So this is Chemistry 108, Chemical
Principles I at York College. We’re continuing in
chapter 1. Today is February 10th 2015. Okay so
before we get into the material, I’d want to kinda remind you of what I told
you last time in recitation. So this is one of the recommended
calculators. Remember you’re not allowed to use a
graphing calculator, and I recommended a couple of- or we
recommended a couple of models in the syllabus. You don’t have to get
this one right, but this I recommend because it’s at least when I
looked kind of the cheapest calculator that is widely available that’s that’s gonna do. So Casio FX 260 solar probably about 10 bucks if you go to like Staples or CVS or something
probably 20 bucks if you go to the bookstore and its solar right, so you don’t have to worry about
running out of batteries and it has everything you need and some things that you don’t but you know that’s okay. So how do I type? Okay, so I lost the name, how do I type 3.0
times 10 to the 4th into my calculator? So I’m gonna type 3.0 right, so I’m gonna do 3.0 and it’s going to come out like this, and then I’m going to hit this button “EXP”. On your calculator. it might say “EXP” depending on who makes it right,
might say “XP”, it might say “E”, it might say “EE”. You might have to
hit the shift button or the second function button to get it but you’re gonna hit the button that
that gives you that. What that means is times 10 to the power of. Right so 3.0 is 3.0 and to get times 10 to the power of, you
hit the “EXP” button and usually- well on this
calculator it’s gonna give you something like this, right. The small numbers over here and then I’m gonna type up my 4, so
this is gonna be 3.0 times 10 to the 4th. 3.0 “EXP” 4. What that means is 3.0 times 10 to the 4th. You
don’t need it a multiplying sign, you don’t need a
carrot. Right you don’t need a- you don’t need this thing or you don’t
need the up arrow thing. This will do everything and this will do
it right every time. If you use the- if you actually write
out multiply 10 exponent or carrot 4, sometimes that’s gonna mess
up your order of operations right and so you’re gonna get the right
answers but the as usually what that means is you’re gonna get the right answers for this part, but this part is gonna be so never use
your calculator. To type in scientific notation this is
how you want to do it what about negative 5.1 times 10 to -12 so this is what on on this simple calculator that’s what
we’re going to do we’re gonna type in 5.1 when that’s gonna give me 5.1 5 point 1 and then there’s this plus minus
sign on your calculator notice it’s not the subtract sign to subtract line is
gonna mess you up here it’s the plus/minus sign and some
calculators it’ll be a little minus in parentheses a press that button and I get my big my big big okay the negative sign disappeared I’m gonna
get my big negative sign over here I think the font color is not translating onto the projector summit in 5.1 plus/minus that’s going to mean negative 5.1 then
I’m gonna hit the XP but want to hit the XP but my putting 12 I hit the plus/minus key again and
that’s going to make my exponent negative so somehow that negative signs are not
translating I’m correctly but there’s negative sign
here the negative sign here right okay that’s because a.m. -12 means there’s a \$10,000 since it’s not going to be on
your screen it’s the most calculators unless you
tell it to do explicitly it’s going to try to fit them onto the
screen and if it doesn’t fit onto the screen it’ll put into scientific
notation a few tips you might not want to fit on the screen
right you might not wanna write down like six zeros because I’ll fit on your screen there’s
ways depending on your calculator how to force it to always give me Center
notation we can look at that later you have a different calculator doesn’t
quite work for you come see me and will get that will you know look at
how to use your particular model as well okay so let’s do some chemistry we’re going to do a couple
more examples because um this conversion thing with
dimensional analysis with multiplying and dividing and crossing
out that’s really the guts love how you’re
going to solve probably three-quarters of the problems
that you do in this class them record the mathematical problems to do
in this class so we got in make sure that you understand so let’s do this another problem 360 seconds to the -1 over to the first thing I want to point
out her the first thing on ask years what is that mean exponent -1 00 0 take a card if you got a card her and you can go over in a min dark
marker for if it slide in Pathmark around if you
need it okay so what is this exponent -1 what
does that mean or what is a negative exponent me it’s one divided by if you see the negative it’s one divided
by so my said 10 to the minus to what that equals is one over 10 squared the negative exponent means that we flip it and put it into
the denominator so what is seconds to the -1 me equals one over one over seconds and then I want to convert
that over to hours to -1 right that means one over hours they don’t have an idea
what one over seconds measures well there’s no distance red just one over meters over second or
something miles over second gives us speed some love you I have some experience thinking about this
even if you don’t know it anyone ever heard of a unit called hurts yeah where did you where you heard that
talking about the speed of the processor its talking a bit tells you usually get
hurt sir megahertz and hurts is a repetition rate how many times
something happens every second the numerator is there’s no numerator it’s not meters per
second is not miles per second it’s just something happened per second something happen this many times per
second so who when you talk about like gigahertz
that many calculations are that many steps per
second went to the more higher the gigahertz
the faster your your phone works so let’s convert 300 seconds to the -1 over to hours to -1 and let’s do it this way let’s put our heads together gently with our neighbor or friend if you don’t have
friends make some and down and what’s let’s see what you
can come up with okay so one over seconds um the way to do this or one way to do
this is to go first from seconds to minutes
and then from minutes onto hours if you will if you know how to do it all at once
that okay but I’m gonna do it in steps right so 360 times one over seconds the second is in the denominator right that means if I wanna cancel it
with the conversion factor how do I cancel where does the second
have to be on top by two seconds needs to be on top so seconds and first I’m gonna go from
seconds to minutes how many seconds in a minute very good
sixty seconds in one minute and when I do that cancellation now if I were to stop here what up what
I get I would get one over minutes but I’m I’m not stopping at
minutes I wanna go from one over minutes 21 over hours so how I’m gonna go from one over
minutes to one hour hours I need my minutes on top my hours on the bottom so 60 minutes in
one hour when I cancel that I’m gonna get minutes and minutes and
what’s left one not ours one over hours ours is still in the denominator right so I’m gonna do 360 time 60s time sixty and if I think I i by which want what 29 how many zeros 000 30 or one point 29 times 10 to the 50 96 1.2 96 tak three zeros times 10 to the one two
three four five six 1.29 six times 10 to the six hours to -1 up we haven’t talked about significant
figures yet so that’s why left it as is and so it’s a 1.3 times 10 to the six hours to -1 yep home it depends where you move it from right
I’m so this number its big write some numbers
are big bigger than one explains can be positive if numbers are decimal smaller than one they’re gonna
be negative explains can be negative yeah move it to get it 828 you’re moving it
to the right right so that would be -1 -2 -3 when you say which way you move it it
can be tricky because if you’re moving it from here to go that way it’s one director Mueller from here to
go that way it’s the other direction so the way our I would think about it is numbers that are big bigger than one get positive exponents numbers that are
less than one get negative exponents thats that sort of not gonna once you wrap your head around that
that’s not going to confuse you right cuz you sometimes have to go from here
to here sometime let go from here to here gonna be like Wat right left wait which
one up well this is Hannah see the and then 10 to the 6 means
it’s a big number rate so that means it’s this right so
you’re gonna move it this way yeah and it was negative you would move
it that way okay so questions here other questions here yep to because h2 the negative one is the same as what one over H right that’s what the
negative one means yeah are you could or you can also put
wanna rage if you want that’s that’s a good one kept saying I had all you can about okay so we’re going to here’s the one you did
in recitation are you at least attempted to recitation
what we’re on 3.77 grams over centimeters cube two kilograms or
meters cubed me that’s what you did on Thursday I
don’t think we got answered with we did okay let’s do different one her up up okay so 3.77 times 10 to this 10 square centimeters per second over
two kilometres are kilometers per cillo second killer
second sort of a stranger in it but nothing wrong with that we can put a
killing from a second and so what kind of property are we
measuring here sorry distance over time so that’s a at
a speed owner rate or something 00 all I remember out in a sec before we move on from this one someone
asked me I was going around the room this is a
really big number free attention to number gets smaller
and I didn’t really have time to explain and
I wanted to explain to everyone doesn’t make sense that this number gets
bigger remember what is what over second means it means I do something occurs this many
times every second if something occurs this many times our
second what’s going to happen when I think
about how many times it occurs every hour me a lot bigger right and so this make sense okay now put our heads together gently and do it okay so I’m let’s let’s let’s put it together so there’s two ways I can and I wanna go from centimeters 2 km written
there’s the way I like to do it is to go
from centimeters to meters and then for meters to kilometers and so
I can do my CM to M two ways rate 200 centimeters people’s
one meter or I can do one centimeter people’s one times 10 to the negative to meters either of these will work just fine the same thing for the camera so let’s I do this out I remember you’re going to have to know
how many k is in am and how many seein how many
am in all that stuff for dinner table okay so 3.77 times 10 squared centimeters her second because centimeters on top we can do that first well have to we
could do the second first we wanted to centimeters two meters what where’s the centimeters gonna go
nor smears centimeters on bottom meters on top and so up I do want me centimeter equals 1
times 10 to the negative two meters if I
wanna could also do 101 both them work exactly the same so centimeters in centimeters cancel I get now if I stop here what would my
unit B and see idea a sec my stop here what my unit B meters per
second alt you can just write 10 to -2 I write like
this because how are you going to put this into your calculator this is going to go into your calculator
if you do on your calculator one the negative to right because 10 to the -2 is one-time Center -2 in terms of what
you put in your counselor okay so we’ve got meters per second we don’t
want meters per second wanna get to km right kilometres can I get from
m2k a as I can I do that got here workers here number one step at a time I see someone you trying to do
something with km over Aston s oversee in one step at a
time right pain centimeters to meters meters
to kick kilometers %ah one km equals one times 10 to the third or
1000 meters and when I do that I’m going to cancel meters an meter never stop here and get campers second right Commons per second last
thing I want to do is change my seconds to killer seconds and so how am I gonna
do that a thousand second so where’s the second
gonna go here the second goes on top right that’s just like this question
down here with the one over second the second the
denominator so when I can to let the second goes in
the numerator seconds over killer seconds one sec I one kilo second equals one-time 10 to the third seconds seconds and second cancel and so what’s the unit
that I’m left with here kilometers overkill seconds and I get three-point 7 seven times 10 to the hero or just three-point 77 km over KS very good princess her questions yessir now okay yes Leo you do you look like a okay so I got 10 to 20 um this is 10 to the two when I multiply I add the exponent right so to plus mine at -2 going 0 when I divide us attract rights as 0 -3 is -3 when I multiply I at -3 plus
three people 0 you could do that right because you
could if you wanted to you could do you can combine meters centimeters to meters and the meters 2km
if you know how to do that if that makes sense to you again I like to do it step by step so I
don’t get confused but if you’re happy with that’s fine other
questions okay very good so let’s take a step back into temperature so up temperatures one instance one of the very few instances where you
won’t be using dimensional analysis where you won’t be using this kinda crossing out thing to convert between units so temperature
members a measure the hot mister congressman object and temperature comes in three different
I flavors I’m Calvin degrees Celsius two degrees
Fahrenheit and Calvin is actually the SI unit for
temperature and you can have Miley Calvin and Michael Calvin and kill ok
Alvin and so on and as long as you’re using
the metric system within the Calvin scale you do it with
me dimensional analysis the way we just I the way we just looked at it but if
you’re converting between calvin in degrees Celsius to Kelvin in Fahrenheit
or Fahrenheit Celsius you’re not right and this is one of the
few instances where not and the reason you can kinda see here and because 0 points are different and in order to do two dimensional analysis 10 the most imp what what are the requirements is that
00 raid 0 meters is the same as 0 millimeters in the same as you’re ok la
matters is the same as 0 miles 70 feet right but here the the zero
points are all different men so you can’t convert directly through multiplying by
conversion factor her the way it’s written here we’re looking
at two important temperatures and their important temperatures one because we are familiar with them but we’re
familiar with water the freezing point of water in the bump on water and two because they’re very there they
illustrate what’s going on it so the one that we might use most often in
daily life rate if you listen to the temperature on
the radio or Harry check whether not calmer
whatever 32 is the temperature at which water
freezes in degrees Fahrenheit 212 is a temperature at which water boils
and degrees Fahrenheit when today it was it was supposed to
reach like thirty six something like that 35 36 some ice me
might melt right that some degrees Fahrenheit in
Celsius which is what you typically use in the chem 109 lab water reason 0 and boils at a hundred and the Kelvin scale water freezes 273 and boils at 373 so the first conversion that we’re gonna
look at this Celsius to Kelvin what’s the difference between 0 and 100 under 10 is 100 what’s the difference
between 373 in 273 also 100 so what that tells you is the number of steps between water freezing and water boiling in both cases
a hundred way to the steps are the same size it’s
just that to get from here to hear what you need
to do you need to bad 273 02 273 is therapist is only three a hundred to 373
is also plus 273 right in here is normal body temperature where those
are you going into the medical field or just a few I you know take your temperature you get sick 98.6
fahrenheit 37 degrees Celsius is normal body
temperature 37 plus two 73 310 it to get from Celsius to Kelvin
you’re gonna at 273 what if I want to get from Calvin over
celsius some practice only three very good so come into Celsius degrees Celsius to
Kelvin Calvin 2 degrees Celsius is Calvin -2 73
gives you degree Celsius that 334 it gets a little more a little hairier when you go from
celsius to Fahrenheit fahrenheit celsius because a hundred steps here 32 212 how many steps there 212 minutes 3280 right so there’s more
steps in the Fahrenheit scale to to cover the
same distance means each step is smaller Peyton so
before we do any have so so in addition to
doing some adding and subtracting we’re going to have to do something
about the size of the steps before we do that leads to an example what is equivalent to 98 on the Celsius
298 Calvin on the Celsius scale it how do I get from Calvin celsius
subtract so to ninety eight minutes to 73 gonna gimme 25 are happy now or not why we’re not happy because well we need a unit rate so 25 degrees
Celsius because 298 Calvin you can’t just leave
us hanging out with our unit so number unit number unit both of them have number and unit okay so here’s our our
picture again when so here we’re going from zero to
100 here we’re going from 3212 here to 100 degree here to 180 degrees so if I look at a
hundred eighty by put it if I make myself a
fraction 180 over 100 and I reduce that that’s going to reduce well I can reduce those 18 over 10 it
can reduce to nine over five and if I look at a
hundred over 180 that’s going to reduce to 5 over 9 so these two fractions are going to be important we’re
converting Fahrenheit to Celsius insulted track so here’s the formula for converting celsius to
Fahrenheit if I have degrees Celsius I’m gonna
multiplied by 9 divide by 5 or 1.8 if you want and
then add 32 the multiplying by 9.5 the nine divided
by five that takes care of the different size in the steps in adding 32 accounts for the offset between your
degree Celsius and 32 degrees Fahrenheit now for wanted works okay so let’s leave it there for
now if I want to do that’s what I want to do so but Celsius
to Fahrenheit let’s do an example if it is 30 degrees
of it outside what is the temperature in degrees Fahrenheit okay so had just getting so here’s the formula her fact degrees Fahrenheit equals nine
fist and resources for 32 right and and I know the degree Celsius tempering the
result is 30 degrees Celsius some implemented for an article 9 divided by five times thirty-plus 32 and 9 divide by five times 30 is going to be
54 right 54 plus 32 is going to give me degrees Fahrenheit because 86 eighty-six
degrees Fahrenheit Eagles 30 degrees Celsius and now if
only it were that w outside questions here and by the way I put up I slides for lectures up to last Thursday I put them
up on Blackboard over the weekend so you can get those
and review them if you want and then these will be coming up soon
questions here cell if I want to take this formula and I
want to isolate degrees Celsius in fact get degrees Celsius on one side
by itself that I’ve got the formula for the other
conversion and so those have you were kinda more
mathematically inclined you can try to figure this out when you gonna do you gonna do not
subtract 32 from all sides and then you’re going to multiply by five nights right so what we’re gonna
get is this degree Celsius equals 5/9 times degrees Fahrenheit minus 32 now if
you don’t see the exact math I’m not gonna go over it right now but
we can go over it come to my office and can go through how to get it degree
Celsius equals five nights times ministering to so F minus 32 takes you
from 32 basically down 20 and and then the five nines gives you the scaling right between the smaller more numerous units here and the larger less numerous units here
so if you have a fever 104 degrees Fahrenheit what is your temperature in
Celsius here’s the formula again 104 is a you know fairly bad fever so we’re going
to do we’re gonna plug in degrees Fahrenheit -32 times by nice 104 -32 gives me 72 I’m not mistaken 72 times 59 equals 40 to 40 degrees Celsius equals 104 degrees Fahrenheit and again we have
on both our statements herein number and unit questions here okay there’s no questions at this point
will take a ten-minute break now we will finally use those handouts
and I ask you to bring last Thursday when we come back from
break okay so the next thing we’re going to do is a
significant figures also known as what I like to call
uncertainty in measurement and because students like to ask why do we have to no significant figures
and the reason is because this isn’t a math class this is a class in science man and so our numbers have some to cut your chemistry is is is just a matter the numbers that we
use have some basis in fiscal reality right I’m if you’re in math class 3.72 is just 3.72 but in chemistry 3.72 meters is a certain
distance and its 3.72 because we measure 3.72 we didn’t measure 3.7 we didn’t measure
3.8 we didn’t measure 3.72 to and we measure
3.72 and so some numbers are exact others are an exact right and so this is what does that mean so exact numbers are
numbers that we can count I have five fingers on my
hands right there’s no question that there’s
five fingers on my hands even though you know win I’m driving maybe only see one of them
um there’s exactly 12 eggs in a dozen right that we
know by definition thank you somebody left I’m
have theirs by definition dozen means 12 right so
bye bye does an exam by 12 X there’s no question there’s 12 there’s
actually more than 60 to the front row there’s eight seats in the front row six of them
are empty where the eight seats in the six empty ones are not there’s no uncertainty exactly 100 something dollars on so
exact numbers are def determined either by definition for by
counting right and so what another example of an
exact number you can thank a number students in this class there are 50 seven or so students 57 I think it’s 57
on but I could go to my roster and count
them 12 57 you got two years straight I mean there there’s 31 days in January there’s lotsa def exact numbers so water in exact numbers in exact numbers are numbers that we
obtained by measurement right and so I by the way let’s take a step back your prefixes in terms of the metric system those are exact numbers there’s exactly
100 centimeters in 1-meter there’s exactly 1,000 km one 1-meter those are by definition numbers
obtained by measurement on the other hand are inexact she would mean well and why the exact it depends first an
instrument right if you are measuring with her really quote good ruler for example you might be able to
measure two decimal places if you’re measuring
with the really crude ruler you might be able to measure
no decimal place to depend on the instrument and it
depends on the person and it depends on how good you are if
you’re making insurance how good Anna how good you are at reading the instrument that your that you’re using so I mean example who heard the weather report this
morning and how what what did they say how how hunter who called me today 36
degrees okay and so if you went outside and you said well it’s 36 degrees is it well Hannah this is for the spring I mean
this is for the fall right when if I ask a question how hot is it
outside I’m really asking what the temperature in the air right and we could say 75 degrees Fahrenheit
that release only five for really thirty six well it depends it
might be is that 75.4 is its own 5.43 is it right it could be any or all of them and we couldn’t if it was if we had the most precise thermometer
that we could imagine we got something like this we
couldn’t really say that this is wrong but we reckon really say that these are
wrong but we could say that this is more right
right it depends on what it depends on how
good a thermometer using and also from a more philosophical sense it depends on what we want to use that
number for right I if I just want to know whether I
should wear shorts or or pants list so I need to know I don’t need to know this so there’s no
reason to buy a thermometer that’s going to measure
this appalling you to know is whether to wear shorts pants so here’s an example right here’s three
thermometers here’s and you can imagine each of these
three right so here’s one thats marked every 10 degrees here’s one that marker 10 degrees but
has these one degree units in between and here’s a digital
one press the button and it gives me a
temperature so what the temperature who thinks it’s
seven the for within 75 we think that 76 we think it’s only seven we think that
something else so I’m gonna say it’s seventy are not only five i think is what I
wrote I miss 875 if you said 76 in less I took another measuring
instrument like a ruler and measured between 1780 I couldn’t say
that 76 is wrong I can say it’s only five is wrong what do I know for certain I know for certain it’s between 1780 and I
kinda know it’s toward the middle somewhere so if I seventy six so if I’m using this thermometer I have no basis and physical reality no basis in my measuring tool to
say it’s seventy 5.5 or 75.8 where some 26.2 way because I don’t even know about 75
or 76 I can’t make a more precise measurement
that so this measurement ban has to significant digits significant figures wire they
significant because they have a basis in reality based on them to learn using or this one okay so summaries are hand and tell me
what you think okay so um yes princess Sony 5.5 just cuz she’s a princess
doesn’t mean you have to agree with their yes kaelin some 5.4 yes no name tag and 5.3 any other guesses any other yes Leo 25 thank 3528 okay so what do I know I know for certain it’s 1234 by between
75 and 76 but beyond that I can’t say no. any if you are wrong read it could be unless I take another
instrument and measure rate in which case I’m kinda
cheating so I’m gonna say it’s only 5.4 cuz that’s
what I think it is I but if you said it’s only 5.5 I’m not
going to say it’s I can tell you’re you’re incorrect so
1090 two digits for certain one digit thats I’m estimating I’m estimating it so it
still has a basis and physical reality so based on
this I get 3 significant digits in my measurement let’s say it was instead of going there is right here well what I
get if it was here I’m all I would get a
seventy because I have no way of measuring tense right but it was here it would be 70.0 if you put seventy and 70.0 into your calculator your
calculators gonna think it’s the same thing but it’s not in terms of chemistry because seventy mean to use
this coming up crimea thermometer 70.0 means
you use this very much nicer thermometer and then if
I turn the Sun Sony 5.43 there something in their measuring temperature does not
magic so this has for significant digits so when you’re making when you’re in the
lab in CHEM 109 and your for example looking at your
cylinder and this is mill leaders instead of degrees Celsius what’s that
going to be that’s gonna be 75 points something okay the digits a measured quantity including one that we’re not sure afraid
we’re not sure that one those are significant anything beyond
that is going to be insignificant so water how that comes to the rules for significant figures and that’s
what’s on your hand up why do we need rules for significant figures because if you a lot of times when you
digits any multiply by something else or three significant digits your calculators going to be like 18
digits right and not all those 18 digits have a physical basis in reality basis and fiscal reality
great here only these three digits have a basis and
physical reality and what this significant figures
calculations and definitions and stuff that we’re gonna go over what that does is help us to
make sure that are calculated values reflect real-life and not just the mouth calculator so rules for significant figures all 90 digits are significant if you see it
372 during its only 2.44 all those digits
are significant so all 090 digits are significant what does that mean that
means the rest of the world we’re gonna be looking at have to do with what number zeros determining whether zeros in a number are significant that
is have some basis in physical reality or don’t how many significant figures for where zeros between 90 digits are significant so what does
that mean that means in a number like 808 .3 this 0 a significant that means its that 0 is telling us that it’s not 818 or 828 its 808 that 0 has meaning so between 9:00 digits their significant if
I were to rate this 327 point 03 this 0 forget about the decimal point you’re
significant 3 27.03 04 between 9:00 did significant the Rose at the beginning a number are
not significant so if I were to change this to this this 0 at the beginning a number not
significant this 0 also to begin number not significant
this 0 significant some more examples I think so 0.035 those two leading zeros
are insignificant because there at the
beginning a number there insignificant because they’re just
their place holders where they’re not telling us her if we were using a a ruler red all we have to do is kinda shrink down a
ruler and we get these two numbers over here Orvis was meters and I converted it to centimeters right
what would I do multiply by 100 I get 3.5 for those zeros disappear so insignificant zeros at the beginning a number so that has
two significant digits okay so this is kinda like that one how many significant digits on this
number or very good this hero significant the
zeros are not significant and so this as for significant digits question
so far zeros at the and a number are
significant if there’s a decimal point in the number 3.0 per that 0 is significant because there’s a decimal point in other
words whoever was making the measurement or writing your question took the time to
write 3.0 that means the point zero mean something it’s not 3.1 it’s not 3.2
its 3.0 so this is to sin if in fact digits sorry would well that means it’s 3.0 0000 there are significant right has zeros at the end of a number are not
significant there’s no decimal point so what does that mean that 0 is not significant a decimal point this can be confusing so what’s the best way if you haven’t 0 at the and to make your
point any idea whether it’s significant or not let’s say the answer really is 320 when you do a calculation and your
answer with the cracked content significant digits 320 there’s two ways
to force this to be significant you can put the dust mop end so I can write it like this 320 point and nothing after that that’s kind
of strange right nobody does that outside of sign out a scientist yet well thirty 2.0 but then it’s not three
in 20 more but you’re on the right track very good I can put incentive notation 3 points 20 times 10 10+2 what to right that means there’s three
significant figures if I were to write 3.2 times 10 to the
two that would mean there’s two significant
figures right and so choosing to rate this or this forces me to to to realize there’s either three or
two significant figures so ira 320 dot that would force me to say home 0 significant because the decimal point group world
rate if the number has a decimal point the zeros are significant and the other way is this right three-point
20 times tent to her forces this 0 to be significant also because the
decimal point roll questions okay so what about calculations so where those that’s a summary of the the
rules sign your sheet so row calculations are calculations is
where kinda becomes important how do I know how to report my answer so that my answer reflects white is really going on rate in terms of my measurements this is kinda VOD a general principle
your least certaine measurements we have a whole
buncha measurements and your combining them in some
calculation the one that has the least certainty
limits my answer right so if I have one measure in other words if I have one measurement
where I use the really really good good thermometer right and a second measurement where I used to
really really cheap thermometer a lousy one when I add those two
together my answer is going to be determined or the the the the certain to your how could my answer is is going to be limited by the one time I used that the lousy
thermometer because have one question with a lot of one
measurement with a lot of uncertainty another measurement with little
uncertainty I combine them together what’s going to look like well the
little uncertainty is gonna come to get washed out and I’m gonna be left with the big
uncertainty so a rule for multiplication and division the answer has to contain the same number of
significant figures as the measurement with the fewest significant figures so back to our volume example lifetimes
with times height if II do a calculation right I have I’m it’s a measurement in a
box my boxes 3.21 times 5.0 172 by 10.40 one centimeters her the unit here is going to be what centimeters cute and when I type this
into my calculator typing 3.21 times 5.0 in seven times
10.40 one I’m gonna get this you can try it if you write this down your answer is not correct because that
does it does not reflect what these mean physical right what these mean as measurements in
only reflects what they mean is numbers I’m gonna have to think about my
significant figure rose so I want my answer I need to round my
significant figures as the measurement with the fewest
significant figures so this one has three how many significant
figures here for and how many here 5 so how many digits or how many digit should where should I round this one to have
three because three is the fewest so how do I round this to three
significant figures yes so I’m going to just keep the first second and third so that means I’m
gonna round of starting here her five point 5036 is greater than half alright so that rounds up and I get 168 centimeters cue questions here okay number in europe so world to is for addition subtraction the answer has the same number I love
decimal places as a measurement with the fewest decimal place little different in that in multiplication and division which we
looked at in the last line we’re counting the total number
significant digits here we’re just counting decimal places that is digits
to the right the decimal point so I box went to the store and bought some
jewelry 98.4 grams one that’s a point 125 grams and one
that’s point eight grams how much to get in total well these are measured values right and
because they’re measured values they’re not exact so when I do my addition disclose
this place this and I put on my in on my calculator I’m
gonna get this 10 7.40 5 that’s not correct right it’s only correct in terms of the
numbers but not in terms of physically what I’m adding up so for addition and subtraction I’m going
to think about the measurement with the fewest decimal
places so how many decimal places here one how many here I’m here right and so one is the smallest under the is right
some gun around the soft to one decimal place somewhere around of up to the first decimal place I’m gonna
get 107 points for grams questions okay good number in okay okay just for completion make surprise precision
accuracy measurement precision how closely individual measurements
agree with each other I accuracy how close individual measurements are to
the correct are true answer rain so here we have poor accuracy but
good precision here we have good accuracy and
precision here we have someone who doesn’t know
how to play darts I’m okay question so far okay let’s just make things a little more
normal okay let’s do this problem over here significant figures 320 1.4 km plus 1.13 km divided by 5.4 66 hours
plus 2.23 hours so this is going to give us kilometers
per hour except now we’re putting stuff all
together rate we’re doing sums addition some more
addition and then some division 5.46 hours plus 2.23 hours so what I’m gonna have to do
it and then have to do the stepwise let’s do the numerator first 320 1.4 up hours plus 1.1 13 hours and that’s going to give me 300 28 to point 53 hours right top a columbia climbers is that correct that’s why is it not correct it only has one decimal place right
because addition and subtraction is the answer has the same number of
decimal places as the one with the fewest decimal places so
the fuse decimal places one so this is going to be 322 points 5 right so 320 two-point 5 kilometers and what about my hours so I’m gonna do five-point 46 6 hours plus to appoint to 3 hours 6 96 7.69 six hours but do I need to do some rounding yes have to round up to how many decimal
places to right because this is too this is 32 is
more 3 how my gun around us to two decimal places seven-point points 70 hours read the six rounds up you round up a 92 the next higher number which is going to
be basically 10 7.70 hours up okay so what am I gonna get here when you get when you plugging in a
couple louder cable box okay so is this correct know how many where we going to round to how many 3 this has three significant figures 0
significant right and because it doesn’t places for so how am I going around this 23
41-point 9 so this is wrong right so it’s for you
not 1.9 kilometers per power questions okay so you think you got it now dude go
home and do ten thousand problems I or until Alex asked asks you to stop and and which made me actually be more
than 10,000 in the meantime nope I have another it eight minutes and I in10 to use
them you had to break already okay so this is up books this is now a chapter 2 and so the way I like to think about chapter 2 is we’re going to learn about atoms and elements were gonna learn
about molecules and compounds and that’s not exact title the chapter but this is the way I like to think about it atoms
elements molecules and compounds and I like to think about it as having looking at the world two different ways
rate so one is the kinda big world the world
that we kinda walk an actin and live in and one
world that’s very very small right the big world is what week Michael
the macro- scopic world right I can and when we talk about
matter on the macro scopic level like we didn’t
chapter one we think about like water are or or or or a bottle we think about very very small we think
about be fundamental building blocks of matter when those are things that we’re gonna
call atoms and molecules macro scopic some microscopic so the big view the world as matters the
stuff is all around us very the some microscopic view says
are way too small for us to see by any sort of normal
means and so on the very very small scale matters
Mina atoms and molecules in the macroscopic
scale matters made up elements and compounds made so in some sense elements basically correspond to Adams and compounds basically correspond to
molecules although there are some exceptions there
right no that’s not a hard fastball roll we’re
going to see some molecular elements but basically that’s that’s the way it
works and so what are elements and compounds and what are marshals well elements are substances types a matter that cannot be decomposed
cannot be broken down into simpler substances bison ordinary chemical means compounds her and so that means there’s on what’s
the correlation between elements in Adams element you only have
other arabs well now only one type about will to leave it there compounds can be
decomposed or can be broken down into simpler substances and compounds are made up of molecules
that contain more than one Adam join together more
than one type about join together her so we think about something like water in
many people even without taking chemistry know that
water somehow is h2o made and they know that age is
Hydrogen and always Oxygen so waters made up I did
not right but a and so water is made up of molecules a water that contain Hydrogen Adams and Oxygen atoms water however is quite different from Hydrogen quite different from Oxygen it’s quite different and then if you just took a cylinder follow Hydrogen in a cylinder for Oxygen mix
them together rate that’s because their join together molecules so here’s a schematic great here’s one way
of looking at Adams oven element here’s another one way of looking at molecules and
compounds we don’t know what these colors mean in terms of the identity and so on but
here you have each sphere represents one Adam love the element that’s red here you have the spheres join together and in each molecule you have 1 I’m thats
purple and three atoms that are green so you
have atoms and elements and molecules and compounds now you some examples helium we have a lady
helium somewhere in this room I neon so on iron molecules and compounds right so samples
water red h2o carbon dioxide user things that we’ve heard over unity and
take taken chemistry co2 her we also have in the middle here what are called molecules on element
what’s the difference between this and this and this their molecules because there too join together but they’re not
a compound because there’s only one color where
there’s only one typeof and they just happen to be joined
together so mark your home in elements molecular elements that the exception I
talked about I mentioned very briefly earlier Oxygen
we breathe could be represented like this made 02 Nitrogen that’s also in the air can be
represented and two yep yeah so tight I get so so you know
something that I haven’t talked yet which is OK any legal her so these are what are
called I atomic elements that means there’s two atoms in one molecule there’s other
examples that are not diatomic right so Sulfur for example can bs8 there to form
Oxygen called ozone thats 03 and so there’s different types of
molecules an element basically here you have an overview of all the different types
of matter that exist okay so I guess amount of time here and so next tuesday week from today will pick up where we left off