2- Units of Measurement

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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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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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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Water boils "'/ "##'C 585 ;

Water free@es 5'/ #'C 85 ;

"!5

emperature Scales

$nits of emperature between


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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


110/129

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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Documents

2- Units of Measurement