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8/12/2019 Medication Math for the Nursing Student (3)
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Medication Math for the Nursing Student
Take the test: 25 practice problems--have fun with your brain.
Review the test with complete answers: Way more than you may want to know
Conversion factors for Nursin !tu"ents: Copy an" make your own cheat-sheet
#bbreviations for Nursin !tu"ents: $now%m an" love%m
&e"&ath 'rrors an" the Nursin !tu"ent: (e afrai") be very afrai"
# *ui"e to +imensional #nalysis: The one-pae all-you-really-nee"-to-know ui"e
,ow to &inimie &istakes: ou coul" save a life
+imensional #nalysis !ummary: # few tips
# Criti/ue of Clinical Calculations: # unifie" approach) 0th e".
Recommen"e" Corrections to Clinical Calculations: # unifie" approach
+imensional #nalysis for everyone else: !ome eneral e1amples here
&e"&ath an" your +#: 3iles an" prorams you can use
*o to top
&e"ication &ath 'rrors an" the Nursin !tu"ent
# shockin number of patients "ie every year in 4nite" !tates hospitals as the result of
me"ication errors) an" many more are harme". ne wi"ely cite" estimate 67nstitute of
&e"icine) 28889 places the toll at 00)888 to ;)888 "eaths) makin "eath by me"ication
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,ow many me"ication errors are miscalculation errors= No one really knows since by some
estimates as little as one in ten errors are reporte" 6epper) 28829. f reporte" errors one
3+# stu"y 6Thomas) et. al.) 288>9 foun" that ?@ were "ue to 88@ proficiency. !ince 88@ proficiency) but we cannot aim for less) an" knowin that we are always at risk
will make us e1tremely careful.
Neither effort) "esire to avoi" error) nor carefulness) however) is enouh. We nee" the riht
tools an" techni/ues that will help us avoi" miscalculations. 7 believe that "imensionalanalysis is the most appropriate tool available to us. 7t is) by far) the best metho" of solvin
me"ication math problems with the least chance of makin errors. #s nurses we%re not
likely to ever use whatever alebra) trionometry) calculus) or statistics we may know an"
6even better=9 we nee" make no effort to learn these subects) but we shoul" strive for a
"eep un"erstan"in of) an" proficiency in) "imensional analysis 6+#9.
The oo" news is that mastery of +# is not at all an unobtainable oal. While few coul"
master a vast subect such as alebra in a lifetime) most stu"ents shoul" be able to master
+# in a few weeks of focuse" effort. &astery woul" mean the ability to solve any problem
that coul" crop up) no matter how it is presente") while avoi"in pitfalls) an" retainin
proficiency in the years to come. Nee"less to say) if 7 thouht that nursin stu"ents were
masterin +#) 7 woul"n%t be writin this paper.
The ba" news) then) is that most nursin stu"ents seem to have a weak un"erstan"in of
+#. &ost can follow e1amples iven in the te1tbookD they can then solve all the practice
problems that follow the same eneral format. 7f /uies or tests also follow the te1tbook
e1amples) most stu"ents succee" brilliantly.
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That all is not well) however) is apparent went problems "o not meet e1pectations. ne
sophomore class stumble" ba"ly on a test apparently for this reason. They coul" all follow)
if imitatively) the e1amples in the te1tbook) an" coul" therefore "o all the practice
problems) but when the test presente" problems in an une1pecte" format) most faile"--only
2 stu"ents passe" the test. 7n their final semester before ra"uatin as RNs) a thir" faile"
another test. This suests a weak un"erstan"in of +#.
4nfortunately most stu"ents have almost) but not /uite) a complete un"erstan"in of +#. 7
believe this is "ue to the te1tbook use" 6Clinical Calculations: # unifie" approach) 0th e".9
almost) but not /uite) presentin a complete "escription of +#. 7t may be that there are too
few nurseEmathematicians to write te1tbooks) an" so a weak foun"ation for +# is lai" for
stu"ents to buil" on. &y aim in writin this paper is to provi"e nursin stu"ents with a
more robust foun"ation to buil" on) an" perhaps re"uce future misa"ventures. 7 am not a
mathematician) but 7 have been "oin +# for A8 years) have ma"e refinements in the
techni/ue over that time) an" as a substitute teacher 7 have tauht it to mi""le an" hih
school stu"ents.
+imensional analysis is your frien". 'mbrace itD learn to love it. 7t is our best "efense
aainst "oin harm to a patient by miscalculation.
*o to top
# !tep by !tep *ui"e to +imensional #nalysisThe followin summary can be use" as a ui"e for "oin +#. !ome familiarity with +# is
assume". While not all steps liste" below will be nee"e" to solve all problems) 7 have foun"
that any problem that can be solve" usin +# will yiel" its answer if the followin steps are
followe". 7 woul" not suest memoriin the se/uence of steps) but rather un"erstan"in
an" practicin them. 4n"erstan"in is more "urable than memory.
>. +etermine what you want to know. Rea" the problem an" i"entify what you%re
bein aske" to fiure out) e..
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!olve: &ake sure all the units other than the answer units cancel out) then "o
the math.
a. !implify the numbers by cancellation. 7f the same number is on the top an"
bottom) cancel them out.
b. &ultiply all the top numbers toether) an" then "ivi"e into that number allthe bottom numbers.
c. +ouble check to make sure you "i"n%t press a wron calculator key by
"ivi"in the first top number by the first bottom number) alternatin until
finishe") then comparin the answer to the first one. &iskeyin is a
sinificant source of error) so always "ouble check.
". Roun" off the calculate" answer.
o (e realistic. 7f you roun" off ?0.?AAAAA to ?0.?A mF that implies that all
measurements were of an e1treme accuracy an" that the answer is known to
fall between ?0.?25 an" ?0.?A5) or ?0.?A H 8.885 mF. # more realistic answerwoul" probably be ?0.? mF or ?5 mF.
o 7f you roun" to a whole number that implies a reater accuracy than is
appropriate) write your answer to in"icate a rane) such as ?5 H 5 mF.
a. #"" labels 6the answer unit9 to the appropriately roun"e" number to et
your answer. Compare units in answer to answer units recor"e" from first
step.
Take a few secon"s an" ask yourself if the answer you came up with makes sense. 7f it
"oesn%t) start over.
This is a fairly bare outline) so refer to #ppen"i1 # for e1amples. The steps are best taught)
rather than read) an" so woul" serve better as a ui"e to tutorin stu"ents than as a self-
teachin ui"e.
*o to top
,ow to &inimie &istakes
#nythin we can "o to re"uce errors by even the smallest "eree is worth "oin. ,ow we
choose to write "own a +# problem) for e1ample) can make a "ifference. !houl" we ust
keep the answer unit in min") circle it in the problem) or actually write it "own= #t best we
will hit what we aim for) so we must be very clear about what we want) about the answer
unit6s9 we are aimin for. Rea"in the problem with the sole) focuse" purpose of
"eterminin the answer unit) then writin it "own 6least we foret or et confuse" later on9
is an e1ample of oo" techni/ue.
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ou can be sloppy an" still et the riht answers most of the time) but eventually you%ll
blun"er because of poor techni/ue. ou%ll triumphantly) like me) write "own tbs is e/uivalent to sayin > tbsEA tsp.
When it comes time to "o the math) the first number can be overlooke") especially if you%re
usin scratch paper with other problems on it) perhaps because it is visually "ifferent an"
not in line with other values. #n error of omission is less likely usin the followin non-
fraction format:
This format is more visually interate") more bri"e like) an" is more appropriate for
workin with factors. 7t is also less confusin when "oin amounts-per-bo"y-weiht-per-
"ose or "ay calculations. 7n this format) the horiontal bar means 888) then "ivi"in
by 58 an" 588. When written in factor form usin bars) mistakes an" confusion are
minimie":
This is) then) another reason to avoi" the fraction format.
erhaps with the e1ception of conversion factors you have memorie") it is a"visable to
actually write "own) in
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4se abbreviations that are clear an" label numbers fully. 4sin a "eree symbol for hour
instea" of
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epper) *inette #. 628829Errors in drug administration by nursesfrom 4n"erstan"in an"
reventin +ru &isa"ventures Conference. #vailable online:
http:EEwww.ashp.orEpublicEproa"Eme"errorEpep.html
Thomas &RD ,o/uist CD hillips J. 6ct. >) 288>9Med error reports to FDA sho a mi!ed
bag"+ru TopicsD >056>9D 2A. #vailable online:http:EEwww.f"a.ovEc"erE"ruE&e"'rrorsEmi1e".p"f
*o to top
&e"&ath ractice roblems for Nursin !tu"ents
The followin problems will test your math ability without wastin your time with
repetitive problems. 'ach problem is a mini-test of some important concept. 7f you miss
any /uestion) review the un"erlyin concept. 7f you et them all riht) ask if you can takethe final.
*eneral &ath
Which of the followin statements are True=
>. 28E0; G 5E>2
2. >BE5 G A >E5
A. > ?E; G >5E;
0. 2EA H AE0 G >E>2
5. 5E H 2EA G > 2E
B. >8 >E5 - B AE5 G A AE5
?. ? >E; 1 AE0 G 5 >>EA2
;. 5E; >E>B G >8. A5@ G 8.A5
>8. 1iv G >0
!ee #nswers
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+imensional #nalysis roblems 6see Conversion 3actors for Nursin !tu"ents9
>. Just as a warm up) how many secon"s are in a "ay=
2. ou are to ive
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B. ou are sha"owin a nurse "urin a clinical who receives an or"er to a"ust the infusion
rate of a pump so that >.B m of li"ocaine are bein "elivere" per minute. ,anin is a >88
cc piyback containin 8.0 rams li"ocaine) a 8.0@ solution. Without writin anythin
"own) the nurse tries to solve the problem on a calculator. #fter the fifth "ifferent an"
incorrect answer you fin" a piece of scratch paper an" offer to show her how to set up the
problem. !he assures you she can always "o problems like this on tests) but a"mits that atthe moment her brain "oesn%t seem to be workin. ,ow woul" you set up an" e1plain the
problem to her=
?. n your first "ay of clinicals at a lon-term care facility you are carin for a resi"ent
receivin total enteral fee"in throuh a '* tube. ,e is receivin B8 mF Jevity per houras or"ere" when the pump fails an" no other pumps are available. ,is over-e1ten"e"
reular nurse hans "rip tubin) a"usts the "rip rate to somethin that mE> mF &!
an" ive 8.2 mF 7K push) but on lookin in the narcotic cabinet you fin" none available an"
the pharmacy is close". 7t occurs to you that you coul" reset the pump to "eliver 8.2 m &!
in 5 minutes) then o back to 5 mFEhr. #t what rate shoul" you set the pump=
. # te1tbook on clinical calculations inclu"es the followin conversion for househol" to
metric: > teaspoon G 5 mF G 5 . #s a home health nurse you nee" to help a client make
homema"e pe"iatric electrolyte solution usin the followin recipe: > F boile" water) A8
suar) >.5 salt) 2.5 lite salt 6$Cl9) 2.5 bakin so"a. !ince only kitchen measurin cups
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an" spoons are available you nee" to convert from metric. The answer) accor"in to the
te1tbook) is > /t boile" water) 2 tbsp suar) >E0 tsp salt) >E2 tsp lite salt) an" >E2 tsp bakin
so"a. What /uestionable assumption "oes the te1tbook make=
>8. 7n another te1tbook you are iven the followin e1ample: The or"er is for
Chloromycetin A88 m 7K bolus via saline lock. Fabel: Chloromycetin > . +irections:
Reconstitute with >8 mF sterile water for inection to yiel" >88 mEmF. ,ow may mF of
Chloromycetin shoul" be a"ministere"= '/uivalents: > G >8 mF) >888 m G >
A88 m 1 > 1 >8 mF G A mF
>888 m >
While the answer >. ,ow woul" you prepare 2 F of A@ so"ium hypochlorite 6bleach9 an" water solution=ou have only a measurin cup.
>2. 7n a home settin) how woul" you prepare > F 6or so9 of normal saline 68.@ NaCl9
usin water an" table salt if you have only a measurin cup an" a teaspoon= n han" is an
unopene" > lb bo1 of salt.
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>A. ou have an or"er to infuse >888 mF of +5W 65@ +e1trose in water9 7K over a perio"
of 5 hr. No pump is available) but the tubin set packae notes that the "rop factor is >8
ttEmF. ,ow woul" you a"ust the "rip rate=
>0. The or"er is for meperi"ine B8 m an" atropine r >E>58) 7&. The meperi"ine on han"
is >88 mEmF an" the atropine is 8.0 mEmF. The two are compatible so you plan to "raw
up both in the same syrine. ,ow much of each will you "raw up=
>5. Taamet is or"ere" 288 m) 7K) /Bh. #vailable is Taamet A88 m in a 2 mF vial of
a/ueous solution. ou are to "ilute a portion of this in >88 mF N! an" infuse over 28
minutes usin a (uretrol with a "rop factor of B8 ttEmF. ,ow much Taamet will you
inect into the (uretrol) an" what will the "rip rate be=
>B. The or"er is for amo1icillin B8 m) po) ti" for a chil" weihin >A lb. The pe"iatric
"osae rane is 28-08 mEkE"ay in three e/ual "oses. 7s the "ose safe=
>?. # chil" with severe poison ivy weihs 25 k an" (ena"ryl po 5 mEkE"ay is or"ere"
/Bh. (ena"ryl is available as a >2.5 mE5 mF solution. What "ose shoul" be iven=
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>;. ou are to infuse heparin 25888 4 in 258 mF N! at >8.B mFEhr. What is the
concentration of heparin solution= When you clear the pump you note that B? mF have
been infuse". ,ow much heparin has been iven=
>. our patient weihs >0A lb) an" you are or"ere" to infuse 258 m "obutamine in 588
mF N! at >8 mcEkEmin. ,ow many millirams of "obutamine will infuse per hour=
28. henobarbital >;8 mEm2E20 hours iven every eiht hours is or"ere" for a chil" whose
(!# 6bo"y surface area9 is 8.2 m2. ,ow much will each "ose be=
2>. ou are to ive Fi"ocaine A8 mcEkEmin to a chil" weihin 55 lb. The piyback
contains >28 m Fi"ocaine in >88 mF N!. #t hat rate will you set the pump=
22. Nipri"e is or"ere" an" you are to titrate to maintain the systolic bloo" pressure at >58
mm ,. #vailable is Nipri"e 58 mE258 mF. The rane is A-B mcEkEmin. # micro"rip
chamber 6B8 ttEmF9 is use" with a pump. our patient weihs >55 lb.
What is the concentration of the solution in mcEmF=
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,ow many mcEmin) lower an" upper rane) coul" be a"ministere"=
Within what rane will the pump rate be set=
What is the titration factor in mcEtt=
The patient%s systolic ( is currently >?8 mm , while receivin the low rane "ose.
7f you increase the ttEmin by 5 tt) how many mcEmin will the patient be
receivin=
#fter > hr) the systolic bloo" pressure is >28 mm ,) so you "ecrease the ttEmin by
B tt. ,ow many mcEmin is the patient now receivin=
2A. ,ow woul" you prepare 588 mF of a >:A5 bleach solution from a >:>8 bleach solution
usin water=
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20. +r. $issoff) wishin to test your perspicacity) or"ers >. milliscruples of &orphine 7K
for each stone of bo"y weiht to be a"ministere" over a A88-minute perio". #vailable is >
ill of &orphine 6&!9 solution havin a concentration of 8.0 pennyweihts of &orphine
"issolve" in >888 "rachms of solution. The patient weihs ? kilorams. #t what rateshoul" you set the pump= our "ru ui"e says that 8.; to >8 m of morphine can be iven
per hour. 7s the or"ere" "ose safe= 6es) all the units of measure are real) if sel"om use")
but the point is you "on%t even have to know what the units are) ust how to et from what
you are iven to what you want to know. !ee the lon list of Conversion factorsfor clues)
then use the (ack button on your browser to return.9
25. ou have come "own with a ba" case of the eebies) but fortunately your ran"mother
has a sure cure. !he ives you an eye"ropper bottle labele":
Take > "rop per >5 lb of bo"y weiht per "ose four times a "ay until the eebies are one.
Contains r ; heebie bark per "r >88 solvent. B8 "ropsG> tsp.
ou weih >2; lb) an" the 0-o bottle is half-full. ou test the eye"ropper an" fin" there
are actually B0 "rops in a teaspoon. ou are oin on a three-week trip an" are "eeply
concerne" that you miht run out of ranny%s eebie tonic. +o you nee" to see her before
leavin to et a refill=
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*o to top
#bbreviations for Nursin !tu"ents
4nits of &easure
c G cup
cc G cubic centimeters
cm G centimeters
"r G "rams
"ss G 2 teaspoons
fl G flui"
ft G foot
G rams
al G allon
l G lass
r G rains
t G "rop
tt G "rops
in G inches
k G kilorams
F G liters
lb G poun"
m G meters
mc G microrams
m'/ G milli/uivalents
m G millirams
mF G milliliters
mm G millimeters
o G ouncept G pint
/t G /uart
tbsp G tablespoons
tsp G teaspoons
4 G unit
ther #bbreviations
a G before 6ante9
#(* G arterial bloo" as
#(T G antibiotic therapy
ac G before meals 6ante cibum9
#+ G riht ear 6auricula "e1ter9
#+, G anti"iuretic hormone
a" lib G as "esire"
#+# G #merican +iabetes #ss.
am G before noon 6ante meri"ian9
# G aainst me"ical a"vice
a/ G water
#! G left ear 6auricula sinister9
#4 G both ears 6auriculi utro9
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bi" G twice a "ay 6888) >?889
( G bloo" pressure
(4N G bloo" urine nitroen
c G with
cap G capsule
C#+ G coronary artery "isease
C#T G computerie" a1ial tomoraphy
C(C G complete blo" count
C3 G cystic fibrosis
C,3 G conestive heart failure
CN! G central nervous system
C G car"iac output
C+ G chronic obstructive pulmonary "isease
C$ G creatinine phosphokinase
C!3 G cerebrospinal flui"
CK# G cerebrovascular acci"ent
CK G central venous pressure
'C G enteric coate"
'C* G electrocar"ioram
''* G electroencephaloram
eli1 G eli1ir
e1t G e1tract
*3R lomerulofiltration rate
*T G astrostomy
h G hour
hct G hematocrit
hb G hemolobin
hs G hour of sleep) be"time 62>889
7+ G intra"ermal
7C G intracranial pressure
7& G intramuscular
7K G intravenous
7K G intravenous pushEpyeloram
7K( G intravenous piyback$K G keep vein open
&7 G myocar"ial infarction
N* G nasoastric
NJ G nasoeunal
N G nothin by mouth
N! G normal saline
+ G riht eye 6oculus "e1ter9
oint G ointment
TC G over the counter
! G left eye 6oculus sinister9
4 G both eyes 6oculo utro9
p G after 6post9
pc G after meals 6post cibum9per G by
pm G after noon 6post meri"ian9
po G by mouth 6per os9
pr G per rectal
prn G whenever necessary
T G prothrombin time
TT G partial prothrombin time
/ G every
/>h G every > hour
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/2h G every 2 hours
/Ah G every A hours
/0h G every 0 hours 6888) >A88) >?88)...85889
/Bh G every B hours 62088) 8B88) >288) >;889
/;h G every ; hours 68B88) >088) 22889
/" G every "ay 68889
/h G every hour
/i" G four times a "ay 6888) >A88) >?88) 2>889
/o" G every other "ay
/s G /uantity sufficient
R(C G re" bloo" count
R& G rane of motion
s G without
sc G subcutaneous
sl G sublinual
sol G solution
s/ G subcutaneous
!R G sustaine" release
ss G one half
!E! G sins an" symptoms
stat G imme"iately
supp G suppository
susp G suspension
syr G syrup
tab G tablet
ti" G three times a "ay 6888) >A88) >?889
T G telephone or"er
tr G tincture
un G ointment
4T7 G urinary tract infection
K G verbal or"er
K! G vital sins
W(C G white bloo" count
WNF G within normal limits
*o to top
Conversion 3actors for Nursin !tu"ents
!hort list
> cup 6c9 G ; ounces 6o9
> "ram 6"r9 G B8 rains 6r9> "ram 6fl "r9 G B8 minims
> allon 6al9 G 0 /uarts 6/t9
> lass G ; ounces 6o9
> rain 6r9 G B0.; millirams 6m9
> ram 69 G >5.0A rains 6r9
> inch 6in9 G 2.50 centimeters 6cm9
> kiloram 6k9 G 2.2 poun"s 6lb9
> liter 6F9 G >.85? /uarts 6/t9
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> milliliter 6mF9 G >B.2A minims
> minim G > "rop 6t9
> ounce 6o9 G 2 tablespoons 6tbsp9
> ounce 6o9 G ; "rams 6"r9
> ounce 6fl o9 G 2.5? milliliters 6mF9
> pint 6pt9 G >B ounces 6o9
> poun" 6lb9 G >B ounces 6o9
> /uart 6/t9 G 8.0B liters 6F9
> /uart 6/t9 G 2 pints 6pt9
> tablespoon 6tbsp9 G A teaspoons 6tsp9
> teacup G B ounces 6o9
> teaspoon 6tsp9 G 0.A mF
Fon list
> cental G 05)A5 rams 69
> centimeter 6cm9 G >8 millimeters 6mm9
> cubic centimeter 6cc9 G > milliliter 6mF9
> cup 6c9 G ; ounces 6o9
> "rachm G A.55 milliliter 6mF9> "ram 6"r9 G B8 rains 6r9
> "ram 6fl "r9 G B8 minims
> allon 6al9 G 0 /uarts 6/t9
> ill G 0 ounces 6o9
> lass G ; ounces 6o9
> rain 6r9 G B0.; millirams 6m9
> ram 69 G >)888 millirams 6m9
> ram 69 G >)888)888 microrams 6mc9
> ram 69 G >5.0A rains 6r9
> han" G 0 inches 6in9
> inch 6in9 G 2.50 centimeters 6cm9
> kiloram 6k9 G >)888 rams 69
> kiloram 6k9 G 2.2 poun"s 6lb9> liter 6F9 G >888 milliliters 6mF9
> liter 6F9 G >.85? /uarts 6/t9
> meter 6m9 G >)888 millimeters 6mm9
> meter 6m9 G >88 centimeters 6cm9
> milliram 6m9 G >)888 microrams 6mc9
> milliliter 6mF9 G > cubic centimeter 6cc9
> milliliter 6mF9 G >5 "rops 6t9
> milliliter 6mF9 G >B.2A minims
> minim G > "rop 6t9
> ounce 6fl o9 G 2 tablespoons 6tbsp9
> ounce 6o9 G 28 pennyweihts 6"wt9
> ounce 6o9 G 20 scruples
> ounce 6o9 G A>.> rams 69
> ounce 6o9 G 0;8 rains 6r9
> ounce 6o9 G ; "rams 6"r9
> ounce) flui" 6fl o9 G 2.5? milliliters 6mF9
> palm G A inches 6in9
> pennyweiht 6"wt9 G 20 rains 6r9
> pint 6pt9 G >B ounces 6o9
> pint 6pt9 G 0 ills
> poun" 6lb9 G >B ounces 6o9
> poun" 6lb9 G A58 scruples
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> /uart 6/t9 G 8.0B liters 6F9
> /uart 6/t9 G 2 pints 6pt9
> scruple G 28 rains 6r9
> stone G 8.>0 centals
> tablespoon 6tbsp9 G A teaspoons 6tsp9
> teacup G B ounces 6o9
> teaspoon 6tsp9 G B8 "rops 6tt9
> teaspoon 6tsp9 G 0.A mF
*o to top
#ppen"i1 #
3un with +imensional #nalysis
+imensional analysis 6also known as the factor-label metho"9 is by far the most useful
math trick you%ll ever learn. &aybe you%ve learne" some alebra) but "o you ever use it=
'ver foresee usin it= 3or most people the answer is
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*o to top
25 '1amples6To take as a test first) click&e"-math ractice problems9
>.Ho many se#onds are in a day$
kay) so this is not a me"-math problem) but as an intro"uction to "imensional analysis
6+#9) it works fine. 7f you%re up to spee" in +#) skip this answer. therwise) what "o you
"o= 3irst) as with all +# problems) "on%t panic. 7f you have no i"ea what the answer is or
how to come up with an answer) that%s fine because you%re not oin to solve T,' problem.
What you are oin to "o is break the problem "own into several small problems that you
can solve) an" here%s how.
a. #sk yourself)
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Remember that you "on%t nee" to worry about the actual numbers until the very en". Just
focus on the units. lu in conversion factors that cancel out the units you "on%t want until
you en" up with the units you "o want. nly then "o you nee" to worry about "oin the
arithmetic. 7f you set up the bri"e so the units work out) then) unless you push the wron
button on your calculator) you W7FF et the riht answer every time.
2. %ou are to gi&e 'gr ( FeS*' but the a&ailable bottle gi&es only the milligrams of iron
sulfate per tablet +,-( mg.tab)" Ho many milligrams is the order for$
To et from rains to millirams you%ll nee" a conversion factor like > r G B0.; m.
5 r 1 B0.; m G A20 m) so you "eci"e that%s close enouh an" ive > tab.
> r
Roun"in to B8 mE> r) as is often "one) ives A88 m as your answer) which miht cause
you to "oubt if you will be ivin the or"ere" "ose.
A. %ou /ust opened a (00 m1 bottle of guaifenesin and ill be gi&ing 2 tablespoon per dose"
Ho many doses are in the bottle$ In other ords ho many tablespoons are in (00 m1$
588 mF 1 > tsp 1 > tbs G AA tbs
0.A mF A tsp
Roun"in to 5 mF ives you the same answer) so roun"in to 5 mF is reasonable.
0. %ou gi&e your home health patient an unopened (00 m1 bottle of guaifenesin and tell them
to ta3e - teaspoons * times a day as ordered" They as3 you ho long the bottle ill last"
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>.B m F. 1 B8 min 1 >88 mF F. sol G 20.8 mF F. sol
> min > hr 088 m F. hr
Checkin to make sure all the units of measure) e1cept for mF an" hr) cancel out) now is
the time for the calculator. Crunchin the numbers twice 6first 1 1 1 ) then 1 1 1 9an" ettin 20.8 each time) we can now set the pump with confi"ence.
?. n your first day of #lini#als at a long9term #are fa#ility you are #aring for a resident
re#ei&ing total enteral feeding through a E; tube" He is re#ei&ing 50 m1 8 to B8 "rops per mF. The manufacture woul" have calibrate" their"rip chamber an" put the number of "ropsEmF on the packae) an" it is the "rop factor
6"ropsEmF9 that you nee" to know. ou finally fin" the tubin use" an" the packae says
>2 "ropsEmF. our answer will be in "ropsEmin) so:
B8 mF 1 >2 "rops 1 > hr G >2 "rops
> hr > mF B8 min min
or A "rops every >5 secon"s which is easier to count. 7t turns out that 88 mF &! sol 1 8.2 m &! 1 B8 min G >28 mF &! sol
2.8 m &! 5 min > hr hr
Now that you know the rate) you nee" the volume to be infuse":
>88 mF &! sol 1 8.2 m &! G >8 mF &! sol
2.8 m &!
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Just to "ouble check) how many minutes will it take for the pump to "eliver >8 mF at >28
mFEhr=
B8 min 1 > hr 1 >8 mF G 5 min
> hr >28 mF
.A te!tboo3 on #lini#al #al#ulations in#ludes the folloing #on&ersion for household to
metri#: 2 teaspoon @ ( m1 @ ( g" As a home health nurse you need to help a #lient ma3e
homemade pediatri# ele#trolyte solution using the folloing re#ipe: 2 1 boiled ater4 ,0 g
sugar4 2"( g salt4 -"( g lite salt +>l)4 -"( g ba3ing soda" Sin#e only 3it#hen measuring #ups
and spoons are a&ailable you need to #on&ert from metri#" The anser4 a##ording to the
te!tboo34 is 2 t boiled ater4 - tbsp sugar4 2.* tsp salt4 2.- tsp lite salt4 and 2.- tsp ba3ing
soda" 7hat uestionable assumption does the te!tboo3 ma3e$
While > tsp G 5 mF is a vali" conversion factor) > tsp G 5 is vali" only when measurinwater. .A Ecc9 woul" weih B.5 rams. The "ensity of ranulate"
suar is 8.? Ecc) $Cl is >.8 Ecc) an" bakin so"a is 8.; Ecc) so a teaspoon of each woul"
actually weih between A.5 Ecc an" B.5 Ecc. #ssumin 5 Etsp for each seems a bit rouh.
To "o the conversions riht) factor in the "ensity:
!uar: A8 1 > cc 1 > mF 1 > tsp 1 > tbsp G 2. tbsp 6not 2.8 tbsp9
8.? > cc 5 mF A tsp
!alt: >.25 1 > mF 1 > tsp G 8.2 tsp 6close to >E0 tsp9
>.A 5 mF
(akin so"a: 2.5 1 > mF 1 > tsp G 8.BA tsp 6closer to 2EA than >E29
8.; 5 mF
$Cl) with "ensity >) remains at >E2 tsp. +oes takin the "ensity into account really matter=
Realiin that "ensity is somethin to take into account matters) an" until you look up the
"ensities an" factor them in you woul"n%t know if it matters or not.
>8.In another te!tboo3 you are gi&en the folloing e!ample: rder: hloromy#etin ,00 mg
2? bolus &ia saline lo#3" 1abel: hloromy#etin 2 g" Dire#tions: Ce#onstitute ith 20 m1
sterile ater for in/e#tion to yield 200 mg.m1" Ho may m1 of hloromy#etin should be
administered$ Eui&alents: 2 g @ 20 m14 2000 mg @ 2 g
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,00 mg ! 2 g ! 20 m1 @ , m1
2000 mg 2 g
7hile the anser ',' happens to be right4 the set up is not" 7hat error did the te!tboo3
ma3e$
The set up is in error "ue to a failure to fully label units. The >8 mF is 8 mF sterile
water.< ou have to ask) 8 mF of what=< our answer unit) what you want to know) is
8 mF Chlor. solution. !ince you want Chlor.< which is /uite an unnecessary bit of
information for solvin this problem) thouh the te1t incorrectly uses it.
A88 m Chlor. 1 > Chlor. 1 >8 mF water G A mF water 6notM9 >888 m Chlor. > Chlor.
The correct set up shoul" be:
A88 m Chlor. 1 > mF Chlor. sol G A mF Chlor. sol
>88 m Chlor.
>>.Ho ould you prepare - 1 of ,6 sodium hypo#hlorite +blea#h) and ater solution$ %ou
ha&e only a measuring #up"
2 F sol 1 >888 mF 1 A mF bleach 1 > o 1 > cup G >E0 cup bleach
> F >88 mF sol A8 mF ; o
(ut how much water= The solution is ?@ water) riht=
2 F sol 1 >888 mF 1 ? mF water 1 > o 1 > cup G ;.> cups water
>F >88 mF sol A8 mF ; o
>2.In a home setting4 ho ould you prepare 2 1 +or so) of normal saline +0"6 =al) using
ater and table salt if you ha&e only a measuring #up and a teaspoon$ n hand is an
unopened 2 lb bo! of salt"
The key is to clearly un"erstan" what 8.@ means. !alt is measure" by weiht) so 8.@
means 8. parts salt by weiht to >88 parts salt solution 6not water9 by weiht. 7f you knew
the "ensity of ranulate" salt you coul" convert from a "esire" weiht of salt to a volume of
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salt. !ince you can only measure volume 6usin cup an" tsp9) you will somehow have to
"etermine the "ensity of salt. ou coul" look up the "ensity) or what if you poure" the bo1
of salt 6>B o9 into your measurin cup= +oin so you fin" that you have a bit over >2 flui"
ounces of salt. Recallin that "ensity is weihtEvolume) you fiure the "ensity of salt at >B
oE>2.A fl o or >.A oEfl o. What you want to know is the number of teaspoons per /uart.
The set up follows:
>2.A fl o salt 1 8. o salt 1 A2 o 1 2 tbsp 1 A tsp G > >EA tsp salt
>B o salt >88 o salt sol > /t > fl o > tbsp /t salt sol
To make one /uart you woul" first put the salt into a measurin cup then fill to the > /uart
mark.
>A. %ou ha&e an order to infuse 2000 m1 of D(7 +(6 De!trose in ater) I? o&er a period of (
hr" =o pump is a&ailable4 but the tubing set pa#3age notes that the drop fa#tor is 20 gtt.m1"Ho ould you ad/ust the drip rate$
3irst) what "o you want to know= The flow rate in ttEmin) which are the answer units.
What "o you know= ou%re iven that there are >8 ttEmF an" that the infusion rate is
>888 mFE5 hr. !ince you want tt on top an" >8 ttEmF has tt in the riht place) >8 ttEmF
makes a perfectly oo" startin factor--from there you ust nee" to et from mF to min.
The set up then:
>8 tt 1 >888 mF 1 > hr G AA tt
> mF 5 hr B8 min min
ou woul"n%t want to count a full minute) so "ivi"e by A an" count for 28 secon"s.
>0. The order is for meperidine 50 mg and atropine gr 2.2(04 IM" The meperidine on hand is
200 mg.m1 and the atropine is 0"* mg.m1" The to are #ompatible so you plan to dra up
both in the same syringe" Ho mu#h of ea#h ill you dra up$
3or both you want to know mF) your answer unit.
B8 m 1 > mF G 8.B mF meperi"ine
>88 m
> r 1 B0.; m 1 > mF G >.> mF atropine
>58 > r 8.0 m
>5. Tagamet is ordered -00 mg4 I?4 5h" A&ailable is Tagamet ,00 mg in a - m1 &ial of
aueous solution" %ou are to dilute a portion of this in 200 m1 =S and infuse o&er -0 minutes
using a Buretrol ith a drop fa#tor of 50 gtt.m1" Ho mu#h Tagamet ill you in/e#t into the
Buretrol4 and hat ill the drip rate be$
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ou want to know m of Taamet) an" ttEmin.
288 m T. 1 2 mF T. sol G >.A mF T.
>88 mF N! A88 m T. >88 mF N!
The "rip rate woul" be:
B8 tt 1 >8>.A mF T. sol G A80 tt T. sol
> mF 28 min min
Can you count 5 ttEsec= Not likely) so what "o you "o= What if you a""e" a secon"ary set
with a "rop factor of >2 ttEmF=
>2 tt 1 >8>.A mF T. sol G B8 tt T. sol
> mF 28 min min
>B. The order is for amo!i#illin 50 mg4 po4 tid for a #hild eighing 2, lb" The pediatri# dosage
range is -09*0 mg.3g.day in three eual doses" Is the dose safe$
ou want to know mEkE"ay for this chil". What you know is that you will ive B8 m per
>A lb bo"y weiht per "ose or B8 mE>A lbE"ose) which true but is unusable in this form) so
you rewrite it as B8 mE>A lb 1 > "ose. ,ow can you "o that= Consi"er "ivi"in >E0 by 2.
,alf of one /uarter is one eihth) but how to fiure that:
> G > 1 > G > G >
0 0 2 0 1 2 ;2
+ivi"in by 2 is the same as invertin 2 to et >E2 an" multiplyin. #cceleration) to ive
another e1ample) is measure" in feet per secon" per secon" or ftEsecEsec) which is e/ual to
ftEsec 1 sec or ftEsec2.
B8 m 1 2.2 lb 1 A "ose G A8.5 m G A8.5 mEkE"ay--a safe "ose.
>A lb 1 > "ose > k > "ay k 1 "ay
Whenever you have 1 per y per ) rearrane in the form 1Ey an" everythin will stay
straiht.
>?.A #hild ith se&ere poison i&y eighs -( 3g and Benadryl po ( mg.3g.day is ordered 5h"
Benadryl is a&ailable as a 2-"( mg.( m1 solution" 7hat dose should be gi&en$
ou want to know mFE"ose. !ince you want mF on top) start with:
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5 mF 1 5 m 1 > "ay 1 25 k G >2.5 mF
>2.5 m k 1 "ay 0 "oses "ose
>;. ou are to infuse heparin 25888 4 in 258 mF N! at >8.B mFEhr. What is the
concentration of heparin solution= When you clear the pump you note that B? mF have
been infuse". ,ow much heparin has been iven=
ou want to know 4nitsEmF) so nothin tricky here:
25888 4 G >88 4EmF
258 mF
B? mF sol 1 >88 4 G B?88 4
mF sol
>;? mF sol 1 28 4 G ?0);88 4
mF sol
>. %our patient eighs 2*, lb4 and you are ordered to infuse -(0 mg dobutamine in (00 m1
=S at 20 m#g.3g.min" Ho many milligrams of dobutamine ill infuse per hour$
ou want to know mEhr) which has time on the bottom. #fter convertin to >8 mcEk 1
min you note that time is also on the bottom) so this shoul" work as a startin factor:
>8 mc 1 B8 min 1 > m 1 > k 1 >0A lb G A m
k 1 min > hr >888 mc 2.2 lb hr
28.henobarbital 20 mg.m-.-* hours gi&en e&ery eight hours is ordered for a #hild hose
BSA +body surfa#e area) is 0"- m-" Ho mu#h ill ea#h dose be$
ou want to know mE"ose) so you coul" start with > "ayEA "oses or >;8 mEm 2E"ay:
> "ay 1 >;8 m 1 8.2 m2G >?.0 m
A "oses m21 "ay "ose
2>. %ou are to gi&e 1ido#aine ,0 m#g.3g.min to a #hild eighing (( lb" The piggyba#3
#ontains 2-0 mg 1ido#aine in 200 m1 =S" At hat rate ill you set the pump$
ou want to know mFEhr. !tartin with the patient%s weiht usually works out:
55 lb 1 > k 1 A8 mc 1 > m 1 >88 mF 1 B8 min G A?.5 mF
2.2 lb k 1 min >888 mc >28 m > hr hr
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ou want mcEmin an" from the above) oin from 55 to B8 ttEmin:
A.A mc 1 B8 tt G >; mc
> tt > min min
#fter > hr) the systolic bloo" pressure is >28 mm ,) so you "ecrease the ttEmin byB tt. ,ow many mcEmin is the patient now receivin=
ou aain want mcEmin an" are oin from B8 to 50 ttEmin:
A.A mc 1 50 tt G >?; mc
> tt > min min
2A.Ho ould you prepare (00 m1 of a 2:,( blea#h solution from a 2:20 blea#h solution
using ater$
ou want to know how much concentrate" bleach solution 6mF c.b.9 you nee" to make theweaker solution 6mF w.b.9.
>8 mF c.b. 1 > mF b. 1 588 mF w.b. G >0A mF c.b.
> mF b. A5 mF w. b.
To the >0A mF of concentrate" bleach solution you woul" a"" enouh water to make 588
mF >:A5 solution. 7f you fully label all amounts) you shoul" avoi" confusion.
20.Dr" >issoff4 ishing to test your perspi#a#ity4 orders 2" millis#ruples of Morphine I? forea#h stone of body eight to be administered o&er a ,009minute period" A&ailable is 2 gill of
Morphine +MS) solution ha&ing a #on#entration of 0"* pennyeights of Morphine dissol&ed in
2000 dra#hms of solution" The patient eighs 3ilograms" At hat rate should you set the
pump$ %our drug guide says that 0" to 20 mg of morphine #an be gi&en per hour" Is the
ordered dose safe$ +%es4 all the units of measure are real4 if seldom used4 but the point is you
don8t e&en ha&e to 3no hat the units are4 /ust ho to get from hat you are gi&en to hat
you ant to 3no" See the long list of on&ersion fa#torsfor #lues4 then use the Ba#3 button
on your broser to return")
(reakin the problem "own stepwise: #s always) start by askin what "o you want to
know= 7f you%ve worke" with 7K pumps you know they are proramme" in mFEhr) so your
answer will have to be in these units of measure.
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!o) it looks like you%ll have enouh. #t some point you nee" to know how many "rops per
"ose you will nee" to take) so you fiure it out:
#s a practical matter) you can%t take ;.5AA "rops per "oseD you have to roun" off. #t this
point you realie that when you calculate" 22.5 "aysEbottle) you were not fiurin on
"ropsE"ose. ou "eci"e to recalculate to see if roun"in up to makes a sinificant
"ifference.
ou note a small "ifference) but conclu"e that you have ust enouh eebie tonic.
Conclu"in that you have enouh) however) an" havin enouh may not be the same thin.
The story continues:
%ou lea&e on your trip and on the 2th day you run out of geebie /ui#e" %ou didn8t spill any4
and no one too3 any" %ou sit in a stunned stupor trying to figure out here you ent rong in
your #al#ulations"
ou finally realie there miht not have been 2.8 o of tonic in the bottle to bein with. #
measurement like .5 to 2.5 o in the bottle. Recalculatin usin the low an" hih values) you fin" you
ha" enouh tonic to last somewhere between >B an" 2B "ays. 7f you ha" fiure" out the
correct answer of 2> H 5 "ays the first time) you woul" have realie" you ha" only slihtly
less than a 58E58 chance of runnin out) an" woul" have one to see *ranny for a refill.
*o to top
!ummary
+on%t panic. (reak T,' R(F'& "own into small ones you C#N solve.
3iure out what answer unit6s9 you want to en" up with. This is usually easy.
Write "own) in math terms) everythin you know that relates to the problem. ou
may nee" to rea" the problem several times) rephrasin parts of it) so you can
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translate everythin into math terms. ou may nee" to look up a few conversion
factors) but that%s inconvenient) not "ifficult.
ou now nee" to pick a startin factor. 7f possible pick one that alrea"y has one of
the units you want in the riht place. therwise start with somethin you are iven
that is not a conversion factor.
lu in conversion factors that allow you to cancel out any units you "on%t want
until you are left with only the units you "o want 6your answer units9.
7f you can%t solve the problem) pick a "ifferent startin factor an" start over.
+o the math an" solve it. Now "ouble-check your calculations.
#sk yourself if the answer seems riht or reasonable. 7f not) recheck everythin.
*o to top
#ppen"i1 (
*o to top
# Criti/ue of Clinical Calculations: # unifie" approach) 0th
e".
The steps for "oin "imensional analysis are iven in the te1tbook as:
>. +etermine the startin factor an" answer unit.
2. 3ormulate a conversion e/uation.
A. !olve the conversion e/uation.
+eterminin the answer unit or units is crucialD they are not always obvious an" can be
challenin to "etermine. 3or some problems) rea"in the problem correctly is the only
challene. !tu"ents nee" to be able to translate sometimes convolute" 'nlish "escriptions
of a problem into clear) properly labele" factors they can later use to solve the problem.This skill is not emphasie" in the te1tbook. 7f the answer unit is always iven in the
e1amples use") then this is because the e1amples have been contrive" to be more simple
an" consistent than actual problems ten" to be.
7n some real-worl" problems no startin factor is iven) or several possible startin factors
are iven with no way to "eci"e) initially) which to use. 7t is preferable) in such cases) to
"etermine everythin you know that miht be relevant to solvin the problem) then "eci"e)
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after the answer unit is "etermine") which of the factors you know woul" make an
appropriate startin factor.
#ll e1amples use" throuhout the te1t use only numbers havin a sinle unit attache" for
startin factors. #pparently hour< is an acceptable startin unit) but 8 percent errors are a bit worrisome. '/uatin > rain
with B8 millirams when the actual e/uivalency is closer to B0.; m) is /uestionable) as is
e/uatin liters an" /uarts) or > mF to >5 minims 6actually > mF G >B.2A minims9. 7t is
possible to solve a problem an" come up with answers that "iffer by as much as >8@
"epen"in on which appro1imate conversion factors you "eci"e to use. 7f H 5@ errors are
acceptable) then) as an asi"e) any answer to a test /uestion that is within 5@ of the correct
answer shoul" be counte" as correct. 7t is o""ly inconsistent to insist on carryin outcalculations to two "ecimals) roun"in to the nearest tenth) when far reater errors can be
intro"uce" by usin loose appro1imations.
When) in chapter B) a problem involvin amountEbo"y weihE"ay comes up) the solution is
presente" in an unortho"o1 way. The problem 6p. 09 ives 25 mEkE20 hr. When "oin
"imensional analysis it is essential that all the units iven shoul" be use" an" accounte" for.
7norin a iven unit) then pullin it out of thin air at the en" is poor techni/ue) yet this is
what the te1tbook "oes. The solution is iven as:
The problem is that the correct answer units shoul" be how many mF shoul" be
a"ministere" per "ay) or
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7f 5 lb patient at A mcEkEmin:
7n this e1ample) at least) minutes are not omitte" then a""e" at the en") an" the techni/ue
is not even erroneous) but merely confusin to many stu"ents an" visually awkwar". #
stu"ent miht try to loically e1ten" this techni/ue to "etermine mFEhr:
The stu"ent who notices that the answer "oesn%t make sense miht won"er what went
wron. Woul" they realie that when hrEB8 min= Tryin to e1plain how to work
aroun" the poor techni/ue employe" by this e1ample only "is a "eeper hole. The better
response to stu"ent confusion woul" be to have them put a bi O mark over this section of
the te1tbook an" show them a sensible way to set it up:
#nother case of flawe" techni/ue arises in Chapter >8. !tu"ents are iven problems that
re/uire convertin from mFEhr to ttEmin) an" are shown conversion e/uations like the
followin:
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The problem) aain) is that the correct answer unit is 8:
Calculation of 7K 3low Rate When Total 7nfusion Time is !pecifie"
r"er: >888 mF of +5W 65@ +e1trose in water9 7K to infuse over a perio" of 5 hr
+rop 3actor: >8 ttEmF
!tartin 3actor #nswer 4nit
> min tt 6"rops9
'/uivalents: >888 mF G 5 hr) >8 tt G > mF) B8 min G > hr
Conversion '/uation:
> min 1 > hr 1 >888 mF 1 >8 tt G AA.A G AA tt
B8 min 5 hr > mF
3low Rate: AA ttEmin
3or review) let%s o over this problem.
>. There are two errors relatin to the startin factor. ne is proce"ural--there is no loical
way to pick a startin factor as the first step. The other is that min< is a meaninless
factor. 7 can meaninfully say that 7 know there are >8 "rops per mF) but it means nothin
to say that 7 know min< in the conte1t of this problem.
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This table reveals how the authors think about "imensional analysis. They see the startin
factor as somethin ivenD there can be only one startin factorD it has only one unit
associate" with it) an" it forms a special k9) but otherwise
there is no necessary
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Whatever initial "ifficulty this techni/ue may present for stu"ents not alrea"y familiar
with it) it is still the techni/ue of choice an" will save a lot of rief later on. !ome of the
techni/ues contrive" to "eal with these problems work on some problems) but not others.
The techni/ue use" above has the virtue of workin with all problems involvin triple unit
factors.
ae 58: 7n the two e1amples on this pae the #nswer 4nit is incorrectly iven as
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aes >B0) >B5) an" >BB: 7nore these e1amples as above.
aes >??) >?;: #ain) inore the spurious !tartin 3actors an" use the correct #nswer
4nits for the last two e1amples on pae >??) an" e1amples 2 an" A on pae >?;.
aes >;0) >;5: 7nore e1amples. #nother ad ho#variation in techni/ue is intro"uce"without comment in step > of the first e1ample. !tu"ents will et into trouble if they try to
e1ten" this e1ample to other problems. #lso) what if the "esire" answer units were
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7n settin up the conversion factors) it is helpful to write the "enominator first) as this
contains the unit of the prece"in numerator an" facilitates cancellation of successive units.
!olve the conversion e/uation by use of cancellation an" simple arithmetic.
Cancel units first
Re"uce numbers to lowest terms.
&ultiplyE"ivi"e to solve the e/uation.
Re"uce answer to lowest terms) convert to "ecimal) an"Eor roun" off.
Take a few secon"s an" ask yourself if the answer you came up with makes sense. 7f it
"oesn%t) start over.
The te1t in re" represents weak or erroneous techni/ue. 'rrors of omission are notin"icate".
Conclusions
This may be a case of a book bein the worst te1tbook on "imensional analysis available--
with the e1ception of all the others. 7%ve hear" that it is much better than its pre"ecessor.
!everal me"ication math te1tbook titles are currently available) but not havin reviewe"
them) 7 can%t assume any "o a better ob) but 7 think other titles shoul" be looke" into.
There are errors of omission where stu"ents are not iven a complete enouh
un"erstan"in of "imensional analysis to "o all problems that coul" crop up. There areerrors of commission where stu"ents are tauht flawe" or even erroneous techni/ue.
Throuhout the te1tbook) overly simplifie" e1amples are use" that fail to show the rane of
problems that stu"ents may encounter. # wi"er rane of problems) however) woul" have
illustrate" the shortcomins of the techni/ues as tauht) an" may have been omitte" for
that reason.
verall) however) 7 woul" say that this book is /uite useable provi"e" its shortcomins an"
flaws are amen"e". # better roun"e") more robust presentation of "imensional analysis is
"efinitely nee"e". !tu"ents shoul" not only "o well solvin test problems) but come away
feelin confi"ent in their ability to han"le any problems that may come their way in the
future.