•HChemistry Name
1•ChemistryFoundations Period Date
1 .1 PROB L EMS - M EA SU R EM ENTS
1. Writethefollowingnumbers in scientific notation.
Circlethe significantdigits.
a. 0.000250 2.50×10−4
b. 2,000 2×103
c. 0.02081 2.081×10−2
d. 900. 9.00×102
2. Writethefollowingnumbers in standard decimal notation. Circle the significantdigits.
a. 2.150 × 102 215.0
b. 8.8 × 10–4 0.00088
c. 1.00 ×10–5 0.0000100
d. 4.337 ×106 4,337,000
3. Performthe followingoperations,reporting your
4. Howshouldeach measurementbe recorded?
Themass ofsamplesofsolid sodiumbicarbonate wasmeasuredin grams usingan electronic balance.
(a)
204.8 g
(b) 18.40
18.40 g
(c)
0.73 g
(d) 2.00 2.00 g
Thelength ofa strip ofmagnesiumwasmeasured in cmusinga ruler.
(e) 5.5 cm
answerwiththe correctnumberofsignificant
figures. (Assume the number“1” is anexact
1 2 3 4
5 cm
number.)
(f) 5.48
(0.1285)(38.00)
1 2 3 4
5 cm cm
a. (0.08206)(255.) 0.233
(g) 4.02
1
1
1000.
1 2 3 4
5 cm cm
b. 2.56 ×110.99×0.25×
1 92
(h) 0.5 cm
c. 5.6792 +0.6 + 4.33 10.6
1 2 3 4
5 cm
d. 3.70 – 2.9133 0.80
1 22.4
The volume ofsolutionsof copper(II)chloride was measured in mL using graduatedcylinders.
e. (1.74 ×1024)6.0223×1023 1
2460
64.7
(i)
400
(j)
20
f. (0.0385)(100.0 –28.6) 895
300 10
g. (3.26 ×10−3) –(7.88 × 10−5) 3.18 ×10−3
h. (4.02 ×106) +(7.74 ×107) 8.14 ×107
348 mL
7.3 mL
The volume levelofa solution ofpotassium
hydroxide was measured inmLusinga buret.
(k)
14
15
14.38mL
(l)
6
7
7.00 mL
Thetemperature ofwaterina beakerwas measured in Celsius(ºC)usinga thermometer.
(b)Group A’sresultsreportedwithtwo significant figures, while Group B’sresults arereported
(m.)
30
20
28.1°C
(n)
30
20
30.0°C
withfoursignificantfigures. Whatisthe reason forthe difference?
Group A’s simplemetricrulerhaslarger incrementsthan GroupB’s precision micrometer, so Group A’smeasurements
were recordedwithfewersignificantdigits
5. Two groupsofstudents determined the densityof
an aluminumbar. Group Ausesa simple metric ruler, whileGroup Busesaprecisionmicrometer. Thecalculated densitiesareshown below.The accepted valueforthe densityofaluminumis 2.702
g/cm3.(Usecomplete sentencesin yourresponses.)
thanGroupB’s. Therefore the calculated densitiesfrom Group Aalso hasfewer significantdigits thanthosefromGroupB.
(c) Howdoesthe measuringinstrumentaffect the precision ofa setofmeasurements?
Group A(g/cm3)
2.5
2.7
2.7
2.6
Average: Deviation:
Group B(g/cm3)
2.793
2.801
2.805
2.784
Average: Deviation:
The more precise the measuringinstrument (smallerincrements),themoreprecise the measurements.
(d)Which Groupis moreaccurate?Which group is more precise?Howdo you know?
Group Ahas a smaller average percent
errorthan GroupB,so Group A’s
(a) For each group,(i)reportthe measurement usingtheaverage valueandaverage deviation, and (ii)findthe percenterror.
Group A:
calculated density is closer tothe accepted value andismoreaccurate.
AvgValue =
2.5 +2.7 +2.7 +2.6
4
AvgDev. =
=2.625 g/cm3=2.6g/cm3
0.125 +0.075 +0.075 +0.025
4
=0.075 g/cm3
|2.625−2.702|
PercentError =
=2.9%
2.702 ×100%
Group B:
AvgValue =
2.793 +2.801 +2.805 +2.784
4
AvgDev.
=2.79575 g/cm3=2.796 g/cm3
0.00275 +0.00525 +0.00925 +0.01175
= 4
=0.00725 g/cm3
|2.79575−2.702|
PercentError =
=3.5%
2.702 ×100%