":YYYY10:15a) WD$"If it really is YY10:15' WD$"If the zero was missing from 650 you would have 65, obviously a very different number!":YYYY10:15:100:BACK2390' L47:( :WD$"We have a choice about putting the final zero on 32.90. Since we have decided to put it there, it while the zero in 650 is not.":YYYY10:15 ' 300:WD$"It might be easier to keep these two cases separate by realizing that the zero in 32.90 wouldn't have to be there and you would still have the same number (although with different significance).":YYermine the significant digits in any number.":YY110:15:100:BACK2340N% +& :WD$"The most common mistake is to confuse the zeros after the decimal point with place holding zeros.":YY10:15:300:WD$"For example, the zero in 32.90 is significant 0:BACK2340$ 0:Y100140:0,Y279,Y::3:WD$"(bar over zero and zero ":XX108:YY87:5:WD$"surrounded by sig. digits)":XXXX4:YYYY10:5H% WD$"Look over this table very carefully. If you can understand the rules above, you will be able to detYYY10:15:100:BACK2340E# WD$"(bar over zero)":XX108:YY73:5# 0:Y100157:0,Y279,Y::3:WD$"12000":YY77:15:19,8523,85:WD$"4":XX90:5:WD$"Note that it is only necessary to put a bar over the last significant zero.":YY110:15 $ 10::3:WD$"5600":YY63:15:WD$"3":XX90:5:14,7118,71:WD$"If we really do want a place holding zero to be significant, we put a bar over it. Look at the last number."" YY90:15# WD$"It implies that the measurement was between 5590 and 5610.":Yos that only keep the decimal point in place are not significant!"c!~ YYYY10:15:100:BACK2340! 0:Y80YY10:0,Y279,Y::0:Y6070:100,Y110,Y::3:WD$"2 (no place holding zeros)":XX90:YY60:5:100:BACK2340" 0:Y80YY10:0,Y279,Y"3 (no leading zeros)":XX90:5:WD$"2400":15:WD$"2":XX90:5:300:300 t WD$"Look at the last number, 2400. The reason there are only two significant digits is because the zeros only serve to make the number 2400 and not 24.":YY80:15B!v WD$"Zer:WD$"Number Significant Digits in the Number":YY10:15:0,1038,10:78,10260,10:WD$"3432":YYYY10:15:WD$"4":XX90:5:WD$"204503":15:XX90:WD$"6 (0 surrounded by sig. digits)":5J j WD$"4.380":15:WD$"4":XX90:5:WD$"0.00876":15::WD$:3:WD$"2":XX91jG 5:184,130:400:0:5:184,130:3:WD$"3":XX97:5:190,130:400:0:5:190,130L 3:WD$"4":XX107:5:1100,130:400:0:5:1100,130:3:WD$"5":XX113:5:1106,130:400:0:5:1106,130:3::100:BACK2280V ` L46:"NUMBER OF SIGNIFICANT DIGITS = ";N:::N5WD$"SUPER! You are exactly right!":YY30:5B YY80:WD$"There are five digits that are significant in the number 312.91.":XX30:15:233,21:1:48:300:178,130:WD$"1":XX86:YY132:5:300:178,130:0:510,Y15,Y::WD$"This reads 0.06 cm. The leading zeros aren't significant. There is only one significant digit this time.":YY120:15:100:BACK2220$ L45. :WD$"How many significant digits are there in the number 312.91 ?":YY30:15Z8 :21:L45jWD$"Consider what would happen if you measured a short piece of metal with our meter stick.":15 279,6510,6510,105279,105:X1027910:X,95X,105::X1027950:X,90X,95::C0:X110279100:X,85X,95:CC1:CX2,73: Y108125:100:BACK21801232,0:233,3:3:0:L46:WD$"This really isn't TOO hard, is it?":YY10:15:300:WD$"Be careful though--a zero left of the decimal point is only significant if it is surrounded by significant digits!":YYYY1:15:300: 16.20 cm, NOT 16.2 cm!":YY102:15:2265SWD$"This reads 16.20 cm.":YY102:15WD$"Even though the metal piece ''lines up '', we can still use the meter stick to measure to the nearest 0.01 cm. So include the zero if it is ''trustworthy''!":15300:3000,45279,45:279,850,85:X427910:X,75X,85::X1427950:X,70X,75::C1:X14279100:X,65X,75:CC1:1X7,53:C3X3,53:Y87104:0,Y133,Y:):21:"WHAT IS THIS SETTING ? ";A$::(A$,5)"16.20"WD$"WONDERFUL! It'smated digit is a zero.":YYYY10:158100:BACK2100>:WD$"The digit ''0'' can cause complications when you are working with significant digits. For example, consider the following meter stick and metal piece to be measured:":YY10:15: The last digit is estimated but is still ''reasonable''.":YY10:15$300:WD$"We use significant digits to indicate the precision of our measuring instruments. Always include as many digits of significance as your equipment allows, even if the estike sense to read the length to be something like 68.63782 cm.":YY100:15:100:BACK2060_F:WD$"The measurement 68.63 cm has four signifi-cant digits. The 6, 8, and the second 6 are read directly from the meter stick and so are certainly valid.tly read 68.6 from the meter stick and we are estimating the final digit, a ''3'', to give us 68.63 cm.":YY10:15:300YzWD$"Those four digits are reasonably trust-worthy. You can't add any more digits that mean anything. For example, it wouldn't maf metal that we are measuring. (We have lined up the other end with the zero on the meter stick.)":YY100:15:300fWD$"It looks like it is 68.63 cm long.":YYYY10:15:100:BACK2060xpLAST20:150:0:Y103YY10:0,Y279,Y::3:WD$"We can direcX,65X,70::C3:X14279100:X,60X,70:CC1:6X7,48:C3X3,48:RLASTYY:150:WD$"Here is part of a meter stick. (Don't forget that the numbers are centimeters.)":YY10:15:300s\Y83100:0,Y176,Y::300:WD$"Here is the end of a piece o0:15:WD$"(That's when a digit is ''trustworthy''!)"V/YYYY10:15:100:BACK2030\4>:WD$"Let's look at an example to help make this a little clearer.":YY10:15:300:300FH0,40279,40:279,800,80:X427910:X,70X,80::X1427950:ement you are limited by the equipment you use.":YYYY10:15:50,90196,90:L455*300:WD$"A significant digit is a digit you can read directly from the measuring instrument or the first estimated digit past what the instrument reads directly.":YYYY1assume their numbers are exact. For example, writing down a ''3'' means that they are working with 3.00000... with as many digits as they like.":YY10:15:300P 300:L44:WD$"As a new physicist, you don't have that luxury! Whenever you make a measur30,20252,20252,5530,5530,20:300:WD$"Knowing when a number is ''trustworthy'' will help you understand why you have to learn about significant digits.":YY70:15:100:BACK2005 :WD$"When mathematicians work with numbers, they normally rn about them?''":YYYY30:15 300:WD$"A reasonable thing to ask! Turn the page to find the answer...":YY100:15:100:BACK1000  :WD$"A SIGNIFICANT DIGIT is a digit that":XX40:YY30:5:WD$"is reasonably trustworthy.":XX40:YY40:5::c 1023,2:::10:10:"STAND BY... ...GETTING THE MENU!":"RUN MAIN MENU"i o x :3 WD$"As you begin this lesson, your first question should be:":YY0:15:WD$"''What is a significant digit and why do I have to lea:Y180188:10,Y263,Y::0:WD$"<<< LEFT OR RIGHT ARROW OR ESC >>>":XX20:YY180:5:A$:Y180188:10,Y263,Y::3 (A$)8BACK1:" ": A$""BACK0:" ": A$""ĺ" ":"RUN MENU": (7);(7):200 ,ZZ12000:: ZZ11000HT ARROW OR ESC >>>";::1:A$:24:1:" ";j hA$""ĺ" "::1000 jA$""BACK1:" ": kA$""ĺ" ": m21:1:958:(7);(7):102 n 0:Y0LAST10:0,Y279,Y::3: u 49168,0:3LTRL11:X$(WD$,LTR,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XX0:YYYY10:6 XX0:YYYY10:5: d eBACK0Q f49168,0:24:958:24::4:"<<< LEFT OR RIG+'1002:A(X)(X.00051000)1000K16302,0::0:3:232,0:233,3\L45::2000F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:/                            M ? ) ; -  ) ; ; - ) ); ; ; ; ) ) -; ; )  - ; ) ?   eiiLGl6 ani anmm8iiLGl LpLGliALGl6 ani anmm8iiLGl LpLGli                 !!  400:1000c,5:12000/F$"SPECTROMETERS":1023,5:13000`18:958:11)"TYPE 1,2,3,4,5 OR 6":7)"(NO NEED TO PRESS 'RETURN')":21:8)"WHAT IS YOUR CHOICE? [ ]":21:31jA$:21:31:A$:((A$)1)((A$)6)(((A$))(A$))ĺ(7):60000te1000.dF$"CALIPER":1021,255:1023,5:11000NnF$"BALANCE":1023,5:11000lxF$"TIMER":1023,5:12000F$"FORCE TABLE":1023,200:12000F$"AIR TRACK":12000F$"COULOMB":1023,5:12000F$"METERS":1023,5:12000 F$"SCOPE":1023090,50100,1000@L:"PRINTER SET-UP COMMAND RECOGNIZED.":10:"FLIP THE DISK OVER TO LOAD THE SET-UP PROGRAM AND THEN PRESS A KEY.":A$:" "P216,0:104,96:24576,0:"RUN PRINTER SET-UP":T10000ZF$"MICROMETER":1021,255:1023,5:1 ":vu1023,1:6:12:"1. AIR TRACKS"::12:"2. ELECTRIC FIELD MAPPING"::12:"3. ELECTRICAL METERS"::12:"4. OSCILLOSCOPES"::12:"5. SPECTROMETERS"u:12:"6. LAB SKILLS MENU"u60000u(A$)50060,50070,50080,50E TABLE"'Du:12:"6. MORE EQUIPMENT"2Nu60000@]u1025,255obu(A$)50010,50020,50030,50040,50050,30060lu::20:958::1:6:" ":6:" PHYSICS LABORATORY HELP-WARE ":6:" LAB EQUIPMENT MENU ":6:" ":6:" PHYSICS LABORATORY HELP-WARE ":6:" LAB EQUIPMENT MENU ":6:" "::u1023,1:6:12:"1. METRIC MICROMETERS"::12:"2. VERNIER CALIPERS"::12:"3. BALANCES"::12:"4. EVENT TIMERS"::12:"5. FORC:7)"(NO NEED TO PRESS 'RETURN')":21:8)"WHAT IS YOUR CHOICE? [ ]":21:31RNA$:21:31:A$:A$""(((A$)1)((A$)3)(((A$))(A$)))ĺ(7):20040\NA$""40000fN(A$)1150,1000,30000y0u::20:958::1:6:" ":6:" "w*N6:" BY ROBERT J. BEICHNER ":6:" ":>N1023,1:9:12:"1. BEFORE YOU START..."::12:"2. LABORATORY SKILLS"::12:"3. LAB EQUIPMENT"MHN18:958:13)"TYPE 1,2, OR 3"IDE D ON TOP THEN PRESS A KEY. (PRESS ESC TO CANCEL)":A$:" ":A$""Ĺ216,0:30000q2500:"VERIFY ";F$"2216,0:"RUN ";F$::500:"RUN ";F$:' N::20:958::1:6:" ":6:" PHYSICS LABORATORY HELP-WAREON TOP THEN PRESS A KEY. (PRESS ESC TO CANCEL)":A$:" ":A$""Ĺ216,0:30000k.500:"VERIFY ";F$".F$"AIR TRACK"Ĺ216,0:104,96:24576,0:"RUN AIR TRACK":.216,0:"RUN ";F$:2S$"D"210000X2:10:"PUT IN THE OTHER DISK, S00+:10:"FLIP THE DISK OVER AND PRESS A KEY. (OR PRESS ESC TO CANCEL)":A$:" ":A$""Ĺ216,0:(1023)2000,1000,3000,30000,30000 +500:"VERIFY ";F$"+216,0:"RUN ";F$:.S$"C".10000R.:10:"PUT IN THE OTHER DISK, SIDE C ;" AND THEN PRESS A KEY. (ESC TO CANCEL)":A$:" ":A$""Ĺ216,0:20000S)'11020.':10:"THERE APPEARS TO BE A BAD DISK. TURN OFF THE COMPUTER, REMOVE THE DISK AND REPORT THE PROBLEM TO YOUR TEACHER. SORRY!"8'10040*S$"B"*100F$"ERRORS B":11000- F$"ERRORS C":110003Q1023,1:F$"UNITS":15000W1021,1:1023,5:F$"GRAPHS A":15000p1023,200:F$"CALC HELP":15000''ERR210030'ERRERR1H$':10:"I CAN'T FIND THE LESSON. INSERT SIDE ";S$ONS"::9:"4. STATISTICAL METHODS"::9:"5. ERRORS ON GRAPHS"::9:"6. RETURN TO LAB SKILLS MENU"o 60000& (A$)3210,3220,3230,3240,3250,1000 1021,1:F$"ERRORS A":15000 1021,2:F$"ERRORS A":15000 1021,3:F$"ERRORS A":15000 023,2:F$"SIG FIGS B":15000 ::20:958::1:8:" ":8:" ERROR ANALYSIS ":8:" ": 1023,3 5:9:"1. INTRODUCTION"::9:"2. COMPARING TO STANDARDS":d 9:"3. BASIC CONSIDERATIENU"u 18:958:14)"TYPE 1,2, OR 3":7)"(NO NEED TO PRESS 'RETURN')":21:8)"WHAT IS YOUR CHOICE? [ ]":21:31 A$:21:31:A$:((A$)1)((A$)3)(((A$))(A$))ĺ(7):2070 >(A$)2120,2200,1000 H1023,2:F$"SIG FIGS A":15000 1RODUCTION":15000 ::20:958::3:8:" ":8:" SIGNIFICANT DIGITS ":8:" ": 9:10:"1. THE BASICS"::10:"2. CALCULATIONS WITH":13:"SIGNIFICANT DIGITS"::10:"3. RETURN TO LAB SKILLS M:6:12:"1. SIGNIFICANT DIGITS"::12:"2. UNIT ANALYSIS"::12:"3. GRAPHING TECHNIQUES"::12:"4. HANDLING ERRORS"::12:"5. CALCULATION ASSISTANCE" :12:"6. LAB EQUIPMENT" L60000 t(A$)2000,4000,5000,3000,6000,30000 ~1023,1:F$"INT n1000C 23::" STAND BY.....READING THE DISK! ":: ::20:958::1:6:" ":6:" PHYSICS LABORATORY HELP-WARE " 6:" LAB SKILLS MENU ":6:" ": 1023,11002:S$"A"5 38400:ERR0:(1022)255100"BLOAD LETTERS,A$800":"BLOADARROW,A$1500":"BLOADPARENTHESIS,A$1600":1022,0:1023,1I1KEY(49152):I1000KEY128II1:30(49168,0 d(1023)20000,2000,3000,4000,5000,30000        I)R---u -1-3vu?M13M1smNM13MN 5M13  NMMq-M13M1?w ?M .----N) 3vu666n*N >iNI---5??7--5??7--5??7--u@@@C?.- ??N -5?*m ->??w- -3-u7RMJ?I??MI vRR-53M1smN56-3M13-u mR-3v-NI1*-n -u?R-3---u 3?w6N R-53M1?w ?M >6-3M13Mq)66N 56o )6M.nq)566-N5-n n N -n1nq)R-3M1s-N-3M?7nIR-53M1?w n5 76N6-uM17 n n NIM13m1n)n N )3M13M1s-N -3M?76NI )3M13 mN -3M?7 n N )3M:w -N --66vIMM13M13M1s-N M13M13MN IM13M1n >7MqM1s  3MqJM1s 6vI---.-uJ--;.>.>.-u5rVw-->.>.>*.)3M1?w *uIR >RMIN---ޛ-- *NI.)s N )3 >n-uM M13--n N -3M?7M13-u J)36Ms-N -n1n1-u J--n?76--NJ--n?76NII)36M5s-uJM13M1??n n N -66-N I166s-N Mn7 n N 66 ? ?wqImmw M:N)N-n mN-6R 6N56N 5 --NN n:?w1VIM7R?RINIVI 5)3M5.M-Nm1w6-N)sI.-u-->N-N>I> 3--v 5--.-6s-N -޻M:?n -N.--6NI))3M?M1s-Nd )/9BS^ent'2=HYk|&7EWhx *8BSbm}&3BO_lv}" 66N nR>i----nN> ?il6XSXMX(MXSX)100:X0XXLX(XSX)SC(1):YYLY(MXBSY)SC(2):XXLXXXHXYYLYYYHYēXX,YYol@ulJl0I1(D$):(D$,I,1)" "D$"BAD LABEL"l2(D$)20D$"LONG LABEL"l4Q ZZz BAՠ88eeetion of the form:":YY10:15:V$"y = a + b/x":XX100:YYYY30:5:V$"a = "(B)" and b = "(M):YYYY40:15:zk'k,XSXk.X0XXLX(XSX)SC(1):YYLY(MXBSY)SC(2):XXLXXXHXYYLYYYHYēXX,YY:60470k1XX(MXSX)100:XMX60462jI1jX(I)060395.jII1:IN60405mjSX0:SY0:I1N:SXSX1X(I):SYSYY(I)::AXSXN:AYSYNjNUM0:DN0:I1N:NUMNUM(1X(I)AX)(Y(I)AY):DNDN(1X(I)AX)(1X(I)AX):jDN060395jMNUMDN:BAYMAXtk"::V$"For an equato start the lessons.":YY10:15:300:WD$"Go back to the menu and pick the lesson you would like to see.":YYYY30:15:100:BACK2218 :WD$"Nice try, but there isn't anything here. I guess I'll have to send you to the menu myself!":YY50:15:300:L YOU GET HELPFROM A HUMAN! PLEASE SEE YOUR TEACHER.":2223{WD$"You did something wrong, do it again!"::YY140:22220:Y150160:0,Y279,Y::3::YY140:15:100:BACK2210:WD$"You have now finished with the introduction and are ready rrected number into the computer. (By the way, use the PERIOD KEY on the lower right to enter the decimal point.)":YYYY2015:TRYTRY1:21:"TRY IT ==> ";N:N2.485WD$"I knew you could do it!":2226<TRY2ĉ::10:"YOU CAN GO NO FARTHER UNTITURN key. Instead, pretend you meant to type in 2.485. Use the LEFT ARROW to backspace over the 5 and then over the 7.":YY10:15:300TRY0|WD$"Type an 8 over the erroneous 7 and then enter the 5 again. Now press the RETURN KEY to enter the co the mistake, then type in the correction."YYYY10:15:WD$"Just make sure you fix the typing error BEFORE you press the RETURN key!":YYYY20:300:15:100:BACK2200:WD$"Try this for practice. Type in the number 2.475 BUT don't press the RE you do if you make a mistake while typing in an answer?":YY10:15+300:WD$"Well, on a typewriter you would use the backspace key (after you erased the ''typo''.) On the computer you simply press the LEFT ARROW key until the flashing square is overoblems are the letter ''O'' and the number ''0''."YYYY20:15:300:WD$"Keep those keys straight and you shouldn't have any trouble.":YYYY20:15:100:BACK2160D:WD$"There is only one more thing to learn before you start the lessons. What doewriter. Be careful though. Computers are DUMB!":YY10:15:3002WD$"If the correct answer to a question is the number ''1'' and you RETURN after typing a lower case ''L'' you will have confused the poor computer. Another pair of keys that causes prr with information.":15:300:WD$"Find and press the RETURN key.":YYYY30:15v1:A$:A$(13)ĺ(7);(7):2180WD$"Nothing to it!":YYYY10:15:100:BACK2140B:WD$"The rest of the keys are very similar to the ones you will find on a typ"Good. You have decided to finish.":YY10:15:300:WD$"Another important key is the one labeled RETURN. It is used after you type an answer to a question posed by the computer.":YYYY20:15OzWD$"Think of it as a key that ''returns'' to the compute get here in the first place)?":YY10:15:300fWD$"By the way, if you press ESC to go to the menu you should come back and finish the rest of this introduction.":YYYY30:15:WD$"Well, what do you want to do?":YYYY20:15:100:BACK2100p:WD$ue with this introduction.":YYYY30:15MR1:A$:A$""ĺ(7);(7):2130/\::WD$"Anytime that line is at the bottom of the screen you have a choice---do you want to continue with this lesson, go back a page, or go to the menu (the one you used to0:5:WD$"Think of it as ''turning the page.''":XX50:YY60:5MATY83:800CWD$"LEFT ARROW--go back to the previous page.":XX20:YY80:5:TY103:800:WD$"ESC KEY--go to the lesson menu.":XX20:YY100:5(H300:WD$"Press the RIGHT ARROW to contin (LABELED 'ESC' !)":2090423:1:958::WD$"GREAT! Those three keys are used to ''move you around'' while you are working on a lesson. Here's what they do:":YY10:159TX10:TY53:800>>WD$"RIGHT ARROW--continue with the lesson.":XX20:YY5more key that you need to know about, the ''escape'' key.":YY10:15:WD$"Find the ESC key and press it.":YYYY10:15%210,160210,155230,155230,160:50,4850,5073,5073,48:62,50220,155*1:A$:A$""Ģ23:1:(7);(7);"PRESS THE ESCAPE KEYROW key.":YYYY20:15c46,16046,15579,15579,160:61,155200,80:164,78164,80233,80233,781:A$:A$""Ģ23:1:(7);(7);"PRESS THE ARROW POINTING TO THE LEFT!":2070w 23:1:958::WD$"On the upper left corner of the keyboard is one RIGHT!":2040b23:1:958::WD$"You are on your way to CONTROLLING the COMPUTER!":YY10:15 300:WD$"The next step is to find the LEFT ARROW key. (HINT: It is close to the right arrow key.)":YYYY10:15:WD$"Once you find it, press the LEFT ARd until you find a key with an arrow pointing to the right. PRESS THE RIGHT ARROW!":YYYY10:15104,160104,155181,155181,160:142,155185,140:150,138150,140227,140227,138 1:A$:A$""Ģ23:1:(7);(7);"PRESS THE ARROW POINTING TO THE else that will show up a lot is this line at the bottom of the screen...":YYYY10:15 49168,0:21:958:21::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";:a300:WD$"Let's examine the keys listed below. Look around on the right side of the keyboarWD$"Since you have gotten this far, it is safe to assume that you know how to insert a disk into the disk drive and can also read a MENU. (A ''menu'' is just a list of options. You will be seeing a lot of them soon!)":YY10V 15:300:WD$"Something :102 n1 0:Y0LAST10:0,Y279,Y::3:D ,ZZ12000::W ZZ11000:: WD$"o":XXTX2:YYTY4:5:YTY1TY1:TX1,YTX1,Y:: ::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":1023,1:"RUN MAIN MENU" :YY10:5: d eBACK0 f49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" "; hA$""ĺ" "::1000 jA$""BACK1:" ": kA$""ĺ" ": m21:1:958:(7);(7)z#       נàР!,  Ӡ ǠӠ- ǠӠ AҠŠӠ/ҠΠ Ӡ:Ӡ 1 ϠΠӠΠՠҠϠ "נ" ŠĠ àР/ Ҡ ΠӠIԠ(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:{ LTRL11:X$(WD$,LTR,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6 XX0:YY  1002:!3:L45::2000210,50210,70:D110:Y5020(1):X150200:0:X,YX3,Y2X,Y5:3:X1,YX4,Y2X1,Y5:X4,Y2X10,Y2:0::3::F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXXF 100XX,YY:         ȍ38,52,0,61,46,62,5,0,61,54,37,7,0,53,38,0,54,37,60,46,0,53,39,53,62,5,0 38400:1023,99:1021,99:1022,255:3:0:1:103,1:104,64:16384,0:1:"RUN MAIN MENU":38263x 16297,0:16304,0:16297,0:" ":"BLOAD COVER,A$8000":230,64:0,0:1,128:38263:"BRUN CURTAIN":,3,100~  A768830:B:A,B:G 20,0,24,0,27,0,31,0,35,0,39,0,44,0,49,0,52,0,57,0,53,62,36,0,49,38,0,53,55,61,0,53,23,37,0,46,,1010,102:1011,213:1012,112:214,2551002::49234,0::Y123:" ";:::11:12:"LOADING FROM DISK..."::1 "BRUNSPEEDER":" ":"BLOAD SQUEEZE,A$9577":"BLOAD FRONT,A$9177":230,32:0,119:1,145:ple data to try your hand at using your new skills.":YYYY20:157-300:WD$"Well, it's time for you to go back to the menu...":YYYY20:15:100:BACK116107-1000T10001000Liar with graphing, calculating slopes and intercepts, and coming up with an equation relating data is by practicing. You will be doing a lot of that in lab!":YY10:15A7-300:WD$"You might want to talk to your instructor to see if you can get some sam which makes this simple (well, almost simple!)":YYYY20:155n-WD$"If you need to do this your instructor will tell you and also assist you in making your first few logarithmic graphs.":YYYY20:15:100:BACK115706x-:WD$"The best way to get famil:WD$"This technique can be extended to other powers and even square roots, cube roots, etc.":YY10:15:300=5d-WD$"In some situations it is easier to graph the logarithms of numbers instead of the numbers themselves. There is special graph paper madeYYYY20:5:2170,75:3003F-WD$"This agrees with the mathematicians' prediction:":YYYY20:15:WD$"Area = r":YYYY10:XX100:5:2168,128:TX150:TY136:TX2,TYTX2,TY4TX2,TY3TX2,TY:TX4,TY3:TX3,TY3:TX3,TY53P-100:BACK11490n4Z-its--squared centimeters on top and bottom cancel out). The y-intercept looked to be near zero.":YY10:15:30026-WD$"This gives us an equation relating the area of a circle to the radius squared.":YYYY10:153<-WD$"Area = 3.1 (Radius) + 0":XX60:TY78:800:TX208:TY62:800:TX227:TY40:800:2258,98:2277,851(-WD$"We can now draw a straight line indicating the trend in the data.":YY130:15:181,90230,36:100:BACK1146012-q24-WD$"The slope of the second graph was about 3.1 (with no un:0-COUNT1:Y804010:COUNT165,Y2:0170,Y2:COUNTCOUNT1::0170,88:0179,95:5194,95:1206,95:0210,95:1221,95:5225,95B1-WD$"Area (cm )":L8:XX130:YY40:5:2148,48:WD$"Radius (cm )":XX240:YY90:5:L45:TX182:TY87:800:TX193:87:800:TX70:TY78:800:TX80:TY62:800:TX90:TY40:800/ -300:WD$"But look what happens when we change the horizontal scale from radius to radius squared.":YY100:150-180,40180,90230,90:Y409010:178,Y180,Y:X18023015:X,90X,92:X,Y:010010:X,90X,92:X,Y::.,233,3:2:COUNT1:Y804010:COUNT35,Y2:040,Y2:COUNTCOUNT1::040,88:COUNT0:X5010010:COUNTX1,95:COUNTCOUNT1::/-WD$"Area (cm )":L8:YY30:15:218,48:WD$"Radius (cm)":XX110:YY90:5:L45:TX60:TYd out how the area depends on the radius....":YYYY20:15:100:BACK11430-,:WD$"Here's what the graph looks like. It doesn't look like a straight line represents the trend of the data.":YY10:15.,50,4050,90100,90:Y409010:48,Y50,Y:X50:15:300,,WD$"You can even use this method to find relationships between variables that are raised to a power.":YYYY20:15:300K-,WD$"For example, let's say you measured the radius and area of some circles. You graph the results in order to finthe snail's crawling speed for a sound intensity of 34 dB. That's all there is to it.":YY100:15:100:BACK11370 ,,:WD$"This technique of using graphs to establish equations and make predictions is used all the time in the physics laboratory.":YY1:1132,43:0:1115,5:1192,5*,WD$"= 0.082 x 34 dB + 0.5 mm/s":XX40:YY60:5:WD$"mm/s":XX86:YY55:5:WD$"dB":XX92:YY67:5:85,64112,64:WD$"= 3.288 --> 3.3 mm/s":XX40:YY90:5s+,WD$"For example, here is the calculation that predicts :400:100:BACK11340h),:L50:WD$" = 0.082 + 0.5 mm/s":YY10:15:L45*,WD$"speed mm/s sound level":XX0:YY15:5:WD$"(mm/s) dB (dB)":XX0:YYYY11:5:85,24113,24:233,22:1:32:154,43l":XX0:YY125:5:WD$"(mm/s) dB (dB)":XX0:YYYY11:5:85,134113,134:233,22:1:32:154,153:1132,153:0:1115,115:1192,115(,100:BACK11340),100,10020,120:400:122,10070,125:400:133,100160,120:400:160,100220,125slope and y-intercept from the crawling snail experiment to derive the following:":YYYY10:15:WD$"y = mx + b":YYYY20:XX100:5'~,L50:WD$" = 0.082 + 0.5 mm/s":YYYY30:15:L45(,WD$"speed mm/s sound leve inspection of the graph.":YY120:15:100:BACK11300&j,:WD$"Finding the slope and y-intercept of a line allows us to write an equation relating the DEPENDENT VARIABLE to the INDEPENDENT VARIABLE.":YY10:15:300't,WD$"For example, we can use the Y60:5:WD$"RISE y - y":XXXX30:YYYY5:5:WD$"RUN x - x":YYYY15:5%V,2158,61:1181,61:2158,77:1181,77:95,65125,65:148,68188,68:132,67140,67:132,69140,69:50,40210,40210,10050,10050,406&`,WD$"The y-intercept is found bys the INDEPENDENT VARIABLE.":XX120:YY70:5:158,67133,30:300$B,WD$"The Y-INTERCEPT shows up as this ''b''.":XX200:YY30:5:197,33164,23:L45:100:BACK11000Q%L,:WD$"The equation giving the slope is written as:":YY10:15:WD$"m =":XX70:YYY15:WD$"y = mx + b":XX100:YYYY10:5:300:L15:WD$"The ''y'' represents a value along the vertical, DEPENDENT axis.":YY30:15#.,50,40100,30:300@$8,WD$"''m'' is the SLOPE of the line.":XX60:YY120:5:70,115126,30:300:WD$"This ''x'' indicate",T100:B160:200:WD$"The Y-INTERCEPT is usually determined by inspection of the graph. In this case it is 0 g (which makes sense for zero volume!)":YY100:15:100:BACK10960#$,:WD$"The general equation for a straight line on a graph is:":YY10: )(2.7 cm ) = 24 g":XX50:YY105:5:3108,102:3158,102!,WD$"The slope of the line turns out to be the density of the unknown material. Do you see why being able to find the slope of graphed lines is a valuable skill?":YYYY5:15:100:BACK10960allows us to calculate the mass of any volume of the unknown substance by just multiplying.":YY90:15:300 +WD$"Let's say we want to know the mass of 2.7 cm of material....":YYYY10:15:3270,138:100:BACK109609!,T100:B160:200:WD$" (9.0 g/cm" RUN 4.0 cm":YYYY15:5:85,133113,133:3163,135:127,133165,133:120,132118,132:120,134118,134+0:125,130125,140:124,130124,140:3:WD$"9.0 g/cm":XX183:YY130:5:3231,125:100:BACK10960k +T100:B150:200:WD$"Knowing the slope 4.0 cm":XX135:YY55:5:3180,51:0:140,55:170,55:3+T100:B160:200:WD$"The SLOPE is just the vertical RISE divided by the horizontal RUN.":YY90:15k+WD$"SLOPE = = =":YYYY20:XX35:5:WD$" RISE 36 g":XX83:YYYY7:5:WD$ues for the circled points.":YY90:15:WD$"x":XX77:YY82:5:XX157:5:182,89:2164,89:Y65802:80,Y:160,Y:+WD$"x - x = 5.5 cm - 1.5 cm = 4.0 cm":XX60:YY140:5:3140,136:3190,136:3242,136:267,148:189,148:100:BACK109608+WD$"=5:222,17:X27502:X,15:x+WD$"y - y = 50 g - 14 g = 36 g":XX60:YY140:5:267,148:189,148:100:BACK10960+WD$"= 36g":XX165:YY40:5:0:180,45:190,45:170,45:3t+T100:B160:200:WD$"The RUN is given by the difference in the x valXX110:YY55:5:300:T90:B140:200:WD$"To determine the actual RISE we just subtract the y value for the first circled point from the y value for the second.":YY90+15:300:WD$"y":XX15:YY46:5:121,54:X27502:X,51:+WD$"y":XX15:YY10::190,35:3:WD$"RISE":XX165:YY31:5:300p+WD$"As it goes between the calculation points it RUNS horizontally this far.":YY110:15:300z+I13:X851592:0:X,51:J15::3::X851592:X,51:J15:::+0:120,55:130,55:3:WD$"RUN":Y51172:160,Y::300\+WD$"As the line goes from one circled point to the other it RISES vertically this much.":YY80:15:300:I17:Y51182:Y25Y35Y45Ē0:160,Y:J15:a+3::Y51182:160,Y:J110:::+f+0:170,35:180,35tinguish data points from slope calculation points.":YY90:15:WD$"A common mistake is to use the first and last data points to calculate the slope, IGNORING the data in between!"H+YYYY10:15:100:BACK10960R+T100:B160:200:X831602:X,51::e zero volume implies zero mass.":YY80:15:3130,864+WD$"In general though, it is best to pick points within the range of your data. That's what we have done here.":YYYY10:157+100:BACK109609+T85:B160:200>+WD$"Also note that we dis to mark two points on the graph.":YY90:15:100:BACK10960$+WD$"o":XX78:YY47:5:XX158:YY11:5:0:79,5079,52:80,52:80,5181,51:161,15160,15160,16159,16:35*+T100:B130:200:WD$"In this situation (0 cm , 0 g) is a legitimate point sinc:Y63310:COUNT37,Y:042,Y:COUNTCOUNT1::Y6070:0:35,Y40,Y::3:L8:WD$"Mass (g)":XX0:YY25:5:L45+TX50:TY65:COUNT16:TXTX20:TYTY8.9:800::50,65180,6+300= +WD$"Here's the graph. As mentioned before, the first step isY::X,67X,65::50,550,65190,65:L15:XX210:YY10:WD$"Effect of Volume on Mass of Sample.":5:L45+2:0:233,3:049,70:COUNT1:X6618620:COUNTX1,70:X4,74:0X7,70:COUNTCOUNT1::WD$"Volume (cm )":XX205:YY65:5:3267,61r +COUNT0double the volume, we measure twice the mass. Three times the volume yields three times the original mass, etc.":YYYY10:15*300:WD$"Making a graph of our results gives....":YYYY10:15:100:BACK10920h*:X5019010:Y56510:X,Y:48,Y50, will pretend that we have an unknown material to study. After measuring the masses of different sized pieces we find that the mass goes up as the volume increases.":YYYY10:15~*WD$"In fact, the mass appears to be proportional to the volume. If we care to line up the points with a vertical grid line. By picking nice ''even'' x-axis values you reduce your error.":YYYY10:15:100:BACK10730*:WD$"Let's make up another imaginary graph so we can calculate the slope.":YY10:15:300*WD$"Weaphed line.":YYYY10:15:126,39181,39:300*WD$"The first thing you should do is to mark two points on the line, near opposite ends. The farther apart you place the points, the more accurate your slope calculation.":YYYY10:15*WD$"Also take )::10:10:"PLEASE STAND BY... ...GETTING PART OF THE LESSON!":"RUN GRAPHS A"*:WD$"Hopefully you now have an understanding of the SLOPE and Y-INTERCEPT of a line.":YY10:15:300-*WD$"Let's look at how we calculate the slope of a grT10:0,Y279,Y::3:60:YTB:0,Y279,Y::3:I,ZZ12000::\ZZ11000:: WD$"o":XXTX2:YYTY4:5:YTY1TY1:TX1,YTX1,Y::::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":1023,7:"RUN MAIN MENU"Z4::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" "; hA$""ĺ" "::1000 iA$""ĺ" "::10730 jA$""BACK1:" ": kA$""ĺ" ": m21:1:958:(7);(7):100 n0:Y0LASY(1))(Y(2)Y(1)):Y(I)HY:64:52i >B(I)1X(I)X(1)(X(2)X(1))(LYY(1))(Y(2)Y(1)):Y(I)LY:64:52 @L(I)0:R(I)0:T(I)0:B(I)0 DX(I)LXL(I)1 FX(I)HXR(I)1 HY(I)HYT(I)1 JY(I)LYB(I)1 Li dBACK0:49168,0:24:958:2:L(1)R(1)T(1)B(1)0I2:L(2)R(2)T(2)B(2)0ēX(1),Y(1)X(2),Y(2): 8L(I)1Y(I)Y(1)(Y(2)Y(1))(LXX(1))(X(2)X(1)):X(I)LX:64:52 :R(I)1Y(I)Y(1)(Y(2)Y(1))(HXX(1))(X(2)X(1)):X(I)HX:64:52! <T(I)1X(I)X(1)(X(2)X(1))(HYɂ:232,Q1:233,Q2:Q3:Q4:r N72:M82:NX2S,Y:XX2X1S:NXS,Y:MXSS2,Y:15XSS25,Y4:I1150: MXSS2,Y:15XSS25,Y4:NXSS,Y:I1150::: XX0:YYYY10:5: 2L(1)L(2)R(1)R(2)T(1)T(2)B(1)B(2)0ıI 6I1R,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6 Q3(249):Q4(231):Q2(233):Q1(232):1:48:232,0:233,8:100XX,YY:Q1(WD$):((WD$,Q,1))31:99:/+1002:16302,0::0:3:232,0:233,3@:L45:3:10920F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXX100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4: LTRL11:X$(WD$,LT               )B(2)0ēPX(1),PY(1)PX(2),PY(2):sC8L(I)1PY(I)PY(1)(PY(2)PY(1))(LXPX(1))(PX(2)PX(1)):PX(I)LX:64:50C:R(I)1PY(I)PY(1)(PY(2)PY(1))(HXPX(1))(PX(2)PX(1)):PX(I)HX:64:50D<T(I)1PX(I)PX(1)(PX(2)PX(1))(HYPY(1))(PY(2)PY(1"Y"B$"y"B$"N"B$"n"ĺ(7);(7):10880R@*A$" "(B$"Y"B$"y")ė:10730w@*A$" "(B$"N"B$"n")ė:10750@*:100:BACK10727@*1100"x*:100:BACK10727x*1100L7):10870e*M0D$"forward at a speed of "(M)" m/s.">f*M0D$"backwards at a speed of "((M))" m/s.">g*M0D$"NO PLACE!",?l*B1B:T125:B155:200:BB1:WD$"You 0:MY10}=0*BPLY(BSY)(MYSY)(LYHY):MPM((HYLY)(HXLX))((MYSY)(MXSX)):X(1)LX:Y(1)BP:X(2)HX:Y(2)MP(HXLX)BP=:*I1:64:I2:64:50=D*A$"walking":(M)3(M)10A$"running"=N*(M)10A$"FLYING"=X*B$"right":B0B$"left"V>b*8,111:0183,111:181,105181,108f<)WD$"Distance (m)":XX2:YY80:9:WD$"Time (s)":XX200:YY100:5<)21:"ENTER A SLOPE (IN METERS/SECOND) = ";M$:M(M$)<*"ENTER A Y-INTERCEPT (IN METERS) = ";B$:B(B$)=&*LX30:HX180:LY105:HY5:SX0:MX10:SYalking in a Field.":XX200:YY0:5:L45e;)Y510510:X3019015.14:X,Y:::30,030,105190,105;)233,3:2:0:N0:Y1031310!<)N20,Y:NN1:26,Y229,Y2::115,3:020,3:26,529,5:N0:X3017015.14:NX1,111:NN1:X,105X,108::117WD$"Also take note of what that particular line describes.":YYYY20:15:WD$"Try this for half a dozen lines or so. (Enough to give you a feeling for the meaning of slopes and y-intercepts.)":YYYY20:5:)100:BACK10722';):L15:WD$"Results of Wfrom the zero point--in this case the marker.":YYYY6:15O9)100:BACK104409):WD$"You will be given a piece of graph paper. When the computer asks you, enter the slope and y-intercept of a line you would like to see graphed.":YY10:15:)300:marker depends on how many seconds you walk. Distance is the DEPENDENT VARIABLE.)":YYYY6:9)15:300:WD$"The SLOPE of a distance vs. time graph (distance vertical, time horizontal) is just the speed of travel. The Y-INTERCEPT is the starting distance As you walk (at constant speed) directly toward or away from the marker, you keep track of the distance":YY10:15Z8)WD$"to the marker as time goes by.":15:300:WD$"(Time is the INDEPENDENT VARIABLE. You are trying to see if your distance from the possible title. You may be able to think of a better one."6)YY80:15:L15:WD$"Effect of Sound on Snails":XX185:YY10:5:L45:100:BACK10410t7):WD$"Let's try another experiment. You place a marker on the ground in the middle of a large field. '' when drawing the line showing the trend in the data."W5)YY80:15:100:BACK10410;6)T80:B160:200:WD$"One last thing this graph needs is a title--something that briefly identifies what data is graphed. (Don't just repeat the labels.) Here is a on that the snail was crawling even when the music was off.":15:100:BACK1041085)T80:B160:200:WD$"Before we finish with this graph, take a close look at it. Notice that both axes are labeled and include units. Also, we did NOT ''connect the dotsraphed line is its Y-INTERCEPT. This is the place where the line crosses the y-axis (assuming the x-axis starts at zero).":YY70:15:300Q4)WD$"Looking at our graph, we read a speed of 0.5 mm/s when the sound level is 0 dB. This reflects the observatiY20:15:100:BACK104102)T90:B160:200:WD$"This value of 0.082 mm/s per dB is called the SLOPE of the line. You will soon see how to calculate it for any line.":YY80:15:100:BACK104103)T90:B130:200:WD$"Something else which describes a gYY90:15:WD$"4.5 mm/s":XX100:YY97:5:WD$"55 dB":XXXX10:YY107:5:100,105150,105:WD$"= 0.082 mm/s per dB.":XX155:YY100:52|)300:WD$"So every time we turn up the speaker by 1 dB, the snail responds by increasing its speed by 0.082 mm/s.":YYY15:3000h)WD$"So if we divide the increase in the speed (= 5.0 - 0.5 = 4.5 mm/s) by the increase in sound intensity (= 55 - 0 = 55 dB) we will find the increase in speed per dB.":YYYY10:15:100:BACK104101r)T80:B160:200:WD$"We come up with":hat is that rate? For each 1 dB increase in sound level, how much faster does the snail go?":YYYY10:15:100:BACK104100^)T90:B160:200:WD$"As the sound level goes from 0 toward 55 dB, the speed tends to increase from 0.5 toward 5.0 mm/s.":YY70:e the line that best indicates the ''trend'' in the data.":YY80:15:55,50165,5:100:BACK10410.J)T90:B110:200:WD$"So there appears to be a fairly steady increase in the crawling rate of the snail as the sound increases.":YY80:15:300{/T)WD$"W40 dB, 3.8 mm/s) looks like this.":YY80:15:TX135:TY16:800:100:BACK10410-6)T90:B110:200:WD$"Finally, here is the last point at (50 dB, 4.5 mm/s).":YY80:15:TX155:TY10:800:100:BACK10410b.@)T90:B110:200:WD$"It looks like this might b0:B150:200:WD$"Here's the next point at (20 dB, 2.1 mm/s).":YY80:15:TX95:TY34:800:100:BACK10410,")T90:B110:200:WD$"Here's the point at (30 dB, 2.8 mm/s).":YY80:15:TX115:TY27:800:100:BACK10410O-,)T90:B110:200:WD$"The point at ( data table. (You did copy it down on paper didn't you?)":YY80:15:300+)WD$"We see that when the sound level was 10 dB, the crawling speed was 1.3 mm/s. Let's put that point on our graph.":YYYY10:15:300:TX75:TY41:800:100:BACK10410j,)T9 will fit the graph paper quite nicely.":YYYY10:15:300:COUNT0:Y53310:COUNT41,Y:45,Y4:048,Y:COUNTCOUNT1::L8:WD$"Speed (mm/s)":XX0:YY20*(0:Y5060:40,Y45,Y::3:5:L45:100:BACK10410I+)T90:B140:200:WD$"Now look at yourT1::WD$"Sound Level (dB)":XX170:YY58:5:100:BACK10410)(T80:B140:200:0:Y1050:185,Y279,Y::3:WD$"How about the vertical or y-axis? Our speed data goes from 1.3 to 4.5 mm/s.":YY80:15:300*(WD$"Well, if we go from 0 to 5.0 mm/s, we horizontal or x-axis.":YY70:15:300:WD$"Since our sound data goes from 0 to 50 dB, we should use 10 of the grid lines, with each division being equal to 5 dB.":YYYY10=)(15:2:0:233,3:054,60:COUNT1:X7115120:COUNTX,60:0X5,60:COUNTCOUNto have it fit on our graph.":YYYY10:15:100:BACK10370'(:X5516510:Y55510:X,Y:53,Y55,Y::X,57X,55::55,555,55165,55:L15:XX185:YY20:WD$"Here is our graph paper.":5:L45:300((WD$"We see that there are 11 grid lines along the to decide on the scale divisions.":YY10:15&(WD$"Let's do the horizontal scale first. We will start at 0 dB (note that it is not always necessary to start at zero.)":YYYY10:15;'(WD$"Our largest sound intensity is 50 dB, so we have to be sure ails.":YYYY10:15%(WD$"The DEPENDENT VARIABLE is plotted vertically. We want to see if the speed ''depends'' on the sound level we have selected.":YYYY10:15%(100:BACK10110.&(:WD$"The first thing you have to do when setting up a graph is trends in data is to graph them. We will make a graph of crawling speed vertically and sound level horizontally.":YY10:15%(300:WD$"We are taking the sound level as the INDEPENDENT VARIABLE. In this case, we are trying to uncover its effect on snhem to produce a graph.":300:YYYY6:15#(WD$"It isn't too hard to see that as the sound level increases the snail crawls faster. Let's see if we can ''quantify'' the relationship.":YYYY6:15:100:BACK10110~$(:WD$"The easiest way to bring out 1.3":YYYY20:5:XX78:WD$"20 2.1":YYYY10:5:WD$"30 2.8")#x(YYYY10:5:WD$"40 3.8":YYYY10:5:WD$"50 4.5":YYYY10:5:WD$"Write these values down. We will be working with tD((SS51)))"mm/s":XX5:YY82:5S!k(0:Y7090:55,Y160,Y::3:100:BACK10050Y!m(}!n(:WD$"Here is our data table:"!p(YY10:15:WD$"Sound Level (dB) Speed (mm/s)":XX40:YYYY20:5:40,30136,30:154,30230,30c"r(XX80:WD$"10 .58 f(16:X1150:X2195:SS0205:SSS2:SS0X1100 h(0:Y5159:1,Y39,Y::Y8189:1,Y49,Y::3:WD$((10(SS51)))" dB":XX5:YY52:5:Y80 i(ASS5:210,502102A,502A:210,602103A,60:210,702102A,702A:400:Y80:11!!j(WD$(dB (dB is short for ''deciBel'' ---the unit for sound intensity).":YY90:15:300d(WD$"You measure the speed of the snail with the radar gun. It produces the data we listed before...":15:100:BACK10050 e(D(1)1.3:D(2)2.1:D(3)2.8:D(4)3.8:D(5)4900,80:WD$"RADAR":XX5:YY82:5:0,5040,5040,5243,5243,5840,5840,600,600,50:WD$"SOUND":XX4:YYYY30:5K(0:210,50200,40:210,60195,60:210,70200,80:3P(100:BACK10050QZ(T100:B160:200:WD$"You vary the sound level from 10 to 50 ..":YYYY20:15:100:BACK10050<(T90:B160:200:WD$"You use your contacts with the police department to borrow one of their radar units. You also find a sound level meter in the laboratory stockroom.":YY100:15rF(0,8040,8050,7550,9540,900,T90:B100:200:WD$"Ah ha! I think we're on to something!":YY80:15:300!2(WD$"So if we adjust the loudness of the music, we note a change in speed of the snail. If only we had some way to measure the snail's speed and the loudness of the speaker...195,60:205,75200,80:3I(X1150:X2200:Y70:S2:11:100:BACK10050f (N146,Y:T90:B150:200(WD$"Now try the loud music.":YY80:15(210,50200,40:210,60195,60:210,70200,80(Y70:X1100:X2200:S8:11:100:BACK10050K((N88,Y:0:B100:200:WD$"It looked the same to me, what do you think?":YY80:15:300'WD$"Do you suppose snails could be sensitive to the loudness of the music? Let's try it. Soft music first....":YYYY10:15:100:BACK10050'0:205,45200,40:200,6010050'T90:B160:200x'WD$"Slow music first....":YY80:15:N188,Y:X1100:X2200:Y70:S8:11:100:BACK10050'N88,Y:T90:B100:200'WD$"Now try the fast music.":YY80:15'Y70:X1100:X2200:S8:11:100:BACK10050N'N88,Y:T9efinitely don't like music!":YY80:15:300:WD$"What do you suppose it is that they dislike?":15:300'WD$"Could it be the tempo of the music? You decide to try some slow music first and then something with a faster beat....":YYYY10:15:100:BACK:223,56223,65:222,59222,61:226,53226,67:227,56226,65c'227,56227,65:228,61228,63:300'X1190:X2200:Y70:S1:11'210,50200,40:210,60195,60:210,70200,80'N188,Y:X1100:X2190:Y70:S8:11'N86,Yg'WD$"Well...snails do be more complicated than you thought. If the snail moves without any sound at all, what happens when you turn on the music?":YY10:15:300<'230,81255,81255,46230,46230,81220,71220,41240,41255,46:220,41230,46:225,50225,70:224,53224,67es...":YY120:15:300Tj'X1180:X2200:Y90:1:233,8:16:S1:11:100:BACK10030t'T130:B150:200:WD$"It seems that snails don't like speakers, whether there is music coming from them or not!":YY120:15:100:BACK10030~':WD$"This is going t230,101220,91220,61240,61255,66:220,61230,66:225,70225,90:224,73224,87:223,76223,85:222,79222,81:226,73226,87:227,76226,85V'227,76227,85:228,81228,83:300`'WD$"Now you place a snail in front of the speaker and watch what it do0:15:100:BACK10000B':WD$"Here is the experiment that produced those numbers...":YY10:15:300:WD$"You want to find out if snails like music!":YYYY10:15:300:WD$"First set up your equipment--a speaker.":15L'230,101255,101255,66230,66following?":YY10:15:WD$"1.3, 2.1, 2.8, 3.8, 4.5":YYYY20:XX70:5:3008'WD$"Well, they are increasing. That's easy enough to see. But are the numbers increasing at a uniform rate? If it is indeed a uniform rate, then what is that rate?":YYYY3ollow some sort of pattern? If it does, the quickest way to spot it is with a graph.":YYYY10:15:100:BACK1000K.':WD$"It is often difficult to look at a group of numbers and pick up any sort of order. For example, can you find any pattern to the WD$"If you make a series of measurements you would probably want to examine what you recorded. Were all the values the same (within your error estimates) or did the numbers vary?":YYYY20:15s$'300:WD$"If there was a variation in the data, does it fUN MAIN MENU"rL::10:10:"PLEASE STAND BY... ...GETTING MORE OF THE LESSON!":1021,2:"RUN GRAPHS B"':WD$"Why do you have to learn about graphing?":YY10:15:300:WD$"Because it makes data analysis much easier!":YYYY20:15'300:'0:Y0LAST10:0,Y279,Y::3:G0:YTB:0,Y279,Y::3:Z,ZZ12000::mZZ11000:: WD$"o":XXTX2:YYTY4:5:YTY1TY1:TX1,YTX1,Y:: ::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":1023,7:"R68,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" "; hA$""ĺ" "::1000 iA$""ĺ" "::10722 jA$""BACK1:" ": kA$""ĺ" ": m21:1:958:(7);(7):100n(X(2)X(1))(HYY(1))(Y(2)Y(1)):Y(I)HY:64:52z >B(I)1X(I)X(1)(X(2)X(1))(LYY(1))(Y(2)Y(1)):Y(I)LY:64:52 @L(I)0:R(I)0:T(I)0:B(I)0 DX(I)LXL(I)1 FX(I)HXR(I)1 HY(I)HYT(I)1 JY(I)LYB(I)1 Lz dBACK0:491B(2)0ıZ 6I1:L(1)R(1)T(1)B(1)0I2:L(2)R(2)T(2)B(2)0ēX(1),Y(1)X(2),Y(2): 8L(I)1Y(I)Y(1)(Y(2)Y(1))(LXX(1))(X(2)X(1)):X(I)LX:64:52 :R(I)1Y(I)Y(1)(Y(2)Y(1))(HXX(1))(X(2)X(1)):X(I)HX:64:522 <T(I)1X(I)X(1)1))31:99::232,Q1:233,Q2:Q3:Q4:} N72:M82:NX2S,Y:XX2X1S:NXS,Y:MXSS2,Y:15XSS25,Y4:I1150: MXSS2,Y:15XSS25,Y4:NXSS,Y:I1150::: XX0:YYYY10:5: 2 4L(1)L(2)R(1)R(2)T(1)T(2)B(1)X$(WD$,LTR,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6& Q3(249):Q4(231):Q2(233):Q1(232):1:48:232,0:233,8:100XX,YY:Q1(WD$):((WD$,Q,81002:(1021)2107306:0:3:232,0:233,3K:L45:3:10000F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXX100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:$ LTRL11:                    \\2H~\\罽\PPPPPPPPPPPP\\s\s@s@@aL\\ہ\PPPPPPPPPPPP\\\@@@\\:4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" ";EhA$""ĺ" "::1000EjA$""BACK1:" ":EkA$""ĺ" ":Em21:1:958:(7);(7):100 F V$"o":XXTX2:YYTY4:5:YTY1TY1:TX1,)):PY(I)HY:64:50cD>B(I)1PX(I)PX(1)(PX(2)PX(1))(LYPY(1))(PY(2)PY(1)):PY(I)LY:64:50D@L(I)0:R(I)0:T(I)0:B(I)0DDPX(I)LXL(I)1DFPX(I)HXR(I)1DHPY(I)HYT(I)1DJPY(I)LYB(I)1DLgEdBACK0:49168,0:24:958:24:experiments.":YY10:15:300OPWD$"You will now be sent back to the menu. See your instructor to find out if you should continue studying errors.":YYYY20:15:100:BACK20580OP1000R:WD$"That's about all there is to it! The two rules that we1.64 m/s 2% = 1.64 0.03 m/s":YYYY10:15:TX105:TY145:600:TX168:600:100:BACK20560OP:WD$"That's about all there is to it! The two rules that we have discussed are often all you need to evaluate the effects of random error in your laboratory 1.64 meters/second":YYYY10:5:300VMxPWD$"The percentage errors are:":YYYY10:15MPWD$" (0.02/1.23) x 100 = 2 %":XX70:YYYY10:5:WD$"(0.001/0.752) x 100 = 0.1 %":YYYY10:5:195,120215,120:WD$"2.1%-->2%":XX201:YY125:5[NPWD$"Speed = 52 0.001 seconds. What is the speed of the object?":YY10:15:TX78:TY10:600:TX208:600:300$MnPWD$"Speed = distance / time":XX50:YYYY20:5:WD$"= 1.23 meters / 0.752 seconds":XX90:YYYY10:5:WD$"= 1.6356382 meters/second":YYYY10:5:WD$"= RCENTAGE ERROR in the result is the SUM of the PERCENTAGE ERRORS of the measurements.":XX40:L33:YYYY60:5KZPL45:30,50245,50245,11630,11630,50:100:BACK20470bLdP:WD$"Assume that you have found that an object travels 1.23 0.02 meters in 0.72:TY75:600:2218,73:300:WD$"(We get the second result by finding 0.9% of 1200 = 10.8 and rounding to one significant digit.)":YYYY10:15:100:BACK20430mKPP:WD$"Here is the rule:":YY10:15:WD$"When MULTIPLYING OR DIVIDING measurements, the PE error in the area.":YYYY5:15:100:BACK20430I1200 cm.":YYYY10:15:185,68189,68:2:233,3:2220,68:WD$"(We can only keep three significant digits this time.)":15GP300:WD$"Do we just multiply th:100:BACK20390xEO:WD$"How about when we multiply or divide? Then what do we do with the errors?":YY10:15:300 FPWD$"Let's find the area of a shelf top that measures 12.2 0.1 cm by 98.5 0.1 cm.":YYYY10:15:TX87:TY40:600:TX178:600:100lute errors add up and round off:":YY80:15:WD$"0.1 + 0.02 + 0.2 = 0.32 --> 0.3":XX40:YYYY10:5~DON.32ē200,98256,98EO300:WD$"So the calculation comes out to 11.3 0.3.":YYYY10:15:TX220:TY120:600:WD$"(We also round 11.28 to 11.3)":15e absolute error in the result of:":YY10:15:WD$"12.3 0.1 + 3.48 0.02 - 4.5 0.2 ?":XX40:YY40:5:TX67:TY40:600:TX133:600:TX200:600CO21:"WHAT IS THE ABSOLUTE ERROR ? ";N::N.3WD$"Correct--on the first try!":YY60:15dDOWD$"The absos of about 2% for both pieces of data, the result is only good to within about 20%!! Whenever you subtract two values that are close together, the percentage error goes up drastically."BOYYYY10:15:100:BACK20370CO:WD$"What do you suppose is th though we subtracted the data values, we ADD the absolute errors!":YYYY10:15:100:BACK20370AO0:Y5070:0,Y279,Y::3AOWD$"Also look at what happened to the percentage errors.":YY50:15BOWD$"Even though we started with percentage error2630,12630,50:100:BACK20300@O:WD$"Here is another example:":YY10:15:WD$"12.2 0.2 volts - 10.1 0.2 volts =":YYYY10:15:WD$"2.1 0.4 volts":XX190:YYYY10:5:TX27:TY20:600:TX127:600:TX210:TYTY10:600aAO300:WD$"Notice that even:WD$"In general:":YY10:15:WD$"When ADDING OR SUBTRACTING measurements which include absolute error estimates, the ABSOLUTE ERROR in the result is the SUM of the ABSOLUTE ERRORS of the measurements.":XX40:L33:YYYY60 @O5:L45:30,50250,50250,1we will include the extreme possiblities of 5.4 and 6.0 kg.":YY70:15:TX179:TY80:600:300>OWD$"Note that the absolute error in the result is the sum of the absolute errors:":YYYY20:15:WD$"0.3 = 0.1 + 0.2":XX80:YYYY10:5:100:BACK20260?O":15=jOWD$"3.3 kg + 2.7 kg = 6.0 kg":XX40:YYYY10:5:300:WD$"So the result of the addition is probably somewhere between 5.4 and 6.0 kg.":YYYY10:15=tO100:BACK20260]>~O0:Y80160:0,Y279,Y::3:WD$"If we write the result as 5.7 0.3 kg ? kg":XX20:YYYY20:5:TX41:TY60:600:TX119:600:TX198:600:100:BACK20260=`OWD$"Consider the extreme values of the data. Taking lower limits we have:":YYYY10:15:WD$"3.1 kg + 2.3 kg = 5.4 kg":XX40:YYYY10:5:WD$"Taking upper limits gives:"Another thing you have to worry about is the cumulative effect of errors when doing calculations. For example, if you have two measurements that should be added, what do you do with the errors?":YY10:15:300QN300:WD$"Consider for example this piece of data:":YYYY10:15^*HNWD$"4.55 0.04 volts":XX100:YYYY20:5:f this short lesson. It's time to ESC back to the menu.":YYYY30:15:100:BACK10110`('1000f( N(*N:WD$"We have already examined the implicit method of handling uncertainties by the use of significant digits.":YY10:15:300)4NWD$"Sometimes t:YYYY20:15"''100:BACK10080''::WD$"Whenever your lab exercise results in a number to be compared to a ''standard'' or expected value, use the PERCENT DIFFERENCE to find out how close you were.":YY10:15:300V('WD$"You've come to the end o by the expected value of 6.4 volts. The answer is 1.6%":YYYY20:15:10150&'(A$,3)"1.6"(A$,1)"%"WD$"Don't forget the percent sign! The answer is 1.6%.":YYYY20:15:10150 ''WD$"No! (6.5 - 6.4) / 6.4 gives 1.6 % when multiplied by 100!"A$"1.6 %"WD$"You have it figured out!":YYYY20:15:10150%'(A$,6)"1.5625"WD$"Watch those significant digits. We are limited to two here. The answer is 1.6%":YYYY20:15:10150M&'(A$,3)"1.5"WD$"Did you divide by 6.5? You should divideit! Let's try one more just to make sure you have it.":YY10:15:WD$"Find the percentage difference between a measured value of 6.5 volts and an expected value of 6.4 volts.":YYYY20$'15=%'"PERCENT DIFF. = ";A$:A$"+1.6%"A$"+1.6 %"A$"1.6%"WD$"x 100":XX240:YY70:5:91,75230,75#t'300:WD$"= -6.942889 % = -6.94 %":XX80:YY110:5:WD$"(The '100' is mathematically exact, so it has as many significant digits as needed.)":YY130:15:100:BACK10050$~':WD$"That's about all there is to determine the value to be 8.31 g/cm while a handbook lists 8.93 g/cm .":YY10:15:2:3216,18:3148,28:300)#j'WD$"Percent Diff. =":YY60:15:WD$"8.31 g/cm - 8.93 g/cm":YYYY7:XX95:5:3148,60:3225,60:WD$"8.93 g/cm":XX135:YY80:5:3190,78:80:YY70:5:15,67230,67!V'300:WD$"This is positive if you were too high and negative if your value was smaller than expected.":YY110:15:100:BACK10030o"`'::WD$"Let's say you were trying to find the density of copper. From the experiment you :YYYY20:15:100:BACK10000 B':WD$"Percent":XX10:YY30:5:WD$"Difference":YY40:5:WD$"=":XX80:YY35:5:WD$"(measured value - expected value)":XX20:YY55:5:WD$"x 100":XX235:YY63:5:0,20274,20274,870,870,20!L'WD$"expected value":XXtually got 0.003 m, you might think you were pretty close.":YY10:15:WD$"Actually you were off by 25%--not so hot!":YYYY10:15 8'WD$"There is a simple formula that allows you to see how close you were to an expected value. Turn the page to see it."ue.":15$'300:WD$"Merely subtracting what you got from what you should have gotten does not give you a real idea of how you did.":YYYY10:15:100:BACK1000.':WD$"For example, if you should have measured a diameter to be 0.004 meters and you ac experiment will attempt to find a value for a ''standard'' piece of information. You may be searching for the density of lead or the charge to mass ratio of an electron, but you need to know ''how"'YY10:15:WD$"close'' you were to the expected val2170:WD$"You will now be sent back to the menu. Your instructor will tell you if you should learn about error analysis in more detail, or if you are ready to face your first lab!":YY50:15:100:BACK22001000':WD$"Quite often your labdings tends to make them cancel out.":YY10:15:300WD$"Don't count on the errors completely cancelling, but don't be afraid to take more measurements. An average of a lot of data is usually more valid than any one reading.":YYYY20:15:100:BACKted the data. These things all happen randomly."YYYY10:15:WD$"So how do you reduce the effects of random error?":YYYY20:15:100:BACK21505:WD$"Since random errors will sometimes be positive and sometimes be negative, taking a lot of reaoo high and sometimes it will be too low. There is no way to tell which way it will be."1YY10:15:300:WD$"It is also possible that you slightly bumped a device while reading it. Maybe there was a slight variation in electrical voltage which affecne the direction (+ or -) of the error.":YYYY60:5:L45pp10,65240,65240,10210,10210,65:100:BACK2110Yz:WD$"For example, when estimating the value of a reading between the finest division lines on a device, sometimes your estimate will be t?) Every procedure in lab should be studied for possible errors!"c\YYYY10:15:100:BACK20709f:WD$"It is much harder to account for the other type of error.":YY10:15:XX20:L35:WD$"RANDOM ERRORS occur by chance. It is impossible to determi each length measurement, you would eliminate this systematic error.":YYYY10:15:300BRWD$"Other possibilities include poorly calibrated voltmeters or a mass balance that was not properly zeroed. (Maybe your lab partner tightens micrometers too muchwere using a meter stick to measure length, a careful examination might reveal that the end of the stick is dented, resulting in an extra millimeter being erroneously added to each measurement."WHYY10:15:300:WD$"By remembering to subtract 1 mm fromt do not occur by chance. It is usually possible to determine the amount and direction (+ or -) of a systematic error and correct the data.":XX20:L35:YYYY30:5410,82245,82245,15510,15510,82:100:BACK2040>L45::WD$"For example, if you understand some of the sources of errors in measurement.":YY10:15:300 WD$"There are two basic types of errors: SYSTEMATIC and RANDOM. Let's consider systematic laboratory errors first.":YYYY10:15:300*WD$"SYSTEMATIC ERRORS are errors tha thickness.)":YYYY10:15:300 WD$"There are several ways to explicitly handle error. 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