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a really good things to do to
practice it's just more practice because you know how we talk
about repetition repetition repetition for this chemistry
course fires those neurons grows those dendrites case so
%HESITATION that would be really good tool for you to use but now
these are all going to be pieces of the pie raise your head
practice problem sets lecture powerpoints things we do in
class and then you got the homework in learning objectives
so those are all together they make all the pieces of the pie
so if you want a really good grade you need to do all of them
if you focus on just a few of them then your grade will
diminish accordingly K. so the more you use them about all
those pieces the better off we'll be so think about that
there's lots of tools and resources but you do have to
take advantage of those to be able to be successful and if
we're struggling with purchasing a textbook we do have books on
reserve in the library and also in the science tutor center
so if you have an old edition
and you're just like Hey what's the new one saying about this
and you can always go there and read them or if you can't get
your book right now you could at least it's on reserves that you
have access to that okay so I just wanted to let you know
about that as well okay where we left off talking
about six six we practice with those same fix
I guess that was Tuesday the day
so we were all supposed to study with then how much time when we
leave Blackshirt twenty four hours or else it starts to fade
so I hope we studied it now that down now and you remembered
leading zeros what we say about leading zeros
never significant middle zeroes
in all ways ends heroes only if there's a decimal okay
and you remember when we talked about calculating with those
yeah so when you're adding and
subtracting answer needs to be in the least number of
decimals very good multiplying
dividing least number of big big for K. don't mix up
those who think the exact same thing as a decimal knows they
don't make those that now when you're measuring things remember
we talked about that you measure something and you're going to
take all the markings and then what
an estimated digit that occurs
between the marks right okay seen estimated it so it's always
one estimated digit whenever you're measuring anything so
we'll do that and that we can that we practice doing a
calculation because how many times can you around
once
and when you round once at the
you guys got that down so we did
practice example didn't we okay so remember how we did that
alright well let's just put up another one just to kind of
refresh our memory and then I want you to do one
alright so let's do this one
eight point zero two times three point one
minus four eighteen point eight
four princes there times point five five okay and do its
imprint the seas first with multiplication and division so
the rule is least number up then fix okay so how may say
things here three how many say things here
too so why should my answer have two all right so when I put this
in the calculator my get around here
no no so what am I going to do
to indicate to stick the extra mind me
a little box that summer box off
to write but when you type this in your
calculator you're keeping all the numbers are you
they don't round here
but we have to keep track so
this is just a mental way to keep track unless you want to
just memorize that that it's too and remember you can do it that
way too but I think it's easier if we just box it off and you
know how to try to remember alright so the same thing here
minus in the same thing so I got how many sick things here
for how many say things here too
okay so my answer has to have how many too okay so here's the
answer in the calculator someone a box off to don't round you're
not gonna say eight point two you're going to leave it at a
point one six two box office eight point one
here's twenty four point eight six two box office twenty four
now I'm subtracting so what's the rule when I'm subtracting
least number I love decimals okay now
remember we're trying to keep
track so you count what's in the box
Hey cal what's in the box how
many decimals are in this box zero how many decimals are in
this box new ones so my answer should be have how many decimals
least number lease number zero
Kayser racy that you count
what's in the box so it's going to be zero because
that has zero guests most that has won in the least number is
zero some account what's in the box so my answer has to have
zero so you put that in your calculator you get sixteen point
seven okay but I have to have zero decibels right so so that
would round two exactly seventeen
our is that makes sense
okay also now I want you to do
one case we're gonna do this one this is twenty four point six
six eight one times
two point three eight and that's
imprint the seas plus three three two point five
eight K. I want you to do that one
cases in New York on that one
and see if you can figure out what that should be
paying attention to our sigue
sigue rules great thank you
everybody signed the role
missing anyone I can't say I think I'm missing
a couple people surveil signed the role
awesome
looks like we're gonna admit
okay
sorry
are you guys doing around here
good okay
and got it
many
okay so looks like we got it
okay great now check with your neighbors make sure you have the
same answer if you don't understand it explain to each
other wire why not so get together to talk about it
if the people next you have the
same answer check the other direction
turn around somebody
yes
and that was really bad
he looked
okay center near neighbor
sideways are behind you check your answer
and you don't remember their
names introduce yourselves day so make sure you know each
other's names remember I'm from Tuesday
yeah that is already getting in
there and you guys check yeah how about you guys and you guys
Jack alright I think all right they they're very understanding
check to make sure everybody around you understand it
do you have the same answers the
people around you sent them Casey
a CD of the same answer
I can't tell Casey your name
this is Casey Elena case in a way not only
gives us like okay yes so check your answers
they should be exactly the same if they're not why not
yeah
I did go part since last month
if you have let's say this
twenty seven is a resentment and this means you have to go up one
okay so to go out nine thing going
yes because think of it as
twenty nine if you're gonna go up one was twenty nine become
dirty so then that becomes thirty not twenty nine
right
yeah okay
if you're not sure find your lab
partner now some questions what did you guys get for your
answer three nine one point three okay
you have it now yes if you don't find out
why not okay so turned around to find
somebody who's got the three nine one point three and ask
them why is it not that okay so double check
I asked somebody why you don't
have that number if you don't have the numbers everybody have
it they're right understand why
all right we think in
questions
Hey remember the box off your
answer after the first step right
okay
Hey anybody have any questions
and think about that one were good
okay
you got that alright that's so
easy we've done it with one step now we don't multiple steps so
easy well let's bring in more one with the exponential
yeah all right let's do that one
okay let's do this one
let me show you how this works
eighty five point three minus twenty one point four
eight nine divided by
zero point zero five nine okay
so we're gonna do what's in print to cease person you know
that some traction so it's the least number of love
decimals okay so let's do that
one so six three point eight one one
provide a binary right that zero
point zero five nine okay at least number of decimals well
how many decimals does this one have one and the other number
has three so the least number is one so I better box off one
right so it's gonna be six three one point a very good now
divided by zero point five nine so it's the least number of love
or dividing big big all right now when you
count the same fix which ones are you going to
count in this first number all this said fix or in the box
but you're going to use all the numbers in your calculator but
you're going to count the ones in the box K. that's
why we put the boxer help us keep track of that
so we're gonna count the ones in
the box so how many sick because you're in the box three how many
say things here too so my answer should have two six six okay so
when I put this I get one point are one zero eight one point
five four two three seven three and I'm only supposed to have
how many six six two wow how my going to write this showing only
two six six and
all right this is where we use
scientific notation right okay so I got to have this so can I
write just step can I write down eleven
no because one thousand eighty
one is not the same thing is a lot
this is the one thousand eighty
one dollars you're not going to accept eleven are you know so we
would write that one point zero eight one five four two three is
going and put an exponential notation times ten to the what
three
right now I wanna box off my two
six six so this rounds to one point one times ten to the third
and that's how you would put it in
now there's another way you
could have done it you could have said eleven zero zero
now there's no decimal here is
there so if there's no decimal those
zeros don't count and so how many sick fixes this have to do
so this is the other way you could have done it you could
have written it is one one zero zero with no decimals that March
two six six or you could read it like this
usually this one but it's
totally acceptable to do this one with the zero zero it's
totally fine exponential notation rumor prefer but to
find the other way okay that makes sense okay great
so easy what great now you can do that let's just add one other
easy being the rule again
one more
the main thing role
now when you are working with
scientific notation if you are multiplying and
dividing so case and this is scientific notation
if you are multiplying and
dividing multiplying and dividing
the rule is the same that's fine
where it's always been
they just got the same fix as
usual but if you are adding and subtracting
then there's another layer that
we have to add and that is that if you are adding and
subtracting your exponents the axe ponens
must
me the same
that's like saying apples and
apples you can't compare apples and bananas are not the same
thing they're fruit yeah that's true but they're not the same so
what we want is to be exactly the same in order to count the
decibels with think things it doesn't matter
it's only the adding and
subtracting that it does okay so this is our one other additional
little role no problem right listed example of that two eight
two point four times ten to the fifth
minus one point one zero zero
times ten to the third times two point eight nine seven
three okay so these two numbers are going to be in parentheses
so we're gonna subtract these
and multiply it by the two point eight nine seven three prices do
with imprint sees first now we've got exponential scientific
notation don't worry so when we say what has to be
the same exponents alright let's take a
look at the experience I have a five and have a three
are those the same
yeah and they can be the same
okay as questions of how we're
gonna make me say we're going to move the decimal on one of them
okay and I would move the
decimal on this one I am it's a three I gotta move
it over you know until we get to five so I'm gonna do that
someone to move it over one two so this would be to eight two
point four times ten to the fifth minus point zero one one
zero zero times ten to the fifth now they're the same
okay now the reason why I would
want to move this one is because zeros in the front
the think tanks now since is a
good way to go DeRosa friend doesn't mess with anything fixed
I'm fine now if we had trouble trying to go from here to there
were like wow I don't know if I can do that then let's just
break it down one point one zero zero times ten to the third go
ahead and expand this out this is a positive number so that
means going to be big right okay so one two three so this becomes
eleven zero zero now if you want to be five then
don't I need to move this decimal back five
one two three four five so this
becomes zero one one zero zero times ten of them
Casey can step it out like this
if you have trouble thinking are and I got to move it to the left
maybe you might get confusing move it to the right
okay so so break it down
remember if it's positive you want to go to the right maybe a
big number and then whenever we're talking about scientific
notation you move that many decimal places to the left but
you leave it positive because when you expand it back out it's
going to be a big number so positive expanded back out
it's a big number alright so this is how we would
do it now it's the same so yes you can go ahead and put that in
your calculator but your calculator
who will give it to you with an
exponent that's not five you still have to keep it the
same in order to compare apples to apples so I still have to
keep it to the five exponent
so
it would be two eight two point
three eight nine times ten to the fifth now your calculator
it'll give it to you times ten and seven
you can't count does most of its
ten of the seventh why not because what we say
the exponents what
must be the same
so in your calculator give this
to you is a seven is that the same know we gotta
make it be five again it has to be the same this
attractive and they have to be the same to count them they have
to be the same so they all got to be five
now let's count the decimals how
many decimals do I have here one how many dozens do I have
here five
you see that one two three four
five five decimals in this number and over here on this
numbers one so my answer better have how many
one I can count it because it's
the same exponent so here's the one
two eight two point three that's
what I'm boxing off that makes sense
has to be the same exponent and
then I can count decimals no you don't need to do that was
saying things and multiplying and dividing just only when
we're adding and subtracting okay so they're saying the
exponent cannot the decimals now I keep going
now since I multiplying and
dividing what my answer has to be an least number of what
saying fix do I care about exponents now I don't care let's
just can't think fix remember to count them where
and the box how we say things
are in the box for how many sig figs over here
five case of my answer better
have least number which is for now in this case it's totally
fine to change the exponent because Hey we don't care it's
multiplying and dividing and remember how we talked about
scientific notation you just want one that's small
I mean one digit and then the
decimal alright so this would be eight point one this is higher
calculator gives it to a point one eight one six five six times
ten seven that's fine you can have a seven
exponent that's fine sway calculator does a four yeah
great doesn't have to be five in fact we want to be seven
because then there's only one digit right here
okay then we walk softly said
%HESITATION forcing fix right now when we say yeah forcing
things one two three four okay so this would be eight point one
eight one but then we rounded to a point
one eight two times ten to seven and that your final answer that
you would put it okay
so we go so got it all right
excellent so that's the one other additional thing that we
need to do in our calculations with saying things calculation
in multiple steps alright yeah we got that okay well that's the
digit part oh by the way you guys know how to type this in
your calculator right yeah but that in
okay how are we putting that
into our calculator how would you pipe in
%HESITATION something like one point three times tended to how
would you type that in your calculator
how do you do it
one
right very
times
then
carrot to okay that's not a very
good way to do it I know that's a common way to do it we all do
that way but I wouldn't recommend it
yes because the problem with
this is that the calculator will do order of operations so it
will multiply these two and raise the whole thing the power
tunes square unless you put this in parentheses so you either put
that in parentheses all the time which is a lot of numbers that
you put into the calculator or we have what's called the
easy button so if you're looking on your
calculator can you see that II button
okay so what you would do is one
point three and then you hit that eve button
and then say to
no times no ten no carrot do not
put times ten because in that increases all year %HESITATION
answers by a factor so don't do that
this evening does name times can raise to
so you would say one point three
button and then all you do is to
everybody see that on your
calculator there may find your E. button
it may be a different color if
it's a different color you might have to push that second
function different color on your calculator
gazer I can find it
it might be green your Ebert
might be green so you gonna have to push the green button first
writing green letters above
another button nope nope that means square
giving you square in the whole number don't do that
don't do do not do
yeah
there you go and then to no no
no no times you don't put a time do not put time did not put time
this is all you're putting one point three even Latin to know
times no ten no carrot not being like that
okay thereby see that
one point three and then hit the
easy button and to now when you do that your
calculator is gonna know Hey I know what you mean now and they
don't have to keep put them princesses all the time
exactly
yeah but don't do that because
what if it's not a two what if it's a three and then you have
to say times ten so now you start the whole thing and then
if you do that then you have the parentheses around the whole
thing again you have to have parentheses if you do it that
way so look what all you're putting in which is more room
for error what if you forget the parentheses you're you're and
you're done the calculator will give you an
incorrect answer if you put this in parentheses
you can use this but it's gonna take a lot more time and effort
and there's more room for error I would do it this way
okay so I suggest you do it this
way all the time now some of us may not have any button you may
have what's called an E. X. P. button
okay there may have an E. X.
piece some of these calculators happy buttons these time usually
have an easy button okay %HESITATION this kind of
calculator over here has usually it maybe an E. X. P.
button are you have in either case some
of them that look like this have what's called an E. X. P. button
does the same thing case either use the E. or use any acts he
all right so
might be an E. X. P. button
there you go there's any XP
button case so you would use that one and not an easy years
calculator now she does not have any E. on this one instead she's
got XP that means the same thing you do
it the same way that you're using the XP
all right
yeah she doesn't have to do this
thing got that going on lazy alright awesome
okay those numbers
what we want to talk about next
is
well now when we're talking
about measurements did we say Hey there's a number and what
else we put with it the number and we need like
twenty four units case so we gotta have a unit let's talk
about the units now we have different math unit
systems we have
the English system that you guys
know the English system yards and all that stuff %HESITATION
if you're not familiar with the English system like how many
meaning yard or how many quarts in a gallon those kinds of
information pieces will be put in the exam or it's on the back
and periodic table but the metric system you're going to
need to know that we will not give those to you
now there's also the SI system
international what does that mean well that means that look
at all these things look at all these distances for me you know
all these distances which one is the standard one
that's what the SI unit is okay
well let's talk about this metric system you guys familiar
with the metric system yeah okay you know how it works by powers
of ten all right %HESITATION all I'm
gonna say then is memorize these okay
there are more but we don't need
more this is fine you know back in the day gig at and mega and
although used to be unknown but now with computers were like oh
yeah how many gigs is that you know we use that in everyday
vernacular so memorize this I do want to draw your attention to
the way that these are written be very careful I like to
memorize it this way so I put this in here and this is the way
I will do it in class because it's easier for me to remember
like if I say centimeter send to us century where we
think in a hundred so it's easy for me to remember centimeter
one need her is a hundred centimeters
so that's the way I memorize
that okay so let's talk about that
one one meter is a hundred
centimeters that's the way I like to remember that or another
worst right a hundred centimeters I can write one
point zero times ten to the two I can do that right
yeah but look at the other way
now we're saying instead of one meter
instead of one meter
I'm talking about one piece of a
meter which is called a centimeter so one centimeter
is how much of a meter
one one hundred this
okay so one hundred which is
another way of saying point zero zero one which is another saying
one point zero times ten to the minus two meters
now this is where can get really
confusing minus to positive to the customer those numbers are
this isn't centimeters Mrs in meters sometimes we reverse that
a lot so be very careful on which way you've memorized it I
like to do this one and I'll do this one in class if you've done
memorizing this one and just go with this one don't mix and
match do one or the other don't mix
and match makes it harder okay so that's the metric system now
we talked about and %HESITATION these prefixes so meter is the
base unit and then you've got to give meter does centimeter
millimeter but you can also do the same with leaders right
mellow leader sent the leader you do this with gram milligram
center grammar you can change those units Graham means what
mass leader is volume meter me length okay
you know a meter squared
is now in an area how about a
meter cute volume K. this the meters about
like this okay this is a meter cute now the SI unit is a
standard so length is a meter you would think volume would be
leader right but it's not you're like why why can't we do
that okay it's not you think it would be but it's not okay well
let's think about what a meter is amber volume it's the cubic
meter okay it's meter cute that's the
standard for volume and you think well how much is a cubic
meters at a leader no this is only here at
a leader is like this cubic
meters okay so that is not the same
case you don't know how much a leader is almost like a court a
passing around you can take a look at that so one cubic meter
is not a leader what equals that leader one cubic decimeter
okay in that cell leader so
don't be thinking a cubic meters leaders not to keep a decimeter
and another thing you might want to keep in mind this is one
leader another unit we use a lot is one cubic centimeter
for those in nursing one cubic
centimeter equals what one mellow leader
okay we're gonna use this one a
lot so you might want to that mine what's another word for
cubic centimeter those in nursing CCA's sun arcing says
one CC equals one milliliter because CC stands for cubic
centimeter okay so might one remember that
all right that's the metric system you do need to know the
metric system okay
now let's talk about the things
that we measure remember check all the marks
plus one measured estimated digits always talk about the
things that we're gonna manager and one of the things we
measures temperature so you know what happens to the molecules if
we increase the temperature and we add heat temperature is
increasing what's happening to the motion of the particles
they are faster right so the
more you heated up the faster we got writers like Mr he
okay that's the way the motion
goes now let's talk about the three
skills you guys are familiar with these three yeah we've had
all the time water freezes at thirty two balls at two twelve
this is Celsius is kind of like the metric want water freezes at
what zero and boils that hundred nice even number six thirty two
am to twelve years lightens alright so this is a reference
point now has a hundred zero two hundred means a hundred marks
thirty two to two twelve is a hundred eighty marks
so is one degree Celsius the
same as one degree Fahrenheit no it's not
because I got the same amount is
divided into a hundred intervals this is divided into hunter Nady
so one degree is not the same
right and course we know the
temperature references different when we said the more you heat
up an object the faster the motion
goes okay what happens if you start calling it their own what
happens slow it down gets cooler and is there a point where you
just thinking okay what's what's as cold as I could get when that
mean I'm slowing it slowing it down until all motion
stops
okay getting colder than that
right okay all motions dog and what
would that be absolutely is because we can go with it so
we're going to say absolute zero and that's a rather skip that's
the Kelvin scale so the Kelvin scale
absolute zero is as cold as we
can go will zero is because we can go know what is water freeze
at freezes at two seventy three now to be more accurate it would
be two seventy three point one five
okay but for this course we're
gonna just stick with the two seventy three
are we okay with that
all right old and it was not
exactly but we're just going to go with that for this level two
seventy three is where water freezes so water boils at three
seventy three so there are how many marks between two seventy
three three seven three hundred okay so does that mean one
degree Kelvin is equal to one degree Celsius yes it does
and we'll use that later but one
degree Celsius is the same as one degree Kelvin
but the temperature reference
points are those the same
no so be careful now if you want
to convert between zero Calvin and our Celsius and Calvin what
we have to do to convert between Calvin Celsius
add to send me three to which
one yes all right so that's one of
our questions that would be Celsius plus two
seventy three equals Calvin can you guys can do that one
right we're comfortable with that
that formula is provided on the
back of the periodic table for you temperature formulas okay
and then let's talk about the other ones have a going from
Fahrenheit to catch how are Fahrenheit to Celsius
very high the Celsius noon
alright here's our equations now
think about where it came from thirty two why are we talking
about thirty two what temperature does water freeze on
Celsius zero what's the temperature
doesn't freeze at very high thirty two okay there's the
difference right there so we got taken account thirty two what is
behind this thing nine fence wall there were a hundred and
eighty marks and they're a hundred marks
so what's the ratio of a hundred
and eighty two hundred yes or you might see it as one
point eight sometimes you might see the formula B. one point
eight right here what's a hundred eighty to a hundred so
that's where the form is came from again this is going to be
on the back of the periodic table so are we comfortable with
doing temperature conversions yeah alright so you needed you
do need to be able to do temperature conversions
okay well there's another thing
that we measure and let's see if you can tell me
about this one out and starts killing weights go
if you may be familiar with
kilograms asked around %HESITATION leader
that was just curious to see how much a kilogram weighs so this
is one kilogram so if you want to feel the weight of one
kilogram yeah exactly two point two pounds that's how much that
would be so let's talk about another thing that we can
measure all right so if we can do this
with
okay
this is %HESITATION
this is baking soda
now you know this is vinegar
with what happens when we put vinegar and baking soda together
you get that do we get a
reaction okay how do you know that what's
going to happen busy right so fizzing occurs
case if I put this now because you see this thing
that means the gases being released right
okay so that means you know
reactions happening is it can we talk about chemical properties
so when you put baking soda and vinegar together in chemical
property baking soda is it releases a gas if I put golden
vinegar together Mike I get the same thing
no no we went all right so
%HESITATION and if you guys know you guys know what's being
released carbon dioxide so this is the
kind of same thing that happens when you put sea shells in
vinegar and we talked a lot about that alright so
alright so that's producing CO
two all right so with light this
candle right now what you watch the
flame okay so watch the flame
and I'm going to pour this on
top of the flame okay so see what happens
can I pour all this on top of
the line alright here we go
give it a second do is reacting
alright here we go
in
yeah
I went out
I get the poor all that honor
why would I go out
what what it needs oxygen in the
flame need oxygen okay so if there's no oxygen
that means I've smother the flames somehow
how would I smell the fine
with CO two you mean I can pour
CO two there is air and land on the
hand what I can pour gas to another
gas yes you can CO two is heavier they are we should say
not heavier but dancer so by going like this you can't see CO
two but it's in there and so by tilting the bigger what happened
as a CO two poured out landed on the candle and
smothered it so we call that not so much
heavier but we call that density so that's another thing that
we're gonna measures density there's an old riddle that says
which weighs more a ton of bricks
or a ton of cotton
yeah ends on the answer be the
same a ton of bricks weighs the same as a ton of gotten them all
the time but if you're thinking bricks
what you're not thinking about is how much it weighs but you're
thinking about its density yes birds would be more dense so
what is density how do we define density
density is mass over volume very
good okay so density is define
as mass over volume
now we need to remember it's
mass over volume not volume over mass
we always get that makes that
specially on exams start mixing this up case let's think of a
way to remember that density is and I'm gonna draw heart because
we love chemistry chemistry of course we do
some draw hard because we love
and then I'm gonna draw a line
through there and what we have ma'am over me map now
okay so this is what density is
now we need to figure out if I gave you mass I give you volume
you can calculate density right used by those out what if I gave
you density and volume
okay can you sell for mass yeah
and since this is divided by were you going to do to get
volume out of the bottom multiplied on the other side
right so the volume times density is equal to mass alright
now what if you're solving for volume
okay now do we have trouble
figuring out how to arrange that because like
you said it was mass divided by
density will you know if we have trouble let's
separate out first we say volume
times density is mass and if I'm trying to solve for volume then
it is mass divided by density now if you have trouble with
that let's do a little cheat sheet triangle
okay we've seen this before
camera drawn like this so I draw a line across in one down so I'm
gonna put density here density is equal to mass I'm gonna put
mass over Walliams now if I want density I say mass
divided by volume if I want mass these are side by side now so
its density times volume and if I want volume
yes what's on top mana so you
must put mass divided by density okay that's another common
mistake that we make now isn't how do we measure volume
sometimes especially adamant your regular object you're going
to do this in lab so if I have a graduated cylinder
and I have this much volume in
here if I drop a block in here
what's going to happen to the
volume of water it's going to go up how much
does it go up why by the volume of the block right
here's the block so this volume is equal to the volume of the
block so if you're trying to figure
out density can't you just attract those two
volumes and get the volume of the block
and then you wait a blocking you can get density great
by the same token if you have
density and mass
if you got density you have mass
could you predict the volume calculate the volume all right
so if I know the volume of the block and this is the amount of
my solution could I predict
what the new volume should be
yes and how would you do that
you would what measuring the
Manson mass in the density and you would give the density and
measuring the match you would calculate the volume
and then you can predict Hey the
volumes gotta go up this much because that's the volume of the
block that makes sense now when we're
doing this density you have to have it all be the same density
of the block volume of the block not the water it all has to be
about the block mass in the block lawyer the
block density the block it's all going to be about one
if I had density of water it's
gonna be all about the water massive water volume of the
water density the water you can't mix and match units with
that okay alright we'll hear some
different densities units of density or grams per milliliter
if you're talking are cubic
centimeter if we're talking about solid
grams per milliliter for talking
about liquids to the densities now for talk about gas is a
little different it's Greg Gant grams per liter and when we get
in the gas all chapter for use that as grams per leader the
units are going to be a little different so I need to remember
that but we'll do that later okay so let's look at CO two
five zero two
yeah what's the density
one one point nine six how about
air one point two nine which is more
dense carbon dioxide so if an object
is more dense it's gonna sink to the bottom that's why CO two
fall through the air it's going to sink to the bottom
what happens if you put ice cubes in water do they Ice Cube
sinker float they would be asking for ice
cubes in water where they tend to do float right on the floor
to the top yeah okay well let's look at the
density was the density of ice two point nine two what's the
density of water one so which is heavier or more since they were
dense water is more dense so it's going to be at the bottom
right and that's why I schemes but no that's unusual
because normally solids are more
dense than liquids but water is an unusual substance that way
it is the solid is less dense
than the liquid that rare okay usually the solid is more
dense than the liquid okay well let's talk about ice cubes in
apple alcohol you guys know about all the stuff and beer and
wine and all that kind of stuff right now
okay %HESITATION so if you had
apple alcohol pure apple alcohol and I put ice in it
what's going to happen
the ice would sink when it
yes more dense than a half hour
call so if I had ice and water it was thought by but I snap
I'll call it would sink yeah exactly okay so that's something
that we use to dance or some of the calculations that we have
%HESITATION here's two cans of coke
and that same volume
one is thinks one thinks and the
other what's what's
they're in different
they always thought what if
they're the same liquid now what they're both in water
no one is frozen one is not well
that would it's it's interesting because ice when it freezes it
expands so it would be expanding so
we can't expand it same same
temperature they're the same temperature and they're in the
same water what is what is
what about the densities though
was I tell you if this Pepsi is
thinking in a bigger water was that tell you it is more dense
right or dance how about this one less
dense okay well density is mass or volume
so if the volume is the same
and the densities are different
than what has to be different the mass exactly yeah so
actually this is more dense than that one they would weigh
different amounts and rethink and while why is that well the
difference is actually this is diet
so %HESITATION the sugar that's
present increases the density when you take out the sugar is
less dense so they're talking about those white coke and
they're not kidding here why the mass so that's initially
example density all right well we measure
temperature we measure density and we've got all these
measurements and we know how to do stake big calculations was
put that together what if I want to change one unit from another
okay what if I want to change
grams and kilograms and what if I want to change
readers
the centimeters what I want to
do that but I want to change the units because we have to have
the same years we're going to add things together right we
know that apples to apples so I got a convert navy guys familiar
with commercial yeah
we are
on soon okay because you know we
can use this conversion math it dimensional analysis you might
have heard of that term that way science tutor center will do
some dimensional analysis clinics to help you with this
but this is a map that we have to get down
we're gonna use this all the way
through constantly so it really really really really need to
nail down dimensional analysis we can destroy Kiama treat other
more other additional things that we're gonna do with it
so this is our one of our
building blocks it's very important that you nail this
down so a lot of us are familiar with
that we use it what's the purpose the purpose is to
convert one unit to a different unit and that works great
chemistry my done that in physics %HESITATION if you're
cooking in the kitchen mused about this I mean that all the
time when I'm going for the rest being I'm going from teaspoons
of tables Windsor you know cops and I bring out the dimensional
analysis of my daughter's like other
but it works great it works
great yeah sometimes when you're converting milliliter mill
meters to kilometers you sort a move the decimal the wrong way
happens a lot right well if you use this method you won't have
that problem anymore you'll always get it right
that's the neat thing about this is got built in checks for you
so let's talk about this dimensional analysis what is the
mental analysis is the ability to convert between one unit in
another a what are we gonna use we're gonna use what's called a
conversion factor unit any of the other how are we
gonna relate the two together conversion factor
alright so let's talk about
what's the conversion factor you have to be able to generate
these necessary conversion factors well what is it it's a
ratio it's a ratio of one number and
unit to another number unit now conversion factors has to have
the number can we forget the unit
now so we have to have numbers
and units numbers and units now these
conversion factors okay we send their ratio you have to have
numbers in units where does it come from it comes from true
relationships a true and valid relationship what's a true
invalid relationship it's when you eat great things together
they equal each other and there have different units for example
one but equals how many inches
twelve inches right we know that
these are different units but we know this to be this equal
that's a true about a relationship one foot equals
twelve inches give me some more one is
one interesting point five four
centimeters give me another one okay one million one cubic
centimeter very good how many days a week
seven days is one week
okay so you see how we get these
true about relationships it's things you know to be equal and
they have different units these are true about
relationships this is what we used to make a conversion factor
okay so now we have these relationships how we gonna get
conversion factor it's a ratio let's take but manages a ratio
would be one foot divided by twelve inches
but you know what I can do the
other way to put twelve inches
divided by one foot so for every
June that relationship how many conversion factors do you get
tail always to wire right why don't you tell
well one of them converse feet
to inches and the other one does inches to feet so you always
need to all right let's let's write some more conversion
factors how would you write a conversion factor for inches and
centimeters one inch
okay devoid five four
centimeters for uhhuh
all right you see how we got
that was two weeks and days what would it be
I say let's do days in a week
how about how that how that conversion back to be
seven days
divided by one week
for
one week
ride my seven days awesome right
so now you know how to get conversion factors we're gonna
do it though now that we have them with them
we multiply with conversion factors
you multiply and divide so now
you can multiply divide numbers we know how to multiply and
divide numbers but can we really multiply and divide
units
yes what's a centimeter times a
centimeter centimeter squared
what's a centimeter
times a centimeter times a
centimeter colonel centimeters queue what's
a centimeter divided by a centimeter
no unit number one is no yet
they cancel and other words we
say these cancel so when you divide the word you
cancel the units okay so dividing dividing words
dividing our units
saying units dividing the same
units we say we are canceling I canceling out you say
canceling out the units in other words we end up with no units
okay so we can multiply divide
numbers we mulled wine family
all right so that's how we're
gonna do conversion factors now where do we say conversion
factors come from they come from where
a relationship what about the
relationship what was the we need a true relationship and
we divide out the ratio okay that's how we get
conversion factors from true value relationships and you
divide them out and once we get the conversion
factor we multiply with it and that is the Michelin houses
but the cool thing about dementia analysis is that it
helps us get the ride conversions going so let's just
practice that let's take days and weeks
all right let's say we have
%HESITATION fourteen days fourteen days and I want to know
how many weeks is that all right they think how many
weeks is that now I have one unit and I want to change to
another unit so I'm supposed to use what
the conversion factor
okay this conversion factor
needs to relate these two units and it is going to be seven days
in a week and then I'm going to change that to conversion factor
right okay so that's what you do you
had two units you come up with the conversion
factor but the problem is I have
conversion factors which one do I use
who I want to change days two
weeks that means I have to cancel out the days remember the
only way we said we're going to cancel out the words as if we do
what with it divide so I got to use the one that divides by days
yeah it's a son alright says but
that in here so I'm gonna multiply and I was a one week
divided by seven days
okay now these are multiplied by
the fractions and dividing by days of these cancel and I'm
left with weeks so my answer becomes
two weeks what if I use the
other conversion factor this is where you always watch the units
if I said seven days divided by one week wow let's
multiply this out I got days times days what is agony
days square divided by a week
okay well that does not make any
sense does it so this has a built in math and to make sure
you're going in the right direction with your conversions
case of the units must cancel so multiply them together and the
units must cancel so how do we do this we identified a given
unit board that the days come up with them wrote the conversion
factor where the units are canceling that's all there is to
it so let's say you guys can do this one are let's do it
%HESITATION let's try one where we're going from inches to
centimeters okay so we have our two conversion factors so let's
see if you can do this one really quick here
I convert eight point five
inches in two centimeters thanks if you
can figure that out set it up as he got the eight point five
inches you want to change that to centimeters so you know what
unit has to cancel out right which one you want to get rid of
you want to get rid of the inches
so you know which one unit
you're gonna use art yeah as you know which conversion
factor any use we got two conversion factors up there on
the board which one is the right one to
use yeah
yeah we can
and Dr
are we guys doing back here
okay so it looks like we got it
now turn your neighbor and double check your answers
and talk about it
right
twenty two point four all four
yeah
you get the right answer
where we watched our sick things
didn't we room
whatever we do calculations are
we always going to be thinking sick fakes
yeah every single calculation
you do year again account and pay attention to stick this
on every homework problem on
every class problem on every test problem every single one
now there might be a couple
answers on that exam that are the same but they differ in the
number six sixty you know which one to choose right
yeah you got to pay attention to
those six bags watch that dimensional analysis
right it's like this should be
the six weeks here no just now because this is an
exact numbers one that has an infinite number six
things and decibels all right so what did you guys
get a clear answer twenty one point six twenty one
point six one centimeters okay so the unit that you use was
what units on what conversion factor
two point five four centimeters
on top in one inch on the bottom so that
these can can't interest can cancel right okay we can write
it like that but I'm gonna show you another way that I like to
write this especially when we get going with lots of them it's
a little bit easier I start with my unit eight point five inches
my started and then I draw a line
and then I do these hash marks
okay if I had more conversions I
do more hash marks and what I'm gonna do is I'm
going to write in two point five four centimeters
on top and the one inch on the bottom
okay so this so I'm drawing the lines like this if it side by
side that's multiply if its top and bottom is divided okay so
I'm gonna do it this way just because it's faster than Ryan at
times in bold print the seas and all that they gotta remember to
keep the units now how the six was twenty one point six
discount savings are multiplying dividing answer must be least
number I'll say fix how we think there's a point five
earn three three because we have
just right three how many here three
how many here
and that's an exact number isn't
it it's always one inch
it can't be one point eight
inches right one point zero zero zero zero zero zero remember we
talked about has an infinite number six six
so this is an exact count the
number and has an infinite number six six so the least
number would be one three three infinite
what's the least number three
that's why my answer has three six six
okay so when you're doing this
you're not going to pick one sigue sigue are you
now because it has an infinite
number SO three is the least amount so it's three
alright that makes sense
okay superstition more ram such
fun with this one right well we just did one
conversion that was so easy my gosh just one let's add to that
let's do for three three eight
milligrams and I'm gonna change that two kilograms
okay I'll think about that table
that I memorize there's no conversion between milligrams in
kilograms on that table nothing I remember as what milligrams to
what grams and then grams to kilograms then we have that on
the table okay so when you're doing
something like this and you're like I don't know that
conversion factor then you might need multiple conversion factors
and you can always take it to the base unit which in this case
is grams so I'm gonna do that so I'm
gonna go from milligrams and I'm gonna change that to grams and
then change that two kilograms so in this case were doing more
than one conversion factor and when we do that we write what's
called a road map a road map helps us understand what the
units are that we're going to change from one to the other and
every time I had this symbol this means I need a conversion
factor case of every symbol I need a
conversion factor like this so what I'm saying is milligrams
conversion factor to change it to grams no other conversion
factor changes from grams the kilograms
okay so let's set this one up
all right
I got milligrams and I want to
change it to grants so think about that now the
relationship okay so yeah I remember that
relationship one gram is a thousand milligrams
and that's the relationship
now what has what unit listing
units first what what has to go on the bottom
milligrams and you see why we're
going to put that thousand milligrams on the bottom
it has to why does the thousand
milligrams half to go on the bottom
that way they cancel and then
the one gram goes on top okay now that's that when it's done
go again what do I have on top
right brands and what am I
trying to get to all wow what was that
relationship one thousand grams
one kilogram okay so I've got
grams on top where you think I had to put on
the bottom a thousand grams it has to be
grand and then what goes on top
kilogram
case of the unit's cancel
whatever's left that's what your answer comes out to be in so now
let's count six six how many sick fixed I have here for how
many say fix here FNN him for that how many here
in
it is an exact count a number
don't we define a thousand milligrams are in the ground we
didn't say a thousand point two did we know it's exactly a
thousand no more no less we'd say nine or ninety nine point
nine no it's a thousand is exactly is an exact number one
thousand milligrams a grand you see how that's an exact count a
number all right so how many sick fixes
this one half event one kilogram is infinite and a thousand grams
infinite perfect so I've got four infinite infinite infinite
infinite how much I have for him to have four and we can
put this in scientific notation because it's a bigger number
first I should say more decimals
ten to the minus three kilograms right that's a road map and
that's how we do multiple conversions
well let's say I'm let's
practice doing road maps a little bit more so we can get
some ideas of the concept here all right let's say I want to go
from century two seconds
let's go from the century
century the seconds
alright so we don't have a
conversion factor to between between centurion seconds doing
no so are we gonna have to step
it through some units all right so let's talk about
what those units are gonna be all rights and starting off with
century if you were to get if you were
to do your roadmap what would you say century convert to what
years que you know that unit
yeah okay and then your years
now are you going to go to there were not nearly beer
okay
years and months we can do that
okay but now what
the days and months are not
quite there that's not a concern this yeah mum thirty some months
or thirty thirty one maybe I don't want to do months maybe I
want to go weeks instead okay so it's two weeks
there's fifty two weeks a year
and then what days and then what
hours then one
minutes and then what
seconds perfect okay that's one
what's another what can we do another one what if I don't know
the conversion factor between a century and a year maybe I only
know Centrino decade I could do that
sure I can do that and then I
can go decades to what years okay and then I can go to weeks
if we don't take into account
leap year maybe I can go from years right today's good night
and then we can do the same
thing days hours
minutes
second
okay
see how that works
all right well maybe I might do
this I might say century and there might go to decay
and then I might go to years
what am I go back to decades
I go back in years
and then maybe days
and then again hours
minutes
seconds
well maybe this one I know how
many seconds there are in an hour so maybe I don't need to do
that maybe I could go directly from hours to seconds because I
know that conversion factor I could do that so or any one of
these particularly wrong now could I use any one of these
yes that's the thing about these conversions
there's not always an exact one
way to do it some of you might know more conversion factors in
another year round that may look slightly different from someone
else's but the key point is is that you must have true invalid
relationships with each conversion each conversion has
to have a true invalid relationship can't be making up
stuff okay and if so interviews cancel
then you can use any one of them now some of them are directly in
shorter it's like a road map you're
going from here to Dallas can we take different roads to
get there sure some of us might go
directly there others might take the scenic route and some of us
decades two years back to
decades back to you that was my one drive around
walking time he
all right as long as we get
there and the units are correct case so that's the idea of road
maps so write your when you do these big long conversions right
your roadmap out so you can get an idea of where you're going
it'll help you as you step it through now what conversion
factors are we gonna need for dementia analysis don't be going
up different conversion factors don't Google those things
because you're not gonna be able to Google conversion factors on
the exam so what conversion factors can bring about what
conversion factors are we going to need all the conversion
factors that you need for this course
exam homework and everything
else is going to be in the back of your textbook where it says
useful conversion factors and relationships
yeah this is going to be
provided to you on the exam this is all you need
so when you're with your own
problems and you're working on things in your practicing county
here and using these ones don't Google up other ones
Google other ones just use these for those are your conversion
factors okay so that's the only one you're going to need those
conversion factors thank you okay so that's road maps so we
can do simple conversion we can do lengthy conversions do that's
so easy right he's I can do something a little bit
more complex we're gonna do this one and
we're gonna do one with squares in cubes
alright we got this this is so
easy let's convert
three point seven three times
ten to the eight cubic kilometers south
it's cute it means volume right where to convert that to leaders
let's do our road map how would
we do that cubic kilometers any Arab
leaders well how are you going to
convert cubic something to leaders years remember
okay so
we know that cubic decimeter is
a leader okay so I got cubic decimeter here we also can do
cubic centimeters a milliliter could me
and I can I go milliliters to
leaders sure we'll go ahead and go with
cubic decimeter I keep a dozen meters I can
revert to leaders how about kilometers to destiny years
I'm going to do that
waiters and got their meters
could not okay
I can go three meters
now they have to be cute though
now here's where the problem is I don't know the relationship
doing cubic kilometers in cubic leaders but I do know the
relationship is one thou I know racial ship commoners in meters
right one kilometer is a thousand
meters I know that but how would I get the cute one
all I can queue both sides
because is this an equal fine if the question right by December
one side I knew the other so if I keep this anti Cuba this then
Q. remember means not times three
okay just means one kilometer
times one kilometer times one kilometer most by the numbers
you get one month by the letters you get cubic is equal to one
thousand meters times a thousand meters times a thousand
leader so what is that equal one
times ten to the what nine nine
one time said the nine
meters what
can you this
is your true out relationship
this
is what you're going to use to
get that conversion factor okay
that makes sense
right now we got to the other
one meters in destin meters how we can do that one
well you know meters and
estimators what is it one meter ten dozen meters desi decade
things ten decimeter can you get the cube one
yeah how would you do that
Q. both sides
now if you had this true
relationship now can I set up my unit so they
cancel I can can I
you know which one goes on the
bottom don't you yeah okay
I want you to keep derived the
relationship you're going to use for cubic meters cubic decimeter
and I want you to set up this conversion active either
if you're not sure where to go
or how to start check with your neighbor
make sure your units cancel
you have to cancel those units
you know which one goes on the bottom
and you have to have a true
about a relationship so we got one of them
you have to get the other
they're by no the conversion
unit between cubic decimeter isn't leaders
what is it
one cubic decimeter is one
leader case arena that relationship okay
so get that one
you know what units have to go
on the bottom got cubic kilometers on top guess what
goes on the bottom hearing no longer is and you've
got this truth about relationships
so you put that one in
but
but
okay so watch the road map
watcher roadmap you're going from cubicle lawmakers to cubic
meters you got that and then from cubic meters to what
no cubic meters to what
give a dozen years and then you
gotta go again from Cuba gas meters to leaders
okay
right
alright did you put cubicle
honors on top like you to comment on the bottom
okay what's that you're now
relationship when we say one cubicle honor is one times ten
to the nine cubic meters yeah that
that was your we got that
conversion factor okay good now you got to get the
next conversion factor okay
so remember our conversion
factors that we got that conversion
factors now you need the next one
because you're gonna have
give it commented on the bottom
cubic meters on the top so I need another conversion factor
cubic meters I'm going to get that
one meter is ten estimators
%HESITATION
and I know I know sponsored
it's going to be his father
we do not %HESITATION
we have to multiply that price
click over yeah okay
I think you
and then the
the first five
they keep going in
okay so you see how do you know
how we get from here to there right we can't do it
so how do you gonna go here to a
cube I doubt
leaders
it was one hundred
yeah but no because about one
meter is ten dozen meters but we want to keep it
just like we said one kilometers
a thousand meters and we can't do
so one meters ten dozen years
and now we Cuban okay so you see how we did this
one %HESITATION and then we give
this time because we had one kilometer
equals a thousand meters that's
what we started with and then we can do it
and then this is how it looks so
did now you have the same thing so yeah one meter equals ten
deaths meters well that's like what we did
here so now we're going to Cuba
and then you know how to write
out the cubes right to write out the cubes
said that doesn't go there
secure assist meters or
centimeters I guess you can I keep it out
then that's going to be your
next conversion factor yeah
okay
are we doing back here
I can sense every Cuban it get
that other conversion factors right
I return back here
forget or we lost
completely lost in this room
knows what is going to do that under certain conditions
one meter has tennis meters one
meter has on the hunter's centimeters
decimeter is bigger than a
centimeter yes you know she's invention
well we're thinking bigger as in
more of them there's a hundred of them in the meter
I guess it depends on how you
want to look at bigger okay so you got you got that
right and then you gotta put cubic meters to cubic decimeter
perfect that's perfect well then you go to the net you
got this one so this is what the roadmap is
for such as what to do next you did this you did this
now we can do this
so that's what you do next you
do this one next so that's why we use a romance contel it's
because sometimes were so working on the cover and I were
in this is what that's for and then you have to think about
your about a relationship between those two
okay good
all right so keep going when you
got this word right here is what cubic meters so guess what word
you're gonna put right down here yeah
well you know what's this word
meters and decimeter so they
cancel out no that's the wrong one
so this isn't going to work
%HESITATION
what does that word cubic meters
unit is cubic meters so what do you gonna put on the
bottom meters well here's meters cute
she had about meters can you
have to put meters can't the magic you know one times ten
to the three is cubic decimeter you don't want cubic decimeter
did we want cubic meters so which one is the cubic meters
this is the cubic meters so it's one cubic meter is one goes with
the cubic meter one times ten to three goes with a cubic
decimeter we can't just like change that
mix and match it this is one cubic meter so one
cubic meter has to go on the bottom
so right one cubic meter you see
why we have to do that is because the units have to cancel
if you could keep a dozen meters are not going to cancel is not
going to work so then what goes on top this
one times ten to the third cubic decimeter so
Kim don't forget to keep their
okay then go again
you're almost there now you got
to do the leaders you gotta go from cubic decimeter still
leaders so if I have the word cubic decimeter is on top guess
what has gone the bottom we did you know
so what's this word
what is this
so what goes on the bottom
yes
you see that
okay
you didn't hear that
has to be killed
one meter cute didn't survey
added we had to write that conversion factor so we set one
meter is tan Dessa meters than one meter
queue is ten decimeter scheme right
so one cubic meter is equal to
ten times ten times ten cubic decimeter
not that
this is you see how this is
meters queue so you better have meters cute
one meter Q. does not equal tend
estimators one meter cubicles what
thousands
a thousand cubic decimeter
sought ten thousand cubic decimeter you see how you have
to have the true relationship and the units have to match that
has to be cute yeah
you see how the at least have to
match you don't have a choice alright so there's this word
cubic decimeter so guess what has to be there cubic testing is
now you know what the relationship is right
remember that we talked about
one leader is one leader is one cubic
decimeter yeah okay
okay that makes sense good also
it exactly it just takes
practice perfect
all right so then we got the
answer did you guys find the
relationship between cubic meters to cubic decimeter is
right yeah okay you guys got that is looking
right okay you know your units are
canceling right so when we get
what unit is that
leaders
okay we come up with that
I already got it
without locks
makes sense
okay
I'm
you are watching it in your
calculator are you there using the Ian the XP button yeah be
very careful about about that also in your calculator if you
want to if you're inside this is an IBM calculator issues you can
say this time this time this time this the right number down
then you say this time this time this new writer down bottom and
then you divide the do you do that fine
or you know you can put this top
part in parentheses and you can say this time this time this
time this in parentheses divided by you have to put another
parentheses to say this time this time this
okay don't forget the
parentheses okay that's one way let me tell
you another way if you don't want to do
you know the parentheses thing
dividing all top and then for the season marred by for the
seas I like to do it this way I like to say this number
times this number divided by
that number times is number divided by that number times
this number divided by that number just work my way down and
I don't have to do parentheses or write down what those numbers
are so that's an idea okay
questions
all right
okay are we doing
okay you guys have questions are
we good we get
all right let's go on to the
next one okay this time notice you know
when we did these we never had anything under here
okay well now we're gonna put
something under there right so now we can do cues is like Hey
let's add something are
let's talk about this one gosh
gas prices are falling like crazy aren't very
yeah
gas prices went like crazy
rising ridges up and down okay well the cost of gas is reason
everywhere in Japan the cost of gas is one sixty one yen per
later in the summer of two thousand eight how much that
dollars per gallon of the exchange rate was a hundred
eight yen per dollar what's my starting unit that I'm working
with IBM pearl leader and what am I
trying to change that to dollars per gallon okay so here
we go I've got a hundred and eight yen now how to write that
yen her leader K. it would be per later so I'm
gonna put one leader that's per leader so
now we have something on the bottom
one leader okay now what I want
to do is convert that two dollars
%HESITATION her
yeah yeah oh I'm sorry one sixty
one good catch one sixty one yen per liter okay and then I want
to change that and I'm going to convert that two dollars per
gallon so what we're doing is
essentially two conversions yen to dollars and leaders two
gallon so what is this two road maps so
I've got yen going into dollars and then I've got leaders going
to gallons alright well let's take yen to
dollars do I have a true value
relationship that gets me between yen and dollars
yeah what is it
yeah that's the one oh eight yen
per dollar okay that's my conversion factor here
one so what eight yen
it was one dollar okay what
about the next one leaders two gallon or like how do we do that
well and you look in the back of your textbook and you find the
commercial that's true because a one gallon
as reports import let's go let's say we we don't use our let's
just say we will use the courts one when having more fun
is there a court's one
leaders to courts
zero five
okay let's do that one but then
do we know courts two gallons a by no courts the gallons
there is none there right now
that purports mountain right now okay that's kind of stuff will
be given to an exam by just kind of monies that just throw all
the English alright so how do we do that English metric units
there all right how do we do that I've got yet on top because
in the bottom so I'm going to I'm going to
look at my conversion factor and I say oh yeah it's one eight
point zero and what is on top one dollar
okay yen's cancel I'm left with
dollars I'm getting there now I got to convert leader so I can
do it all in one chain so five got leaders I need to cancel out
the leaders and so where am I gonna put
leaders we've always been on the bottom
I can put on the bottom they will cancel Abby what
leaders times leaders in our get leader squared
I guess I had a word so it has
to go on top of the combat leaders on top and then we're
going to do court so that's one leader
is to one point zero five seven
and courts and then my leaders cancelled
and then I got courts on the
bottom so now what courts on top why we put the
courts on top so these after cancel yes and
then what do I want I want gallons right so it's one down
is for courts so the answer comes out to be five point six
four dollars per gallon and that's your answer
all right that makes sense
okay
well that finishes at chapter
one so why you wanted to mention
analysis and save big there are going to be using that all the
time right there because we're going to use it all the time
so these kinds of things we're
going to be using every time so we did and we start doing other
problems we're going to use this stuff to solve those problems
guy really nail this stuff down okay will get ready start
chapter two and that this would be a good time %HESITATION
breast take breaks so we will come back in
fifteen minutes and will do
chapter two alright let's take a break
all

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