Review of SigDig

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