22
Chapter 2 In addition to assisting physicians, registered nurses work to promote patient health and prevent and treat disease. 2.1 – Units of Measurement 2.2 – Measured Numbers and Significant Figures 2.3 – Significant Figures and Calculations 2.4 – Prefixes and Equalities 2.5 – Writing Conversion Factors 2.6 – Problem Solving using Unit Conversion 2.7 – Density Write the names and abbreviations for the metric or SI units for: length, volume, mass, temperature, and time.

2.2 – Measured numbers and significant fiures - chem.usu.eduion.chem.usu.edu/~scheiner/LundellChemistry/lectureslides/ch02... · ... Units of Measurement 2.2 – Measured Numbers

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Ch

apte

r 2

In a

dd

itio

n to

ass

isti

ng

p

hysi

cian

s, r

egis

tere

d

nu

rses

wo

rk to

pro

mo

te

pat

ien

t he

alth

an

d p

reve

nt

and

tre

at d

ise

ase.

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Wri

te th

e n

ame

s an

d a

bb

revi

atio

ns

for

the

me

tric

or

SI u

nit

s fo

r:

len

gth

, vol

um

e, m

ass,

tem

per

atu

re, a

nd

tim

e.

Scie

nti

sts

use

the

met

ric

syst

emo

f me

asur

em

en

t an

d a

m

od

ifie

d v

ers

ion

cal

led

Le

Syst

eme

Inte

rnat

ion

al

d’U

nit

es(S

I u

nit

s) a

s an

off

icia

l sys

tem

use

d th

roug

ho

ut

the

wo

rld

for

unit

s o

f le

ng

th, v

olu

me,

mas

s, te

mp

era

ture

, an

d ti

me.

Len

gth

in th

e m

etr

ic a

nd

SI s

yste

ms

is b

ase

d o

n th

e m

ete

r, w

hic

h is

sli

gh

tly

lon

ge

r th

an a

yar

d.

1 m

= 1

00 c

m1

m =

39.

4 in

1 m

= 1

.09

yd2.

54 c

m =

1 in

Vo

lum

e is

the

sp

ace

occ

upie

d b

y a

sub

stan

ce.

Met

ric

un

it: m

3

SI u

nit

: lit

er

1 L

= 1

000

mL

1 L

= 1

.06

qt

946

mL

= 1

qt

Th

e m

ass

of a

n o

bje

ct is

a m

eas

ure

of

the

qua

nti

ty o

f mat

eri

al it

co

nta

ins.

1

kg

=

100

0 g

1 k

g

= 2

.20

lb45

4 g

= 1

lb

Met

ric

un

it: g

ram

s (g

)SI

un

it: k

ilog

ram

s (k

g)

On

an

ele

ctro

nic

bal

ance

, th

e

dig

ital

re

ado

ut g

ive

s th

e m

ass

of a

nic

kel,

wh

ich

is 5

.01

g.

Tem

pe

ratu

re te

lls

us h

ow h

ot o

r co

ld

som

eth

ing

is.

Met

ric

syst

em: C

elsi

us

(°C

)SI

sys

tem

: Kel

vin

(K)

Wat

er

fre

eze

s at

32°

F, o

r 0°

C, o

r 27

3.15

K

Th

e K

elv

in s

cale

for

tem

pe

ratu

re b

eg

ins

at th

e lo

we

st p

oss

ible

tem

pe

ratu

re, 0

K

Tim

e is

me

asur

ed

in u

nit

s su

ch a

s:Ye

ars

(yr)

Day

s H

our

s (h

)M

inut

es

(min

)Se

con

ds

(s)

Th

e S

I an

d m

etr

ic u

nit

for

tim

e is

the

se

con

d (

s).

Wh

at a

re th

e S

I un

its

for

the

foll

owin

g?

A.

Vo

lum

e

B.

Mas

s

C.

Len

gth

D.

Tem

pe

ratu

re

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Ide

nti

fy a

num

be

r as

me

asur

ed

or

exac

t

De

term

ine

the

num

be

r o

f sig

nif

ican

t fig

ure

s in

a m

eas

ure

d

num

be

rs

Mea

sure

d n

um

ber

s: a

re th

e n

umb

ers

ob

tain

ed

wh

en

yo

u m

eas

ure

a q

uan

tity

suc

h a

s yo

ur h

eig

ht,

we

igh

t, o

r te

mp

era

ture

.

Tak

ing

a m

eas

ure

me

nt:

No

tice

the

num

be

rs a

nd

m

ark

s at

the

en

d o

f th

e

ob

ject

.

Estim

ate

the

fin

al d

igit

b

etw

ee

n th

e m

arke

d li

ne

s.

Tak

ing

a m

eas

ure

me

nt:

No

tice

the

num

be

rs a

nd

m

ark

s at

the

en

d o

f th

e

ob

ject

.

Estim

ate

the

fin

al d

igit

b

etw

ee

n th

e m

arke

d li

ne

s.

Sig

nif

ican

t fig

ure

s:th

e n

umb

er

of d

igit

s in

a m

eas

ure

d n

umb

er

incl

udin

g th

e e

stim

ate

d d

igit

.43

.026

g

0.00

2650

m

1044

000

L

1044

000

LW

he

n o

ne

or

mo

re z

ero

s at

the

en

d o

f a

larg

e n

umb

er

are

sig

nif

ican

t, us

e

scie

nti

fic

no

tati

on

.In

our

bo

ok

, th

ere

may

be

a d

eci

mal

at

the

en

d o

f a n

umb

er

if th

e z

ero

s ar

e

sig

nif

ican

t.

0.00

04 s

Zero

s at

the

be

gin

nin

g o

f a d

eci

mal

nu

mb

er

are

use

d a

s p

lace

ho

lde

rs

and

are

not

sig

nif

ican

t.

7.90

x 1

0-7

0090

45.7

00

Exa

ct n

um

ber

s:N

umb

ers

ob

tain

ed

by

coun

tin

g it

em

s3

bun

nie

s$1

4.22

7 co

ins

Num

be

rs o

bta

ine

d b

y us

ing

a d

efi

nit

ion

that

co

mp

are

s tw

o u

nit

s in

th

e s

ame

me

asur

ing

sys

tem

.1

L =

100

0 m

L1

ft=

12

in

Sig

nif

ican

t num

be

rs d

o n

ot a

pp

ly!

Exa

ct n

umb

ers

do

no

t aff

ect

the

num

be

r o

f sig

nif

ican

t fi

gur

es

in a

cal

cula

tio

n (

see

se

ctio

n 2

.3)

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Ad

just

cal

cula

ted

num

be

rs to

giv

e th

e c

orr

ect

num

be

r o

f si

gn

ific

ant f

igur

es

If th

e fi

rst d

igit

to b

e d

rop

pe

d is

4 o

r le

ss, r

oun

d d

own

3.4

If th

e fi

rst d

igit

to b

e d

rop

pe

d is

5 o

r m

ore,

roun

d u

p3.

6

In m

ulti

pli

cati

on

an

d d

ivis

ion

, th

e fi

nal

an

swe

r is

wri

tte

n s

o th

at it

has

th

e s

ame

num

be

r o

f sig

nif

ican

t fig

ure

(SF

s) a

s th

e m

eas

ure

me

nt w

ith

th

e fe

we

st S

Fs.

7.2

* 1.

33

(2.0

75 *

0.5

85)

8.42

In a

dd

itio

n a

nd

sub

trac

tio

n, t

he

fin

al a

nsw

er

is w

ritt

en

so

that

it h

a th

e

sam

e n

umb

er

of d

eci

mal

pla

ces

as th

e m

eas

ure

me

nt h

avin

g th

e

few

est

de

cim

al p

lace

s.

2.04

5+

34.

110

4.45

0.

838

+ 4

6

25.0

÷5.

0 =

5

(27.1+2.33) 2.112

In a

dd

itio

n/s

ubtr

acti

on

AN

D d

ivis

ion

/mul

tip

lica

tio

n a

re p

rese

nt,

foll

ow o

rde

r o

f op

era

tio

ns.

Pare

nth

ese

s fi

rst –

foll

ow r

ule

s p

ert

ain

ing

to th

at c

alcu

lati

on

.M

ake

a n

ote

of “

corr

ect

SFs

” b

ut k

ee

p th

e e

nti

re n

umb

er

for

use

in fi

nal

ca

lcul

atio

n.

Perf

orm

div

isio

n/m

ulti

pli

cati

on

–fo

llow

tho

se r

ule

s us

ing

the

“cor

rect

” nu

mb

er fr

om th

e fir

st s

tep

(16.

22 +

7.1

33)

* 0.

661

Mu

ltip

lica

tion

/Div

isio

n –

few

est

num

be

r o

f SFs

in o

rig

inal

num

be

rs

= S

Fs in

an

swe

r

Add

itio

n/S

ub

trac

tion

–fe

we

st d

eci

mal

pla

ce in

ori

gin

al n

umb

ers

=

num

be

r o

f de

cim

al p

lace

s in

an

swe

r

Mu

ltip

lica

tion

/Div

isio

n A

ND

Add

itio

n/S

ub

trac

tion

Fo

llow

ord

er

of o

pe

rati

on

s (o

r p

are

nth

ese

s)A

pp

ly r

ule

for

op

era

tio

n d

on

e in

par

en

the

ses

Use

full

num

be

r o

n c

alcu

lato

r in

nex

t cal

cula

tio

n

Do

fin

al c

alcu

lati

on

Ap

ply

rul

e fo

r fi

nal

op

era

tio

n.

11.1

1 -

2.5

-7.

000

= 1

.610

0000

00

72.1

1 ÷

1.1

= 6

5.55

4545

45

(14.

1 +

21.

12)

* 5.

00 =

176

.100

0000

(1.5+73) 2.14

=34.8130

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Use

num

eri

cal v

alue

s as

pre

fixe

s to

wri

te a

me

tric

eq

uali

ty.

A s

pe

cial

feat

ure

of t

he

SI a

nd

me

tric

sys

tem

s is

that

a p

refi

x m

ay b

e p

lace

din

fro

nt o

f any

un

it to

incr

eas

e o

r d

ecr

eas

e it

s si

ze b

y so

me

fa

cto

r o

f te

n.

For

exam

ple

, th

e p

refi

xes

mill

ian

d m

icro

are

use

d to

mak

e s

mal

ler

unit

s.

mil

lig

ram

(m

g)

mic

rog

ram

g o

r m

cg)

Pre

fixe

s ca

n b

e a

pp

lie

d to

gra

ms,

m

ete

rs, l

ite

rs, a

nd

mo

re

Pre

fixe

s ca

n b

e a

pp

lie

d to

gra

ms,

m

ete

rs, l

ite

rs, a

nd

mo

re

Op

hth

alm

olo

gis

t me

asur

e th

e d

iam

ete

r o

f th

e e

ye’s

re

tin

a in

ce

nti

me

ters

(cm

), w

hil

e a

sur

ge

on

me

asur

e th

e le

ng

th o

f a

ne

rve

in m

illi

me

ters

(m

m).

Eac

h o

f th

e fo

llow

ing

eq

ual

itie

sd

esc

rib

es

the

sam

e le

ng

th

in a

dif

fere

nt u

nit

:1

m =

10

dm

1 m

= 1

00 c

m

1 m

= 1

000

mm

Eq

ual

itie

s: c

om

par

iso

ns

that

sh

ow

the

re

lati

on

ship

be

twe

en

two

un

its.

Wh

en

yo

u vi

sit t

he

do

cto

r, h

e o

r sh

e r

eco

rds

your

mas

s in

k

ilo

gra

ms

(kg

) an

d la

bo

rato

ry r

esu

lts

oft

en

in m

icro

gra

ms

(μg

or

mcg

).

1000

g =

1 k

g

1 g

=

100

0 m

g

1 g

=

100

cg

Th

e c

ub

ic c

enti

met

er

(ab

bre

viat

ed

as

cm3

or

cc)

is th

e

volu

me

of a

cub

e w

ho

se

dim

en

sio

ns

are

1 c

m o

n e

ach

si

de.

A c

ubic

ce

nti

me

ter

has

the

sam

e

volu

me

as

a m

illi

lite

r, an

d th

e

unit

s ar

e o

fte

n u

sed

in

terc

han

ge

ably

.

1 cm

3=

1 c

c =

1 m

L

and

1000

cm

3=

100

0 m

L =

1 L

Ide

nti

fy th

e la

rge

r un

it:

mm

or

cm

Ide

nti

fy th

e la

rge

r un

it:

kil

og

ram

or

cen

tig

ram

Ide

nti

fy th

e la

rge

r un

it:

kL

or μL

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Wri

te a

con

vers

ion

fact

orfo

r tw

o u

nit

s th

at d

esc

rib

e th

e s

ame

qua

nti

ty.

Eq

ual

itie

s: u

se tw

o d

iffe

ren

t un

its

to

de

scri

be

the

sam

e m

eas

ure

d a

mo

unt!

1 m

=

100

0 m

m (

103

mm

)

1 lb

= 1

6 o

z

2.20

lb=

1 k

g

Man

y p

rob

lem

s in

ch

em

istr

y an

d th

e h

eal

th s

cie

nce

s re

qui

re y

ou

to

chan

ge

fro

m o

ne

un

it to

an

oth

er

unit

.

You

do

this

eve

ryd

ay…

For

exam

ple

: sup

po

se y

ou

wo

rke

d 2

ho

urs

on

yo

ur h

om

ewo

rk. A

fr

ien

d a

ske

d h

ow m

any

min

ute

s yo

u w

ork

ed

. Yo

u sa

y “1

20 m

inut

es.

Wh

en

yo

u ex

pre

sse

d 2

hr

as 1

20 m

ins,

yo

u d

id n

ot c

han

ge

the

am

oun

t of t

ime

yo

u sp

en

t stu

dyi

ng

. You

ch

ange

d w

hic

h u

nit

you

use

d to

des

crib

e it

.

Any

eq

uali

ty c

an b

e w

ritt

en

as

frac

tio

ns

call

ed

co

nve

rsio

n fa

ctor

sw

ith

on

e o

f th

e q

uan

titi

es

in th

e

num

era

tor

and

the

oth

er

qua

nti

ty in

the

de

no

min

ato

r.

Eq

uali

ty:

1 h

our

= 6

0 m

inut

es

Eq

uali

ty:

100

cm =

1 m

Be

sur

e to

incl

ude

un

its!

Tw

o c

onv

ers

ion

fac

tors

are

al

way

s p

oss

ible

for

any

eq

uali

ty.

Th

e n

umb

ers

in:

•an

y e

qua

lity

bet

wee

n tw

o m

etri

c u

nit

s O

R

bet

wee

n tw

o U.

S. s

yste

m u

nit

s ar

e o

bta

ine

d b

y d

efi

nit

ion

an

d a

re, t

he

refo

re, e

xact

num

be

rs.

•a

def

init

ion

are

exa

ct a

nd

are

no

t use

d to

d

ete

rmin

e s

ign

ific

ant f

igur

es.

•an

eq

uali

ty b

etw

een

met

ric

and

U.S

. un

its

con

tain

on

e n

umb

er

ob

tain

ed

by

me

asur

em

en

t an

d c

oun

t tow

ard

the

sig

nif

ican

t fig

ure

s.

Exc

epti

on:T

he

eq

uali

ty 1

in. =

2.5

4 cm

has

be

en

d

efi

ne

d a

s an

exa

ct r

ela

tio

nsh

ip. T

he

refo

re, 2

.54

is

an e

xact

num

be

r.

Wri

te th

e c

onv

ers

ion

fact

ors

fro

m th

e e

qua

liti

es:

lite

rs a

nd

mil

lili

ters

me

ters

an

d in

che

s (1

m =

39.

4 in

)

me

ters

an

d k

ilo

me

ters

An

equa

lity

may

als

o b

e st

ated

with

in a

pro

blem

that

ap

plie

s on

ly to

that

pro

blem

.

Th

e c

ar w

as tr

ave

lin

g a

t a s

pe

ed

of 8

5 k

m/h

.

On

e ta

ble

t co

nta

ins

500

mg

of v

itam

in C

.

Equa

litie

s st

ated

with

in d

osag

e p

rob

lem

s fo

r m

edic

atio

n ca

n al

so b

e w

ritte

n as

con

vers

ion

fact

ors.

Ke

flex

(C

ep

hal

exin

), a

n a

nti

bio

tic

use

d fo

r re

spir

ato

ry a

nd

ear

infe

ctio

ns,

is a

vail

able

in 2

50-m

g

cap

sule

s.

A p

erc

en

tag

e (

%)

is w

ritt

en

as

a co

nve

rsio

n fa

cto

r b

y ch

oo

sin

g a

un

it

and

exp

ress

ing

the

num

eri

cal r

ela

tio

nsh

ip o

f th

e p

arts

of t

his

un

it to

100

p

arts

of t

he

wh

ole

.

A p

ers

on

mig

ht h

ave

18%

bo

dy

fat b

y m

ass.

To in

dic

ate

ve

ry s

mal

l rat

ios,

we

use

par

ts p

er

mil

lio

n (

pp

m)

and

par

ts p

er

bil

lio

n

(pp

b).

Wri

te th

e e

qua

lity

an

d it

s co

rre

spo

nd

ing

co

nve

rsio

n fa

cto

rs.

Salm

on

co

nta

ins

1.9%

om

eg

a-3

fatt

y ac

ids

by

mas

s.

Wri

te th

e e

qua

lity

an

d it

s co

rre

spo

nd

ing

co

nve

rsio

n fa

cto

rs.

Me

ters

an

d c

en

tim

ete

rs (

len

gth

)

Wri

te th

e e

qua

lity

an

d it

s co

rre

spo

nd

ing

co

nve

rsio

n fa

cto

rs.

Jew

elr

y th

at c

on

tain

s 18

% g

old

(p

erc

en

tag

e)

Wri

te th

e e

qua

lity

an

d it

s co

rre

spo

nd

ing

co

nve

rsio

n fa

cto

rs.

On

e g

allo

n o

f gas

is $

3.40

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Use

co

nve

rsio

n fa

cto

rs to

ch

ang

e fr

om

on

e u

nit

to a

no

the

r.

Th

e p

roce

ss o

f pro

ble

m s

olv

ing

in c

he

mis

try

oft

en

re

qui

res

on

e o

r m

ore

co

nve

rsio

n fa

cto

rs to

ch

ang

e a

giv

en

un

it to

the

n

ee

de

d u

nit

.

Pro

ble

m s

olv

ing

in c

he

mis

try

req

uire

s:

Ste

p 1

:Sta

teth

eg

ive

nan

dn

ee

de

dq

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e g

ive

n u

nit

to th

e n

ee

de

d u

nit

.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel u

nit

s an

d c

alcu

late

the

an

swe

r.

If a

pe

rso

n w

eig

hts

164

lb, w

hat

is th

e b

od

y m

ass

in k

ilo

gra

ms?

(1

kg

= 2

.20

lb)

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

Ara

ttle

snak

eis

2.44

mlo

ng

.How

man

yce

nti

me

ters

lon

gis

the

snak

e?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

Th

e D

aily

Val

ue (

DV

) fo

r p

ho

sph

oru

s is

800

mg

. How

man

y g

ram

s o

f ph

osp

ho

rus

is th

at?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.T

he

“tr

ain

trac

ks”

me

tho

d o

f wri

tin

g c

an

he

lp k

ee

p p

rob

lem

so

lvin

g n

eat

.

Tw

oo

rm

ore

conv

ers

ion

fact

ors

are

oft

en

ne

ed

ed

to

com

ple

te th

e c

han

ge

of u

nit

s.

Inse

ttin

gup

the

sep

rob

lem

s,o

ne

fact

or

foll

ows

the

o

the

r.

Eac

hfa

cto

ris

arra

ng

ed

toca

nce

lth

ep

roce

ed

ing

unit

unti

lth

e n

ee

de

d u

nit

is o

bta

ine

d.

324ℎ 1

60 1ℎ60 1

=259200

How

man

y m

inut

es

are

in 1

.4 d

ays?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

A d

oct

or

pre

scri

be

d a

do

sag

e o

f 0.1

50 m

g o

f Syn

thro

id. I

f tab

lets

co

nta

in 7

5μg

of

Syn

thro

id, h

ow m

any

tab

lets

are

re

qui

red

?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

If y

our

pac

e o

n a

tre

adm

ill i

s 65

me

ters

pe

r m

inut

e, h

ow m

any

min

ute

s w

ill i

t tak

e y

ou

to w

alk

7.5

kil

om

ete

rs?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity

Cal

cula

te th

e d

en

sity

of a

sub

stan

ce; u

se th

e d

en

sity

to c

alcu

late

the

mas

s o

r vo

lum

e o

f a s

ubst

ance

.

Ob

ject

s th

at s

ink

in

wat

er

are

mo

re

de

nse

than

wat

er;

o

bje

cts

that

flo

at

are

less

de

nse

.

Den

sity

co

mp

are

s th

e m

ass

of a

n o

bje

ct to

its

volu

me.

Wh

enyo

un

g,b

one

gro

ws

fast

erth

anit

deg

ener

ates

……

bu

t as

we

age,

gro

wth

slo

ws,

wh

ich

ca

n le

ad to

loss

of b

one

den

sity

.

To p

reve

nt o

steo

por

osis

, b

ones

nee

d c

alci

um

an

d v

itam

in D

. Als

o, i

ncr

easi

ng

mu

scle

st

ren

gth

incr

ease

s b

one

stre

ng

th.

Joh

n to

ok

2.0

teas

po

on

s (t

sp)

of c

oug

h s

yrup

. If t

he

syr

up h

ad a

de

nsi

ty o

f 1.2

0 g

/mL

and

the

re is

5.0

mL

in 1

tsp

, wh

at w

as th

e m

ass,

in g

ram

s, o

f th

e c

oug

h s

yrup

?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

An

un

kn

own

liq

uid

has

a d

en

sity

of 1

.32

g/m

L.W

hat

is th

e v

olu

me

(m

L) o

f a 1

4.7

g

sam

ple

of t

he

liq

uid

?

Ste

p 1

: Sta

te th

e g

ive

n a

nd

n

ee

de

d q

uan

titi

es

(un

its)

.

Ste

p 2

: Wri

te a

pla

n to

co

nve

rt th

e

giv

en

un

it to

the

ne

ed

ed

un

it.

Ste

p 3

: Sta

te th

e e

qua

liti

es

and

co

nve

rsio

n f

acto

rs

Ste

p 4

: Se

t up

the

pro

ble

m to

can

cel

unit

s an

d c

alcu

late

the

an

swe

r.

2.1

–U

nit

s o

f Me

asur

em

en

t

2.2

–M

eas

ure

d N

umb

ers

an

d S

ign

ific

ant F

igur

es

2.3

–Si

gn

ific

ant F

igur

es

and

Cal

cula

tio

ns

2.4

–P

refi

xes

and

Eq

uali

tie

s

2.5

–W

riti

ng

Co

nve

rsio

n F

acto

rs

2.6

–P

rob

lem

So

lvin

g u

sin

g U

nit

Co

nve

rsio

n

2.7

–D

en

sity