- 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