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Basic Skills 
RReevviieeww ooff SSiigg DDiigg 
Partial Nelson Reference: 692-693. 
You must learn the “ambiguous case” 
which is not given in the textbook. 
DDiimmeennssiioonnaall AAnnaallyyssiiss 
(Nelson Page: 709) 
MMeettrriicc PPrreeffiixxeess (ssttuuddeenntt ssttuuddyy oonnllyy)) 
(Nelson Page: 709)
Significant digits will be 
reviewed by example: 
SSttaattee tthhee nnuummbbeerr ooff SS..DD.. ffoorr:: 
11.. 00..112233000000 ________________ 
22.. 00..000000112233 ________________ 
33.. NNuummbbeerrss ssuucchh aass 110000 aanndd 55000000 
NNuummbbeerr ssuucchh aass tthheessee ffaallll iinnttoo tthhee “ambiguous 
case” mmeeaanniinngg tthhaatt tthhee zzeerrooeess mmaayy oorr mmaayy nnoott bbee 
ssiiggnniiffiiccaanntt.. To avoid the ambiguous case use 
scientific notation. 
4.. 11..223300 xx 110055 ________________
Addition and Subtraction Rules 
Perform the following operations: 
11.. 1122..3377 ++ 55..55 == ____________________ 
Rule: Final answers are to have the same precision 
(number of decimal places) as the least precise number so 
final answer is 17.9 
22.. 55..4466 xx 110044 –– 22..0055 xx 110033 
== ((55..4466 –– 00..220055)) xx 110044 ,, (both #’s have same power of 
ten, so precision rules can be applied) 
== 55..225555 xx 110044 
== 55..2266 xx 110044 ,,
Rounding Rules (By Example) 
a. 2.55, Round to 2 SD 
b. 2.65, Round to 2 SD 
c. 2.651, Round to 2 SD 
 22..66 
 22..66 
 22..77 
RRuulleess:: 
When rounding numbers such as 5, 50, 500, 
… round to the nearest even number 
When rounding numbers greater than 5, 50, 
500, … always round up. 
When rounding numbers that are less than 5, 
50, 500, … just drop these numbers 
Know how to deal with “0” (even or odd?)
Rules for Multiplying and Dividing 
SSoollvvee:: 
{{EExxpprreessss ffiinnaall aannsswweerr wwiitthh ccoorrrreecctt nnuummbbeerr ooff SSDD’’ss}} 
(15.5-10.5)/2.00 
Ans. 2.5 
Rule: For mult & div, the final answer must have 
the same number of SD’s as the number with 
the fewest SD’s. Treat exact numbers, which 
are typically counted – ie. 3 cars, as infinitely 
precise (infinite SD’s). When using a formula, 
like 2πr, assume the “2” is exact. 
{Note; BEDMAS rules also apply as in the above 
example}
Dimensional Analysis 
 PPhhyyssiiccaall qquuaannttiittiieess ssuucchh aass length, time 
aanndd mass, etc. mmuusstt aallwwaayyss bbee eexxpprreesssseedd 
wwiitthh aa uunniitt ooff mmeeaassuurree,, ssoo wwee ccaallll tthheemm 
dimensioned quantities. 
 Dimensional analysis ccaann bbee uusseedd ttoo 
ddeetteerrmmiinnee tthhee rreellaattiioonnsshhiipp tthhaatt mmaayy eexxiisstt 
bbeettwweeeenn qquuaannttiittiieess.. This will be shown by 
example.
 It is hypothesized that the energy ooff aa mmoovviinngg oobbjjeecctt (Ek) 
iiss pprrooppoorrttiioonnaall ttoo tthhee pprroodduucctt ooff tthhee oobbjjeeccttss mmaassss aanndd tthhee 
ssqquuaarree ooff iittss ssppeeeedd.. Use dimensional analysis to 
determine if this hypothesis is correct. 
Solution: 
 WWee uussee oonnllyy tthhee base pphhyyssiiccaall qquuaannttiittiieess ffoorr mmaassss [[MM]],, 
lleennggtthh [[LL]] aanndd ttiimmee [[TT]] 
 WWee wwiisshh ttoo pprroovvee tthhaatt EEkk ⍺⍺ mmvv22 
 CCoonnssiiddeerr eenneerrggyy wwhhiicchh iiss oofftteenn mmeeaassuurreedd iinn JJoouulleess 
 AA JJoouullee iiss eeqquuaall ttoo aa NNmm aanndd aa NNeewwttoonn iiss ttoo aa kkgg mm//ss22 
SSoo aa JJoouullee oorr aa ((kkgg mm//ss22 )) mm ccaann bbee eexxpprreesssseedd aass [[MM]][[LL]]22// 
[[TT]]22 ,, this is how we want to express the LHS in base 
physical quantities (which are unitless). 
 NNooww wwee llooookk aatt tthhee RRHHSS ooff tthhee eexxpprreessssiioonn aanndd eexxpprreessss aallll 
qquuaannttiittiieess iinn [[MM]],, [[LL]] aanndd [[TT]] 
 [[MM]][[LL]]22//[[TT]]22 ,, ssiinnccee ssppeeeedd ((vv)) ccaann bbee mmeeaassuurreedd iinn mm//ss aanndd 
tthheenn iinn bbaassee pphhyyssiiccaall qquuaannttiittiieess aass [[LL]]//[[TT]] 
 Since both the RHS and LHS are identical, we can say 
that the hypothesis is correct (just like solving an identity)
Practice Questions 
Workbook Questions 
 PPaaggee 11 QQ##11 ,, 22 
 PPaaggee 22 ## 11 ttoo 33,, RReeaadd mmeettrriicc pprreeffiixxeess oonn ppaaggee 22 
ttoo aannsswweerr tthhee uunniitt ccoonnvveerrssiioonn qquueessttiioonnss 
Try these prior test questions 
 aa..)) 1177..88 mm ++ 332255 ccmm 
 bb..)) 22..1155 xx 1100 -- 44 -- 88..55 xx 1100 -- 66 
 cc..)) ((1155..00 -- 1100..55))22//55..0000

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Grade 12 U0-l1-ReviewofSigDig

  • 1. Basic Skills RReevviieeww ooff SSiigg DDiigg Partial Nelson Reference: 692-693. You must learn the “ambiguous case” which is not given in the textbook. DDiimmeennssiioonnaall AAnnaallyyssiiss (Nelson Page: 709) MMeettrriicc PPrreeffiixxeess (ssttuuddeenntt ssttuuddyy oonnllyy)) (Nelson Page: 709)
  • 2. Significant digits will be reviewed by example: SSttaattee tthhee nnuummbbeerr ooff SS..DD.. ffoorr:: 11.. 00..112233000000 ________________ 22.. 00..000000112233 ________________ 33.. NNuummbbeerrss ssuucchh aass 110000 aanndd 55000000 NNuummbbeerr ssuucchh aass tthheessee ffaallll iinnttoo tthhee “ambiguous case” mmeeaanniinngg tthhaatt tthhee zzeerrooeess mmaayy oorr mmaayy nnoott bbee ssiiggnniiffiiccaanntt.. To avoid the ambiguous case use scientific notation. 4.. 11..223300 xx 110055 ________________
  • 3. Addition and Subtraction Rules Perform the following operations: 11.. 1122..3377 ++ 55..55 == ____________________ Rule: Final answers are to have the same precision (number of decimal places) as the least precise number so final answer is 17.9 22.. 55..4466 xx 110044 –– 22..0055 xx 110033 == ((55..4466 –– 00..220055)) xx 110044 ,, (both #’s have same power of ten, so precision rules can be applied) == 55..225555 xx 110044 == 55..2266 xx 110044 ,,
  • 4. Rounding Rules (By Example) a. 2.55, Round to 2 SD b. 2.65, Round to 2 SD c. 2.651, Round to 2 SD  22..66  22..66  22..77 RRuulleess:: When rounding numbers such as 5, 50, 500, … round to the nearest even number When rounding numbers greater than 5, 50, 500, … always round up. When rounding numbers that are less than 5, 50, 500, … just drop these numbers Know how to deal with “0” (even or odd?)
  • 5. Rules for Multiplying and Dividing SSoollvvee:: {{EExxpprreessss ffiinnaall aannsswweerr wwiitthh ccoorrrreecctt nnuummbbeerr ooff SSDD’’ss}} (15.5-10.5)/2.00 Ans. 2.5 Rule: For mult & div, the final answer must have the same number of SD’s as the number with the fewest SD’s. Treat exact numbers, which are typically counted – ie. 3 cars, as infinitely precise (infinite SD’s). When using a formula, like 2πr, assume the “2” is exact. {Note; BEDMAS rules also apply as in the above example}
  • 6. Dimensional Analysis  PPhhyyssiiccaall qquuaannttiittiieess ssuucchh aass length, time aanndd mass, etc. mmuusstt aallwwaayyss bbee eexxpprreesssseedd wwiitthh aa uunniitt ooff mmeeaassuurree,, ssoo wwee ccaallll tthheemm dimensioned quantities.  Dimensional analysis ccaann bbee uusseedd ttoo ddeetteerrmmiinnee tthhee rreellaattiioonnsshhiipp tthhaatt mmaayy eexxiisstt bbeettwweeeenn qquuaannttiittiieess.. This will be shown by example.
  • 7.  It is hypothesized that the energy ooff aa mmoovviinngg oobbjjeecctt (Ek) iiss pprrooppoorrttiioonnaall ttoo tthhee pprroodduucctt ooff tthhee oobbjjeeccttss mmaassss aanndd tthhee ssqquuaarree ooff iittss ssppeeeedd.. Use dimensional analysis to determine if this hypothesis is correct. Solution:  WWee uussee oonnllyy tthhee base pphhyyssiiccaall qquuaannttiittiieess ffoorr mmaassss [[MM]],, lleennggtthh [[LL]] aanndd ttiimmee [[TT]]  WWee wwiisshh ttoo pprroovvee tthhaatt EEkk ⍺⍺ mmvv22  CCoonnssiiddeerr eenneerrggyy wwhhiicchh iiss oofftteenn mmeeaassuurreedd iinn JJoouulleess  AA JJoouullee iiss eeqquuaall ttoo aa NNmm aanndd aa NNeewwttoonn iiss ttoo aa kkgg mm//ss22 SSoo aa JJoouullee oorr aa ((kkgg mm//ss22 )) mm ccaann bbee eexxpprreesssseedd aass [[MM]][[LL]]22// [[TT]]22 ,, this is how we want to express the LHS in base physical quantities (which are unitless).  NNooww wwee llooookk aatt tthhee RRHHSS ooff tthhee eexxpprreessssiioonn aanndd eexxpprreessss aallll qquuaannttiittiieess iinn [[MM]],, [[LL]] aanndd [[TT]]  [[MM]][[LL]]22//[[TT]]22 ,, ssiinnccee ssppeeeedd ((vv)) ccaann bbee mmeeaassuurreedd iinn mm//ss aanndd tthheenn iinn bbaassee pphhyyssiiccaall qquuaannttiittiieess aass [[LL]]//[[TT]]  Since both the RHS and LHS are identical, we can say that the hypothesis is correct (just like solving an identity)
  • 8. Practice Questions Workbook Questions  PPaaggee 11 QQ##11 ,, 22  PPaaggee 22 ## 11 ttoo 33,, RReeaadd mmeettrriicc pprreeffiixxeess oonn ppaaggee 22 ttoo aannsswweerr tthhee uunniitt ccoonnvveerrssiioonn qquueessttiioonnss Try these prior test questions  aa..)) 1177..88 mm ++ 332255 ccmm  bb..)) 22..1155 xx 1100 -- 44 -- 88..55 xx 1100 -- 66  cc..)) ((1155..00 -- 1100..55))22//55..0000