2- Units of Measurement
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Transcript of 2- Units of Measurement
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8/18/2019 2- Units of Measurement
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Measurements
Units of Measurement
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Measurement You are making a measurement when you
Check you weight
Read your watch
Take your temperature
What kinds of measurements did you make
today?
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Standards of Measurement
When we measure, we use a measuring tool
to compare some dimension of an object to
a standard.
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Measurement in ChemistryIn chemistry we
♦do experiments
♦measure quantities
♦use numbers to report measurements
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Metric System SI!
Is a decimal system based on "#
$sed in most of the world
$sed by scientists and hospitals
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$nits in the Metric System length meter m
%olume liter &
mass gram g
temperature Celsius 'C
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Stating a MeasurementIn e%ery measurement there is a
♦(umber
followed by a
♦ $nit from measuring de%ice
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&earning Chec)What is the unit of measurement in each of the following
examples*
+. he patient-s temperature is "#'/.
0. he sac) holds 1 lbs of potatoes.
C. It is 2 miles from your house to school.
3. he bottle holds & of orange soda.
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Solution+. '/ degrees /ahrenheit!
0. lbs pounds!
C. miles
3. & liters!
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Measurements
Measured (umbers and
Significant /igures
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Measured (umbersWhen you use a measuring tool is used to
determine a quantity such as your height or
weight, the numbers you obtain are calledmeasured numbers .
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4eading a Meterstic)
. l. . . . I . . . . I5 . . . .I . . . . I6. . cm
/irst digit )nown! 7 .** cmSecond digit )nown! 7 #.8 .8* cm
hird digit estimated! between #.#19 #.#8
&ength reported 7 .81 cm
or .8: cm
or .88 cm
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;nown < =stimated 3igits ;nown digits and 8 are "##> certain
he third digit : is estimated uncertain!
In the reported length, all three digits
.8: cm! are significant including the
estimated one
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=xact (umbers ?btained when you count objects
soccer balls
" watch
6 pi@@as
?btained from a defined relationship
" foot 7 " inches
" meters 7 "## cm
Not obtained with measuring tools
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&earning Chec)Classify each of the following as an exact "!
or a measured ! number.
+.AAABold melts at "#:6'C
0.AAA" yard 7 5 feet
C.AAA+ red blood cell with diameter : x "#96 cm
3.AAAhere were : hats on the shelf
=.AAA+ can of soda contains 511 m& of soda
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SolutionClassify each of the following as an exact "! or a
measured! number. Bi%e reason.
+. 4equires a thermometermeasuring tool!
0. " /rom a definition in $.S. system
C. (eed measuring tool to determine
3. " Counted the hats
=. Measured
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17
Measurements
Significant /igures in Calculations
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18
Significant /igures in
Measurementhe numbers reported in a measurement
are limited by the measuring tool
Significant figures in a measurement include
the )nown digits plus one estimated digit
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19
Counting Significant /igures (umber of Significant /igures
52."1 cm6
1.: ft
:1.: lb AAA
".11 m AAA
Complete +ll non9@ero digits in a measured number
are significant or not significant!.
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(umber of Significant /igures
#.##2 mm "
#.#"1: o@ 5
#.##6 lb AAAA
#.###: m& AAAA
Complete &eading @eros in decimal numbers are
significant or not significant!.
20
&eading Deros
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(umber of Significant /igures
1#.2 mm 5
##" min 6
#.8# lb AAAA
#.##6#1 m AAAA
Complete Deros between non@ero numbers are
significant or not significant!.
21
Sandwiched Deros
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(umber of Significant /igures
1,### in.
## yr "
62,:## gal 5
1,##1,### g AAAA
Complete railing @eros in numbers withoutdecimals are significant or not significant! if
they are ser%ing as place holders.
22
railing Deros
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23
&earning Chec)
+. Which answers contain 5 significant figures*
"! #.68:# ! #.##68: 5! 68:#
0. +ll the @eros are significant in"! #.##5#8 ! 1.5## 5! .#1# x "#5
C. 156,:81 rounded to 5 significant figures is "! 151 ! 151,### 5! 1.51 x "#1
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24
Solution
+. Which answers contain 5 significant figures*
! #.##68: 5! 68:#
0. +ll the @eros are significant in! 1.5## 5! .#1# x "#5
C. 156,:81 rounded to 5 significant figures is ! 151,### 5! 1.51 x "#1
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+ calculated answer cannot be more precise
than the measuring tool.
+ calculated answer must match the least
precise measurement.
Significant figures are needed for final answers
from "! adding or subtracting
! multiplying or di%iding
25
Significant (umbers in Calculations
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26
+dding and Subtractinghe answer has the same number of decimal
places as the measurement with the fewest
decimal places.
1. one decimal place
< ".56 two decimal places :.16
answer :.1 one decimal place
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In each calculation, round the answer to the
correct number of significant figures.
+. 51.#1 < "E.: < ." 7
"! 1:.81 ! 1:.2 5! 18
0. 12.E1 9 "2. 7
"! 6#.81 ! 6#.85 5! 6#.8
27
&earning Chec)
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28
Solution+. 51.#1 < "E.: < ." 7
! 1:.2
0. 12.E1 9 "2. 7
5! 6#.8
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29
Multiplying and 3i%iding
4ound or add @eros! to the calculated answer
until you ha%e the same number of significantfigures as the measurement with the fewest
significant figures.
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30
&earning Chec)
+. ."E F 6. 7"! E ! E. 5! E."E2
0. 6.5"" G #.#8 7"! :".12 ! : 5! :#
C. .16 F #.##2 7
#.#"#1 F #.#:#
"! "".5 ! "" 5! #.#6"
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31
Solution
+. ."E F 6. 7 ! E.
0. 6.5"" G #.#8 7 5! :#
C. .16 F #.##2 7 ! ""
#.#"#1 F #.#:#
Continuous calculator operation 7
.16 x #.##2 ÷ #.#"#1 ÷ #.#:#
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Measurements+ccuracy and Hrecision
32
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ow close a measurement is to the actual or true %alue
good accuracy
true %alue
poor accuracy
true %alue
33
+ccuracy
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ow well se%eral measurements agree with
each other
good precision
poor precision
34
Hrecision
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What can you say about the accuracy and
precision in each of the following
Bood precision, poor accuracy
Bood precision, good accuracy35
+ccuracy and Hrecision
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Match the following terms
"! +ccuracy ! Hrecision
AAA ow close a measurement is to the true %alue.
AAA ow close se%eral measurements
are to each other.
Can you ha%e data that are precise, but not
accurate* Why or why not*36
&earning Chec)
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Match the following terms
"! +ccuracy ! Hrecision
A"A Is how close a measurement is to the true %alue.
AA Is how close se%eral measurements
are to each other.
Jes. 3ata can be precise, but not come close to
the true %alue.37
Solution
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38
&earning Chec) rue"! or false !. Measurements can ha%e
poor accuracy and poor precision
good accuracy and poor precision
poor accuracy and good precision
good accuracy and good precision
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40
Measurements
Hrefixes and
=qualities
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Increase or decrease basic unit by "#
/orm new units larger or smaller than the basic
units
Indicate a numerical %alue
prefix = value
" )ilometer 7 "### meters
" )ilogram 7 "### grams
41
Metric Hrefixes
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42
Hrefixes that Increase A $nitHrefix Symbol Kalue
giga9 B " ### ### ###
mega9 M " ### ###
)ilo9 ) " ###
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43
Hrefixes that Decrease A $nitHrefix Symbol Kalue
deci9 d #."
centi9c #.#"
milli9 m #.##"
micro9 mu! #.### ##"
nano n #.### ### ###"
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Indicate the prefix to use for
". + mass that is "### times greater than " gram
"! )ilo ! milli 5! mega
. + length that is "L"## of " meter*
"! deci ! centi 5! milli
5. + unit of time that is "L"### of a second.
"! nanosecond ! microsecond 5!millisecond
44
&earning Chec)
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". "! )ilo
. ! centi
5. 5! millisecond
45
Solution
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46
=qualities
State the same measurement in two different units
length
"#.# in.
1.6 cm
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Lengt
" m 7 "## cm
Mass
" )g 7 "### g
!olume" &7 "### m&
47
Some Metric =qualities
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+. "### m 7 " AAA "! mm ! )m 5! dm
0. #.##" g 7 " AAA "! mg ! )g 5! dg
C. #." & 7 " AAA "! m& ! c& 5! d&
3. #.#" m 7 " AAA "! mm ! cm 5! dm
48
&earning Chec)
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49
+. "### m 7 " AAA ! )m
0. #.##" g 7 " AAA "! mg
C. #." & 7 " AAA 5! d&
3. #.#" m 7 " AAA ! cm
Solution
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Bi%e the %alue of the following units
+. " )g 7 AAAA g
"! "# g ! "## g 5! "### g
0. " mm 7 AAAA m
"! #.##" m ! #.#" m 5! #." m
50
&earning Chec)
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+. " )g 7 AAAA g
5! "### g
0. " mm 7 AAAA m
"! #.##" m
51
Solution
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52
Some +merican =qualities" ft 7 " inches
" lb 7 ": o@
" quart 7 pints
" quart 7 6 cups
he quantities in each pair gi%e the same
measured amount in two different units.
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" in. 7 .16 cm
" qt 7 E6: m&
" & 7 ".#: qt
" lb 7 616 g
" )g 7 .# lb
Remember these for exams.
53
Some Metric9+merican =qualities
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"xample #
+t the store, the price of one pound of red peppers is
.5E.=quality " lb red peppers 7 .5E
"xample $
+t the gas station, one gallon of gas is ".56.
=quality " gallon of gas 7 ".56
54
=qualities gi%en in a Hroblem
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/ractions in which the numerator and denominator arequantities expressed in an equality between those units
=xample " in. 7 .16 cm
/actors " in. and .16 cm
.16 cm " in.
55
Con%ersion /actors
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Write con%ersion factors that relate each of
the following pairs of units
+. &iters and m&
0. ours and minutes
3. Meters and )ilometers
56
&earning Chec)
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+. liters and m& " & 7 "### m&
" & and "### m&
"### m& " &
0. hours and minutes " hr 7 :# min
" hr and :# min
:# min " hr
C. meters and )ilometers " )m 7 "### m
" )m and "### m
"### m " )m
57
Solution
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58
Measurements
Hroblem Sol%ing
$sing Con%ersion /actors
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". + person has a height of .# meters. What is
that height in inches*
Initial unit 7 m /inal unit 7 AAAAAAA ! 0lood has a density of #.#1 gLm&. If a person
lost #.5# pints of blood at "2'C, how many
ounces of blood would that be*
Initial 7 pints /inal unit 7 AAAAAAA
59
Initial and /inal $nits
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Initial unit .1 hr
Conversion Final
factor unit .1 hr x :# min 7 "1# min
" hr
cancel Answer (2 SF)
!
ow many minutes are in .1 hours*
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"
&earning Chec)
+ rattlesna)e is .66 m long. ow long is the
sna)e in cm*
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#
Solution
+ rattlesna)e is .66 m long. ow long is the
sna)e in cm*
! 66 cm
.66 m x "## cm 7 66 cm
" m
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ow many seconds are in ".6 days*
$
&earning Chec)
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$nit plan days hr min seconds
$ %& "xact
".6 day x 6 hr x :# min x :# sec
" day " hr " min
7 ". x "#1 sec
%
Solution
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5
$nit Chec)
What is wrong with the following setup*
".6 day x " day x :# min x :# sec 6 hr " hr " min
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$nit Chec)
".6 day x " day x :# min x :# sec
6 hr " hr " min
$nits 7 day.
Lhr.
Not te final unit needed
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+n adult human has 6:1# m& of blood. owmany gallons of blood is that*
&
&earning Chec)
S l ti
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$nit plan m& 't gallon
Setup6:1# m& x " qt x " gal 7 ".5 gal
E6: m& 6 qt
3 SF 3 SF exact 3 SF
8
Solution
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4ead problem
Identify data
Write down a unit plan from the initial unit
to the desired unit
Select con%ersion factors
Change initial unit to desired unit
Cancel units and chec)
3o math on calculator
Bi%e an answer using significant figures
9
Steps to Hroblem Sol%ing
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&!
&earning Chec)
If the s)i pole is 5.# feet in length, how long is
the s)i pole in mm*
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&"
Solution
5.# ft x " in x .16 cm x "# mm 7
" ft " in. " cm
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&earning Chec)
If your pace on a treadmill is :1 meters per
minute, how many seconds will it ta)e for you to
wal) a distance of 261# feet*
S l i
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Initial
261# ft x " in. x .16 cm x " m
" ft " in. "## cm
x " min x :# sec 7 6## sec
:1 m " min
final '$ %&(
&$
Solution
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&%
Measurements
3ensity
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3ensity compares the mass of an object to its
%olume
3 7 mass 7 g or g
%olume m& cm5
(ote " m& 7 " cm5
&5
3ensity
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&
&earning Chec)
?smium is a %ery dense metal. What is its
density in gLcm5 if 1#.## g of the metal occupies
a %olume of .cm5*
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&&
Solution
! Hlacing the mass and %olume of the osmium metal
into the density setup, we obtain
3 7 mass 7 1#.## g 7
%olume . cm5
7 .11 gLcm5 7 .1 gLcm5
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+ solid displaces a matching %olume of waterwhen the solid is placed in water.
55 m&1 m&
&8
Kolume 3isplacement
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What is the density gLcm5! of 62 g of a metal ifthe metal raises the le%el of water in a graduated
cylinder from 1 m& to 55 m&*
55 m&
1 m&
&9
&earning Chec)
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8!
Solution
! : gLcm5
Kolume m&! of water displaced
7 55 m& 9 1 m& 7 2 m&
Kolume of metal cm5!7 2 m& x " cm5 7 2 cm5
" m&
3ensity of metal 7mass 7 62 g 7 : gLcm5
%olume 2 cm5
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Which diagram represents the liquid layers in
the cylinder*
;! ;aro syrup ".6 gLm&!, K! %egetable oil
#.E" gLm&,! W! water ".# gLm&!
"! ! 5!
8"
&earning Chec)5
;
(
W
W
W
K
K
K(
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;! ;aro syrup ".6 gLm&!, K! %egetable oil
#.E" gLm&,! W! water ".# gLm&!
"!
8#
Solution
;
W
K
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+ substance has a density of 5.2 gLm&.
3ensity 7 5.2 gLm&
=quality 5.2 g 7 " m&
Con%ersion factors.5.2 g and " m&
" m& 5.2 g
8$
3ensity as Con%ersion /actors
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8%
3ensity Connections
Mass Kolume
kg )
g m) *cm$+
mg
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he density of octane, a component of
gasoline, is #.8# gLm&. What is the
mass, in )g, of 281 m& of octane*
85
&earning Chec)
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8
Solution
"! #.:"6 )g
$nit plan m& g )g
=qualities " m& 7 #.8# g and " )g 7 "### g Setup
281 m& x #.8# g x " )g 7 #.:"6 )g
" m& "### g
density metric
factor factor
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8&
&earning Chec)
If blood has a density of ".#1 gLm&, how
many liters of blood are donated if 181 g of
blood are gi%en*
"!
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88
Solution
"!
$nit Hlan g m& &
181 g x " m& x " & 7 #.162 &
".#1 g "### m&
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, 55.9 kg person disp-aces 5&.# ) of water
when sumerged in a water tank. What is
the density of the person in g/cm$?
89
12amp-e3
, 55 9 kg person disp-aces
4nformation3
i6en3 m 7 5 59 2 "!% g
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,pp-y the so-ution maps0e'uation.
9!
, 55.9 kg person disp-aces
5&.# ) of water when
sumerged in a water tank.
What is the density of the person in g/cm$?
i6en3 m 7 5.59 2 "!% g
V 7 5. 2 "!% cm$
ind3 density g/cm$
:o-ution Map3 mV →
1'uation3
$%
%
cm"!2.5
g"!259.5==
V
m
7 !.9&& g/cm$
7 !.9&& g/cm$
V
m =
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assignment
;ractice0What
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9#
&earning Chec) + group of students collected "1 empty
aluminum cans to ta)e to the recycling center. If
" cans ma)e ".# pound of aluminum, how many
liters of aluminum 37.8# gLcm5! are obtained
from the cans*
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9$
Solution
"! ".# &
"1 cans x ".# lb x 616 g x " cm5
" cans " lb .8# g
x " m& x " & 7 ".# &
" cm5 "### m&
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9%
Hlatinum has become a popular metal for fine jewelry. + man gi%es a
woman an engagement ring and tells her that it is made of platinum.
(oting that the ring felt a little light, the woman decides to perform a
test to determine the ring-s density before gi%ing him an answer
about marriage. She places the ring on a balance and finds it has a
mass of 1.26 grams. She then finds that the ring displaces #.11: cm5
of water. Is the ring made of platinum* 3ensity Ht 7 ".6 gLcm5!
Sh l th i b l d fi d it h
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95
She places the ring on a balance and finds it has a
mass of 1.26 grams. She then finds that the ring
displaces #.11: cm5 of water. Is the ring made ofplatinum* 3ensity Ht 7 ".6 gLcm5!
Bi%en Mass 7 1.26 grams
Kolume 7 #.11: cm5
/ind 3ensity in gramsLcm5
=quation
Solution Map
m and ! d
V
m=
m! V
V
m=
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;ractice0What 4s the =ensity of Meta- if a "!!.! g
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9&
y g
:amp-e ,dded to a Cy-inder of Water Causes the
Water )e6e- to Rise from #5.! m) to $&.8 m)?
ind =ensity of Meta- if "!!.! g =isp-aces Waterfrom #5.! to $&.8 m)
Bi" W i d h Bi i fi
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from #5.! to $&.8 m)
nits and magnitude arecorrect.
Chec)&. Check.
&.2"#5 g/cm$ 7 &.8" g/cm$4ound. :ignificant figures and round.
Solution
< 7 $&.8@#5.!
7 "#.8 m)
5. o--ow the so-ution map to
Sol%e the pro-em.
Solution
Map
%. Write a Solution Map.
C/ N
=quation
g/cm$
/ind#. Write down the 'uantity youwant to /ind and unit.
m 7"!!.! g
disp-aces #5.! to $&.8 m)
Bi%en". Write down the Bi%en
'uantity and its unit.$ sig figs
$ significant figures
m! V
V m =
V
m =" m) 7 " cm$
$$ g/cm#5"8.&cm"#.8
g!."!!==
$$
cm.8#"m)"
cm"m)"#.8 =×
$. Write down the appropriateCon%. /actor and =quation.
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99
Measuring )emperature
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"!!
emperature
Harticles are always mo%ing.
When you heat water, the water molecules mo%e
faster.
When molecules mo%e faster, the substance gets
hotter.
When a substance gets hotter, its temperature goes
up.
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Suppose you place water in a free@er.
+. he water particles mo%e
"! faster ! slower 5! the same
0. he water will get
"! hotter ! colder 5! stay the same
C. he temperature of the water will be
"! higher ! lower 5! the same
"!"
&earning Chec)
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"!$
emperature
Measures the hotness or coldness of an object
3etermined by using a thermometer that
contains a liquid that expands with heat andcontracts with cooling.
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/ahrenheit Celsius ;el%in
Water boils AAAAA'/ AAAAA'C AAAAAA;
Water free@es AAAAA'/ AAAAA'C AAAAAA;
"!%
emperature Scales
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/ahrenheit Celsius ;el%in
Water boils "'/ "##'C 585 ;
Water free@es 5'/ #'C 85 ;
"!5
emperature Scales
$nits of emperature between
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/ahrenheit Celsius ;el%in
Water boils "'/ "##'C 585 ;
"2#' "##'C "##;
Water free@es 5'/ #'C 85 ;
"!
p
0oiling and /ree@ing
& i Ch )
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+. emperature of free@ing water
"! #'/ ! #'C 5! # ;
0. emperature of boiling water"! "##'/ ! 5'/ 5! 585;
C. (umber of Celsius units between the
boiling and free@ing points of water
"! "## ! "2# 5! 85
"!&
&earning Chec)
S l ti
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+. emperature of free@ing water! #'C
0. emperature of boiling water5! 585;
C. (umber of Celsius units between the
boiling and free@ing points of water
"! "##
"!8
Solution
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"!9
/ahrenheit /ormula
"2#'/ 7 E'/ 7 ".2'/ "##'C
1'C "'C
Dero point #'C 7 5'/
'/ 7 EL1 'C < 5
or'/ 7 ".2 'C < 5
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4earrange to find 'C
'/ 7 ".2 'C < 5
'/ 9 5 7 ".2'C
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+ person with hypothermia has a body temperature
of E."'C. What is the body temperature in '/*
"""
emperature Con%ersions
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""#
&earning Chec)
he normal temperature of a chic)adee is "#1.2'/.
What is that temperature in 'C*
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5! 6".# 'C
Solution
'C 7 '/ 9 5!
".2
7 "#1.2 9 5!
".2
7 85.2'/
".2' 7 6".#'C
""$
Solution
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""%
&earning Chec)
Hi@@a is ba)ed at 611'/. What is that in 'C*
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""5
Solution
Hi@@a is ba)ed at 611'/. What is that in 'C*
! 51'C611 9 5! 7 51'C
".2
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""
&earning Chec)
?n a cold winter day, the temperature falls to
9"1'C. What is that temperature in '/*
"
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""&
Solution
5! 1'/
Solution'/ 7 ".29"1'C! < 5
7 98 < 5
7 1'/
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""8
;el%in Scale?n the ;el%in Scale
"; 7 "'C
# ; is the lowest temperature
# ; 7 9 85'C
; 'C
; 7 'C < 85
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""9
&earning Chec)
What is normal body temperature of 58'C in
)el%ins*
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What is normal body temperature of 58'C in
)el%ins*
! 5"# ;
; 7 'C < 85
7 58 'C < 857 5"#. ;
"#!
Solution
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"@5 The density of titanium is %.5% g/cm$. What is
the 6o-ume in mi--i-iters of "$ g of titanium? 5
pts.
. #5 A to (e-6in
&. @#&$ AC to (e-6in
8. ! A to (e-6in
9. @#5! A to (e-6in
"!. $&$ (e-6in @ A
"#"
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