DATE._---.PER|OD
NAME
n
SlCS
S
Use with Chapter2.
DBTERMINING
SIGMFICNT
DIGTTS
Any measurement
is inaccurate
to somedegree.The inaccuracy
stemsfrom severalfactors.The precisionof any measuring
deviceis limited.The persondoingthe measurement
may introduce
error.The
experimental
techniquemay be faulty.Because
a measurement
containssomedegreeof inaccuracy,
the numberof digitsthat arevalidfor the measurement
are alsolimited.
Therearefour basicrulesthatcanbe usedto determine
the numberof significant
digitsin a measurement.
1. Non-zerodigitsare alwayssignificant.
2. All final zerosafterthe decimalpoint are significant.
3. Zerosbetweentwo othersignificant
digitsare alwayssignificant.
4. Zerosusedonly for spacingthe decimalpoint are not significant.
Supposean observermeasures
the speedof an objectand determines
that it is movingat 6.13 mis.
The speedof a secondobjectis determinedto be 5.02m/s.Which digitsare significant
in thesetwo
measurements?
Accordingto rules1 and 3, all the digitsare significant.
Usingthe rulesgivenabove,
detbrminethe numberof significant
digitsin eachof the followingmeasurements.
1 . 23.30cm
4. 1843.02L
7. 2.00012 km
10. 0.000101M5 0 s
2. 3.65kg
5. 8.7010 C
B . 0 . 5 mL
3. 365 kg
6. 2000.12mm
9. 704 000 h
Whenyou performmathematicalcalculations,
the resultof yourcalculations
can neverbe moreprecise
than the leastprecisemeasurement.
Add the followingquantities:44Jkg + 8.002kg + 0.93 kg :
53.032.The leastprecisemeasuremenr,
44.1kg, is preciseonly to the nearestone-tenth.The sum of
the masses,
therefore,mustbe roundedoff to the nearestone-tenth,so the answeris 53.0 kg.
11. Completetheseadditionproblems.
Writethe sum as a leastprecisemeasurement.
a . 3.414s + 10.02s + 58.3 2 5s + 0 . 0 0 09 8 s
b , 1B B 4kg + 0.94kg + 1.0 kg + 9 , 7 7 B k g
12. Completethesesubtraction
problems.Write the differenceas a leastprecisemeasurement.
a. 2104.1m - 463.09m
b. 2.326h - 0.1040B h
P H Y S ICS
SKI LLS 19
Phvsics
NAME
skill
q
1
I
Muhiplyingand dividingare a littledifferent.
In thesekindsof calculations,
the productor quotient
hasthe samenumberof significant
digitsasthe leastprecisenumber.lf you multiply'21.3 cm by 9.80cm,
the answeris 209, not 208.74.Sincethe lessprecisemeasureme
nt,21.3 cm, has'onlythreesignificani
digits,the producthasthreesignificant
digits.
13. Completethesemultiplication
problems.
Writethe productas a leastprecisemeasurement.
a . 10 .19m x 0.013m
b. 140.01cm x 26.042cm x 0.0159cm
14' Completethesedivisionproblems.
Writethe quotientas a leastprecisemeasurement.
a. 80.23m +- 2.4 s
b . 4.30 1kg - 1.9cm3
Averages
follow the samerule.Supposea car travelsarounda trackthreetimes.your measurements
for thethreetrialsare45.0kmlh, 48.21km/h,and47.o24km/h.Determine
the average
speedof the car.
45.0 + 48.21 + 47.024: 140.234
1 40.23 4- 3:46.74466
jl
,i
\./
sincethe leastprecisemeasurement
is45.0km/h,the answercan be preciseonlyto the nearest
onetenth.Thusthe correctanswer,roundedoff, is 46.7km/h.Answerthe followingquestions.
15. An experiment
callsfor 16.156g of substance
A, 28.2g of substance
B, 0.0058g of substance
C,
and 9.44 g of substanceD.
a. How manysignificant
digitsare therein eachmeasurement?
b. What is the total massof substances
in thisexperiment?
c. How many significant
digitsare there in the answerto part b?
1 6 ' Yo u r la b p artnerhasmeasuredl6.5 0 mL o f wa t e r, Y o u a c c id e n t a lly t ip o v e rt h e g ra d ua t e d c y l i n d e r
and spillsomeof the water.You standthe cylinderup, and determine
thatthereare 8.0 mL of
water left.
a. Which measurement
is more precise,
your lab paftner,s
or yours?Explain.
b. How much water did you losewhen you tippedoverthe graduatedcylinder?
20
P HY S I CS
SKILLS
I
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