t 3 c enir e f i t m t en e hap ci r su C ea M · hap t e r 3 “ S ci en t i f i c M ea su r ... o...
78
Transcript of t 3 c enir e f i t m t en e hap ci r su C ea M · hap t e r 3 “ S ci en t i f i c M ea su r ... o...
Chapte
r 3
�Scie
ntific
Measure
ment�
Se
ctio
n 3
.1
Me
asu
rem
en
ts a
nd
Th
eir
Un
ce
rta
inty
�O
BJE
CT
IVE
S:
�C
on
ve
rt m
easu
rem
en
ts t
o
scie
ntific n
ota
tio
n.
Se
ctio
n 3
.1
Me
asu
rem
en
ts a
nd
Th
eir
Un
ce
rta
inty
�O
BJE
CT
IVE
S:
�D
isting
uis
h a
mo
ng
a
ccu
racy,
pre
cis
ion
, a
nd
e
rro
r o
f a
me
asu
rem
en
t.
Se
ctio
n 3
.1
Me
asu
rem
en
ts a
nd
Th
eir
Un
ce
rta
inty
�O
BJE
CT
IVE
S:
�D
ete
rmin
e t
he
nu
mb
er
of
sig
nific
an
t fig
ure
s in
a
me
asu
rem
en
t a
nd
in
a
ca
lcu
late
d a
nsw
er.
Me
asu
rem
en
ts�
Qu
ali
tati
ve
me
asu
rem
en
ts a
re w
ord
s,
su
ch
a
s h
ea
vy o
r h
ot
�Q
ua
nti
tati
ve
me
asu
rem
en
ts in
vo
lve
n
um
be
rs (
qu
an
titie
s),
an
d d
ep
en
d o
n:
1)
Th
e r
elia
bili
ty o
f th
e m
ea
su
rin
g in
str
um
en
t
2)
the
ca
re w
ith
wh
ich
it
is r
ea
d �
th
is is
de
term
ine
d b
y Y
OU
!
�S
cie
nti
fic
No
tati
on
�C
oe
ffic
ien
t ra
ise
d t
o p
ow
er
of
10
�R
evie
we
d e
arl
ier
this
se
me
ste
r!
Accu
racy,
Pre
cis
ion
, a
nd
Err
or
�It
is n
ece
ssary
to
make g
ood
, re
liable
mea
su
rem
ents
in t
he lab
�A
ccu
racy �
how
clo
se
a
mea
su
rem
ent
is t
o t
he t
rue
valu
e
�P
recis
ion �
ho
w c
lose t
he
mea
su
rem
ents
are
to
each o
the
r (r
epro
ducib
ility
)
Pre
cis
ion
an
d A
ccu
racy
Ne
ith
er
accu
rate
no
r p
recis
e
Pre
cis
e,
bu
t n
ot
accu
rate
Pre
cis
e
AN
D
accu
rate
Accu
racy,
Pre
cis
ion
, a
nd
Err
or
�A
ccepte
d v
alu
e =
the c
orr
ect
valu
e b
ased o
n r
elia
ble
re
fere
nce
s
�E
xp
erim
enta
l valu
e =
the
valu
e m
easure
d in the lab
Accu
racy,
Pre
cis
ion
, a
nd
Err
or
�E
rro
r =
acce
pte
d v
alu
e �
exp
. va
lue
�C
an
be
po
sitiv
e o
r n
eg
ative
�P
erc
en
t e
rro
r =
th
e a
bs
olu
te v
alu
e o
f th
e e
rro
r d
ivid
ed
by t
he
acce
pte
d v
alu
e,
the
n m
ultip
lied
by 1
00
%
| e
rro
r |
acce
pte
d v
alu
ex
10
0%
% e
rro
r =
Wh
y I
s t
he
re U
nce
rta
inty
?� M
ea
su
rem
en
ts a
re p
erf
orm
ed
with
instr
um
en
ts,
an
d n
o in
str
um
en
t ca
n r
ea
d t
o
an
in
fin
ite
nu
mb
er
of
de
cim
al p
lace
s
� Wh
ich
of
the
ba
lan
ce
s s
ho
wn
ha
s t
he
gre
ate
st
un
ce
rta
inty
in
me
asu
rem
en
t?
Sig
nific
an
t F
igu
res in
Me
asu
rem
en
ts
�S
ign
ific
an
t fi
gu
res
in
a
me
asure
men
t in
clu
de a
ll of
the
dig
its t
ha
t are
kn
ow
n,
plu
s o
ne
mo
re d
igit t
ha
t is
estim
ate
d.
�M
easure
men
ts m
ust
be
rep
ort
ed
to t
he
corr
ect
num
be
r of
sig
nific
ant
figu
res.
F
igu
re 3
.5
Sig
nif
ica
nt
Fig
ure
s -
Pa
ge
67
W
hic
h m
ea
su
rem
en
t is
th
e b
es
t?
Wh
at i
s th
e
mea
sure
d v
alu
e?
Wh
at i
s th
e
mea
sure
d v
alu
e?
Wh
at i
s th
e
mea
sure
d v
alu
e?
Ru
les f
or
Co
un
tin
g S
ign
ific
an
t
Fig
ure
s
No
n-z
ero
sN
on-z
ero
s a
lwa
ys c
ou
nt
as
alw
ays c
ou
nt
as
sig
nific
an
t fig
ure
s:
sig
nific
an
t fig
ure
s:
3456
3456
has
has
44 s
ignific
ant figure
ssig
nific
ant figure
s
Ru
les f
or
Co
un
tin
g S
ign
ific
an
t
Fig
ure
s
Zero
sZ
ero
sL
ea
din
g z
ero
es d
o n
ot cou
nt a
s
Lea
din
g z
ero
es d
o n
ot cou
nt a
s
sig
nific
an
t figu
res:
sig
nific
an
t figu
res:
0.0
48
60
.04
86
ha
s h
as
33 s
ign
ific
an
t fig
ure
s s
ign
ific
an
t fig
ure
s
Ru
les f
or
Co
un
tin
g S
ign
ific
an
t
Fig
ure
s
Zero
sZ
ero
sC
ap
tive z
ero
es a
lwa
ys c
oun
t as
Cap
tive z
ero
es a
lwa
ys c
oun
t as
sig
nific
ant fig
ure
s:
sig
nific
ant fig
ure
s:
16.0
716.0
7 h
as
has
44 s
ignific
ant figure
s s
ignific
ant figure
s
Ru
les f
or
Co
un
tin
g S
ign
ific
an
t
Fig
ure
s
Ze
ros
Ze
ros
Tra
iling
ze
ros
Tra
iling
ze
ros a
re s
ign
ific
ant o
nly
are
sig
nific
ant o
nly
if th
e n
um
be
r co
nta
ins a
if th
e n
um
be
r co
nta
ins a
w
ritte
n d
ecim
al po
int:
writte
n d
ecim
al po
int:
9.3
00
9.3
00
has
has
44 s
ign
ific
ant figure
s s
ign
ific
ant figure
s
Ru
les f
or
Co
un
tin
g S
ign
ific
an
t
Fig
ure
s
Tw
o s
pe
cia
l situa
tio
ns
Tw
o s
pe
cia
l situa
tio
ns h
ave a
n
have a
n
un
lim
ite
du
nli
mit
ed
nu
mb
er
of
sig
nific
ant
nu
mb
er
of
sig
nific
ant
figu
res:
figu
res:
1.
1.
Co
un
ted
ite
ms
Co
un
ted
ite
ms
a)
a)
23 p
eo
ple
, or
42
5 th
um
bta
cks
23 p
eo
ple
, or
42
5 th
um
bta
cks
2.
2.
Exactly d
efine
d q
ua
ntities
Exactly d
efine
d q
ua
ntities
b)
b)
60 m
inu
tes =
1 h
ou
r6
0 m
inu
tes =
1 h
ou
r
Sig
Fig
Pra
ctice
#1
Ho
w m
an
y s
ign
ific
an
t fig
ure
s in
th
e f
ollo
win
g?
1.0
07
0 m
�
5 s
ig f
igs
17
.10
kg
�4
sig
fig
s
10
0,8
90
L �
5 s
ig f
igs
3.2
9 x
10
3 s
�3
sig
fig
s
0.0
05
4 c
m �
2 s
ig f
igs
3,2
00
,00
0 �
2 s
ig f
igs
5 d
og
s �
un
lim
ited
T
hese
com
e
from
m
ea
sure
men
ts
This
is a
cou
nte
d v
alu
e
Sig
nific
an
t F
igu
res in
Ca
lcu
latio
ns
�In
ge
ne
ral a
ca
lcu
late
d a
nsw
er
ca
nn
ot
be
mo
re p
recis
e t
ha
n t
he
le
as
t p
rec
ise
me
asu
rem
en
t fr
om
wh
ich
it
wa
s c
alc
ula
ted
.
�E
ve
r h
ea
rd t
ha
t a
ch
ain
is o
nly
as
str
on
g a
s t
he
we
ake
st
link?
�S
om
etim
es,
ca
lcu
late
d v
alu
es n
ee
d t
o
be
ro
un
de
d o
ff.
Ro
un
din
g C
alc
ula
ted A
nsw
ers
�R
ou
nd
ing
�D
ecid
e h
ow
man
y s
ign
ific
an
t figu
res
are
nee
de
d (
mo
re o
n t
his
ve
ry s
oon
)
�R
ou
nd
to t
hat
man
y d
igits,
cou
ntin
g
fro
m t
he le
ft
�Is
the
ne
xt
dig
it less t
han
5?
D
rop it.
�N
ext
dig
it 5
or
gre
ate
r?
Incre
ase
by 1
- P
ag
e 6
9
Be s
ure
to
an
sw
er
the
qu
esti
on
co
mp
lete
ly!
Ro
un
din
g C
alc
ula
ted A
nsw
ers
�A
dditio
n a
nd S
ub
tra
ctio
n
�T
he
an
sw
er
sh
ou
ld b
e
rou
nd
ed
to
th
e s
am
e n
um
be
r o
f d
ec
ima
l p
lac
es
as t
he
le
ast
nu
mb
er
of
de
cim
al
pla
ce
s in
th
e p
rob
lem
.
- P
ag
e 7
0
Ro
un
din
g C
alc
ula
ted A
nsw
ers
�M
ultip
lica
tio
n a
nd
Div
isio
n
�R
ou
nd
th
e a
nsw
er
to t
he
sa
me
nu
mb
er
of
sig
nif
ica
nt
fig
ure
s a
s t
he
le
ast
nu
mb
er
of
sig
nific
an
t fig
ure
s in
th
e
pro
ble
m.
- P
ag
e 7
1
Sig
Fig
Pra
ctice
#2
3.2
4 m
x 7
.0 m
Calculation
Calculato
r sa
ys:
Ans
wer
22
.68
m2
23
m2
100
.0 g
÷ 2
3.7
cm
34.2
194
09
28
3 g
/cm
34
.22
g/c
m3
0.0
2 c
m x
2.3
71
cm0
.04
74
2 c
m2
0.0
5 c
m2
710
m ÷
3.0
s2
36
.66
66
66
7 m
/s2
40
m/s
1818
.2 lb x
3.2
3 f
t5
87
2.7
86
lb·f
t5
87
0 lb·f
t
1.0
30
g x
2.8
7 m
L2
.95
61
g/m
L2
.96
g/m
L
Sig
Fig
Pra
ctice
#3
3.2
4 m
+ 7
.0 m
Calculation
Calculato
r sa
ys:
Ans
wer
10.2
4 m
10.2
m
100
.0 g
- 2
3.7
3 g
76
.27
g7
6.3
g
0.0
2 c
m +
2.3
71
cm2
.39
1 cm
2.3
9 c
m
713
.1 L
- 3
.87
2 L
70
9.2
28
L7
09
.2 L
1818
.2 lb +
3.3
7 lb
182
1.5
7 lb
182
1.6
lb
2.0
30
mL -
1.8
70
mL
0.1
6 m
L0
.16
0 m
L
*No
te t
he z
ero
tha
t ha
s b
een
ad
de
d.
Se
ctio
n 3
.3
Th
e I
nte
rna
tio
na
l S
yste
m o
f
Un
its
�O
BJE
CT
IVE
S:
�L
ist
SI
un
its o
f m
ea
su
rem
en
t a
nd
co
mm
on
SI p
refixes.
Se
ctio
n 3
.3
Th
e I
nte
rna
tio
na
l S
yste
m o
f
Un
its
�O
BJE
CT
IVE
S:
�D
isting
uis
h b
etw
ee
n t
he
m
as
s a
nd
weig
ht
of
an
ob
ject.
Se
ctio
n 3
.3
Th
e I
nte
rna
tio
na
l S
yste
m o
f
Un
its
�O
BJE
CT
IVE
S:
�C
on
ve
rt b
etw
ee
n t
he
C
els
ius a
nd
Ke
lvin
te
mp
era
ture
sca
les.
Inte
rna
tio
na
l S
yste
m o
f U
nits
�M
ea
su
rem
en
ts d
ep
en
d u
po
n
un
its t
ha
t se
rve
as r
efe
ren
ce
sta
nd
ard
s
�T
he
sta
nd
ard
s o
f m
ea
su
rem
en
t u
se
d in
scie
nce
are
th
ose
of
the
M
etr
ic S
yste
m
Inte
rnatio
na
l S
yste
m o
f U
nits
�M
etr
ic s
yste
m is n
ow
re
vis
ed
and
na
me
d a
s t
he
Inte
rna
tio
na
l S
yste
m
of
Un
its (
SI)
, as o
f 19
60
�It
has s
imp
licity,
and
is b
ased
on
10
or
mu
ltip
les o
f 10
�7 b
ase u
nit
s,
bu
t on
ly fiv
e
com
mo
nly
used
in c
he
mis
try: m
ete
r,
kilo
gra
m, ke
lvin
, se
con
d, a
nd
mo
le.
Th
e F
und
am
en
tal S
I U
nits
(L
e S
ys
tèm
e In
tern
ati
on
al, S
I)
Ph
ysi
ca
l Q
ua
nti
tyN
am
eA
bb
rev
iati
on
Len
gth
Mete
rm
Mass
Kil
og
ram
kg
Tem
pera
ture
Kelv
inK
Tim
eS
eco
nd
s
Am
ou
nt
of
sub
stan
ce
Mo
lem
ol
No
t c
om
mo
nly
us
ed
in
ch
em
istr
y:
Lu
min
ou
s in
ten
sity
Can
dela
cd
Ele
ctr
ic c
urr
en
tA
mp
ere
A
Na
ture
of
Me
asu
rem
en
ts
� �P
art
1 �
P
art
1 �
nu
mb
er
nu
mb
er
�P
art
2 -
P
art
2 -
sca
le (
un
it)
sca
le (
un
it)
�E
xam
ple
s:
Exam
ple
s: �
20
20
gra
ms
gra
ms
�6
.63 x
10
6.6
3 x
10
-34-34 J
oule
seco
nd
s J
oule
seco
nd
s
Me
as
ure
me
nt
- q
uan
tita
tiv
e o
bse
rva
tio
n
M
eas
ure
me
nt
- q
uan
tita
tiv
e o
bse
rva
tio
n
c
on
sis
tin
g o
f c
on
sis
tin
g o
f 2
pa
rts
2 p
art
s::
Inte
rna
tio
na
l S
yste
m o
f U
nits
�S
om
etim
es, non
-SI u
nits a
re u
se
d
�L
iter,
Cels
ius, ca
lorie
�S
om
e a
re d
eri
ve
d u
nits
�T
he
y a
re m
ad
e b
y jo
inin
g o
the
r un
its
�S
pe
ed
= m
iles/h
ou
r (d
ista
nce
/tim
e)
�D
en
sity =
gra
ms/m
L (
ma
ss/v
olu
me)
Len
gth
�In
SI,
th
e b
asic
un
it o
f le
ng
th is
the
me
ter
(m)
�L
en
gth
is t
he
dis
tan
ce
b
etw
ee
n t
wo
ob
jects
�
me
asu
red
with
ru
ler
�W
e m
ake
use
of
pre
fixe
s f
or
un
its la
rge
r o
r sm
alle
r
SI
Pre
fix
es
� P
ag
e 7
4
Co
mm
on
to
Ch
em
istr
yP
refi
xU
nit
A
bb
rev
iati
on
Me
an
ing
Ex
po
ne
nt
Kilo
-k
thou
sand
10
3
Deci-
dtenth
10
-1
Centi-
chu
ndredth
10
-2
Mill
i-m
thou
sand
th10
-3
Mic
ro-
�million
th10
-6
Na
no-
nbil
lionth
10
-9
Vo
lum
e�
Th
e s
pa
ce
occup
ied
by a
ny s
am
ple
of
matt
er.
�C
alc
ula
ted f
or
a s
olid
by m
ultip
lyin
g
the len
gth
x w
idth
x h
eig
ht ;
thu
s
de
rive
d f
rom
units o
f le
ng
th.
�S
I un
it =
cu
bic
mete
r (m
3 )�
Every
day u
nit =
Liter
(L),
wh
ich
is
no
n-S
I.
(N
ote
: 1
mL
= 1
cm
3 )
De
vic
es f
or
Me
asu
rin
g L
iqu
id
Vo
lum
e
�G
raduate
d c
ylin
ders
�P
ipets
�B
ure
ts
�V
olu
metr
ic F
lasks
�S
yringes
Th
e V
olu
me
Ch
an
ge
s!
�V
olu
mes o
f a
so
lid, liq
uid
, o
r ga
s
will
gen
era
lly incre
ase w
ith
tem
pera
ture
�M
uch
more
pro
min
en
t fo
r G
AS
ES
�T
he
refo
re, m
easuri
ng
in
str
um
ents
are
calib
rate
d fo
r a
spe
cific
tem
pera
ture
, u
sua
lly 2
0
o C, w
hic
h is a
bou
t ro
om
te
mp
era
ture
Un
its o
f M
ass
�M
ass
is a
me
asu
re o
f th
e
qu
an
tity
of
ma
tte
r p
rese
nt
�W
eig
ht
is a
fo
rce
th
at
me
asu
res t
he
pu
ll b
y g
ravity-
it
ch
an
ge
s w
ith
lo
ca
tio
n
�M
ass is c
on
sta
nt ,
re
ga
rdle
ss o
f lo
ca
tio
n
Wo
rkin
g w
ith
Ma
ss
�T
he S
I unit o
f m
ass is the
kilo
gra
m (
kg
), e
ven though a
m
ore
convenie
nt every
day
unit is the g
ram
�M
easuring instr
um
ent is
the
bala
nce s
cale
Units o
f T
em
pe
ratu
re�
Tem
pe
ratu
re is a
mea
su
re o
f ho
w
hot
or
co
ld a
n o
bje
ct
is.
�H
eat
moves f
rom
th
e o
bje
ct
at
the
h
igh
er
tem
pe
ratu
re t
o t
he o
bje
ct
at
the
lo
wer
tem
pe
ratu
re.
�W
e u
se
tw
o u
nits o
f te
mp
era
ture
:�
Cels
ius �
nam
ed a
fte
r A
nde
rs C
els
ius
�K
elv
in �
na
med
after
Lo
rd K
elv
in
(Mea
su
red
wit
h
a t
herm
om
ete
r.)
- P
ag
e 7
8
Un
its o
f E
ne
rgy
�C
onvers
ions b
etw
een joule
s
and c
alo
ries c
an b
e c
arr
ied
out by u
sin
g the follo
win
g
rela
tionship
:
1 c
al =
4.1
84 J
Se
ction
3.3
Co
nve
rsio
n P
rob
lem
s
�O
BJE
CT
IVE
:
�C
on
str
uct
co
nve
rsio
n f
acto
rs
fro
m e
qu
iva
len
t m
ea
su
rem
en
ts.
Se
ction
3.3
Co
nve
rsio
n P
rob
lem
s
�O
BJE
CT
IVE
:
�A
pp
ly t
he
te
ch
niq
ue
s o
f d
ime
nsio
na
l a
na
lysis
to
a
va
rie
ty o
f co
nve
rsio
n
pro
ble
ms.
Se
ction
3.3
Co
nve
rsio
n P
rob
lem
s
�O
BJE
CT
IVE
:
�S
olv
e p
rob
lem
s b
y b
rea
kin
g
the
so
lutio
n in
to s
tep
s.
Se
ction
3.3
Co
nve
rsio
n P
rob
lem
s
�O
BJE
CT
IVE
:
�C
on
ve
rt c
om
ple
x u
nits,
usin
g
dim
en
sio
na
l a
na
lysis
.
Con
ve
rsio
n f
acto
rs�
A �
ratio
� of
equ
ivale
nt
me
asure
me
nts
�S
tart
with t
wo t
hin
gs t
ha
t are
the
sa
me
:
one
me
ter
is o
ne
hu
nd
red
ce
ntim
ete
rs
� w
rite
it
as a
n e
qua
tio
n
1 m
= 1
00
cm
�W
e c
an
div
ide
on
ea
ch
sid
e o
f th
e
eq
ua
tio
n t
o c
om
e u
p w
ith t
wo w
ays o
f w
ritin
g t
he n
um
be
r �1
�
Co
nv
ersi
on
fac
tors
Co
nv
ersi
on
fac
tors
10
0 c
m1 m
=10
0 c
m10
0 c
m
Co
nv
ersi
on
fac
tors
Co
nv
ersi
on
fac
tors
11 m
=10
0 c
m
Co
nv
ersi
on
fac
tors
Co
nv
ersi
on
fac
tors
11 m
=10
0 c
m
10
0 c
m=
1 m
1 m
1 m
Co
nv
ersi
on
fac
tors
Co
nv
ersi
on
fac
tors
11 m
=10
0 c
m
10
0 c
m=
1 m
1
Co
nve
rsio
n f
acto
rs�
A u
niq
ue
wa
y o
f w
ritin
g t
he
nu
mb
er
1�
In t
he
sa
me
syste
m t
he
y a
re d
efin
ed
q
ua
ntitie
s s
o t
he
y h
ave
an
un
limite
d
nu
mb
er
of
sig
nific
an
t fig
ure
s�
Eq
uiv
ale
nce
sta
tem
en
ts a
lwa
ys h
ave
th
is r
ela
tio
nsh
ip:
b
ig #
sm
all
un
it =
sm
all
# b
ig u
nit
1
00
0 m
m =
1 m
Pra
ctice
by w
ritin
g t
he
tw
o
po
ssib
le c
on
ve
rsio
n f
acto
rs f
or
the
fo
llow
ing
:
�B
etw
ee
n k
ilog
ram
s a
nd
g
ram
s�
be
twe
en
fe
et
and
in
ch
es
�u
sin
g 1
.09
6 q
t. =
1.0
0 L
Wh
at
are
th
ey g
oo
d f
or?
�W
e c
an
mu
ltip
ly b
y t
he
nu
mb
er
�on
e�
cre
ative
ly t
o c
ha
ng
e t
he
un
its.
�Q
ue
stio
n:
13
in
ch
es is h
ow
ma
ny
ya
rds?
�W
e k
no
w t
ha
t 3
6 in
ch
es =
1 y
ard
.�
13
in
ch
es
x
1 y
ard
=
36
in
ch
es
Wh
at
are
th
ey g
oo
d f
or?
Wh
at
are
th
ey g
oo
d f
or?
nW
e ca
n m
ult
iply
by
a c
on
ver
sio
n f
acto
r t
o
We
can
mu
ltip
ly b
y a
co
nv
ersi
on
fac
tor
to
chan
ge
the
un
its
.ch
ang
e th
e u
nit
s .
nP
rob
lem
: 1
3 i
nch
es i
s how
man
y y
ards?
Pro
ble
m:
13
in
ches
is
how
man
y y
ards?
nK
now
n:
36
in
ches
= 1
yar
d.
Know
n:
36
in
ches
= 1
yar
d.
n
1 y
ard
= 1
1 y
ard
= 1
36
in
ches
36
in
ches
n1
3 i
nch
es
x
1 y
ard
13
in
ches
x
1 y
ard
==0
.36
yar
ds
0.3
6 y
ards
36 i
nch
es
3
6 i
nch
es
Co
nve
rsio
n f
acto
rs
�C
alle
d c
on
ve
rsio
n f
acto
rs
be
ca
use
th
ey a
llow
us t
o
co
nve
rt u
nits.
�re
ally
ju
st
mu
ltip
lyin
g b
y
on
e,
in a
cre
ative
wa
y.
Dim
en
sio
na
l A
na
lysis
�D
imensio
nal A
naly
sis
pro
vid
es a
n
altern
ative a
ppro
ach to p
roble
m s
olv
ing,
inste
ad o
f w
ith a
n e
quation o
r alg
ebra
.�
A r
ule
r is
12.0
inches long. H
ow
long is
it in c
m? (
1 inch =
2.5
4 c
m)
�H
ow
long is this
in m
ete
rs?
�A
race is 1
0.0
km
long. H
ow
far
is this
in
mile
s, if:
� 1
mile
= 1
76
0 y
ard
s�
1 m
ete
r =
1.0
94
ya
rds
Co
nve
rtin
g B
etw
ee
n U
nits
�P
roble
ms in
whic
h m
ea
sure
men
ts w
ith
o
ne
unit a
re c
onve
rte
d to
an e
quiv
ale
nt
me
asu
rem
ent w
ith a
noth
er
unit a
re
easily
solv
ed
usin
g d
imen
sio
na
l a
na
lysis
�S
am
ple
: E
xp
ress 7
50 d
g in g
ram
s.
�M
any c
om
ple
x p
rob
lem
s a
re b
est
so
lve
d b
y b
reakin
g the
pro
ble
m into
m
ana
ge
ab
le p
art
s.
- P
ag
e 8
6
Se
ctio
n 3
.4
De
nsity
�O
BJE
CT
IVE
S:
�C
alc
ula
te t
he
de
nsity o
f a
m
ate
ria
l fr
om
exp
eri
me
nta
l d
ata
.
Se
ctio
n 3
.4
De
nsity
�O
BJE
CT
IVE
S:
�D
escri
be h
ow
de
nsity
va
rie
s w
ith
te
mp
era
ture
.
Den
sity
�W
hic
h is h
ea
vie
r- a
pou
nd
of le
ad
or
a p
oun
d o
f fe
ath
ers
?�M
ost p
eo
ple
will
answ
er
lea
d, b
ut
the
weig
ht is
exa
ctly th
e s
am
e�T
hey a
re n
orm
ally
thin
kin
g a
bou
t e
qu
al vo
lum
es o
f th
e tw
o�
Th
e r
ela
tion
sh
ip h
ere
betw
een
m
ass a
nd
volu
me is c
alle
d D
en
sity
De
nsity
�T
he
fo
rmu
la f
or
de
nsity is:
m
ass
volu
me
�C
om
mo
n u
nits a
re:
g/m
L,
or
po
ssib
ly g
/cm
3 , (
or
g/L
fo
r ga
s)
�D
en
sity is a
physic
al p
rop
ert
y,
and
do
es n
ot
dep
end
upon
sam
ple
siz
e
Den
sity
=
- P
ag
e 9
0N
ote
tem
pe
ratu
re a
nd
den
sit
y u
nit
s
De
nsity a
nd
Te
mp
era
ture
�W
ha
t ha
pp
en
s to
th
e d
en
sity a
s the
te
mp
era
ture
of a
n o
bje
ct in
cre
ases?
�M
ass r
em
ain
s th
e s
am
e
�M
ost sub
sta
nce
s incre
ase
in v
olu
me
a
s tem
pera
ture
in
cre
ases
�T
hus, density g
enera
lly d
ecre
ases
as t
he t
em
pera
ture
incre
ases
De
nsity a
nd
Wa
ter
�W
ate
r is
an
im
po
rtan
t exce
ption
to
the p
revio
us s
tate
men
t.�
Over
cert
ain
te
mp
era
ture
s,
the
vo
lum
e o
f w
ate
r in
cre
ases a
s t
he
tem
pera
ture
de
cre
ase
s (
Do
you
w
an
t yo
ur
wa
ter
pip
es t
o f
ree
ze
in
th
e w
inte
r?)
�D
oes ice f
loat
in liq
uid
wa
ter?
�W
hy?
- P
ag
e 9
1
- P
ag
e 9
2
