This is a trascriptt from youtube lecture. Makes lecture notes for this for me to study later:
so good morning I hope you are doing
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well we're going to start with one point
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to which that sexuals on something
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called place value will review what the
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place value is I'm going to kind of
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explain to you how it relates to
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addition subtraction and that's what
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we're going in Section 1.3 so if you're
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taking notes take some notes
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hopefully you're taking notes some 1.2
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and we're talking about the play step
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firstly before we get into that there's
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some things that we really should know
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about place value and and some of the
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underlying things that you learn in like
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your math 91 class there's math 90 class
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those things I'm expecting you know are
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things like a number line oh we all
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familiar with the number line raise your
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hand if you're familiar with the number
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line plot numbers on that so I'm
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expecting we know how to make one of
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these things start headed zero for right
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now and put numbers on this number line
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so if we're listening to salad of course
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numbers get bigger as we go to the right
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and we can put poll numbers on a number
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line you guys fill together that little
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head nod if you do okay good deal
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also I'm going to expect you to be able
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to put numbers in order from smallest to
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largest or largest to smallest that's
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something we need to be able to do right
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off the get-go here and lastly how to
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plot numbers between here using
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fractions which we'll go into more
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detail later on in our course so those
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are some ideas that I need to have down
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before we get started well we're going
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to start with is that your place value
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so we'll start with a big number here
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like that
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it's a big number so much money you wish
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there was that I think it probably is
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teaching up still I think I would it's
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an honorable thing to do right at least
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say but that's a tremendous amount of
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money if we're talking about money well
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we know about money or numbers any other
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type of number that we're talking about
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is every single number has what's called
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a place value associated with it every
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one of these numbers these digits has
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what's called a place value what we mean
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by a place value man right right here
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it's simply the position of each digit
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in a number that's the definitions like
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a textbook definition for it what it
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really means is the value of this
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digital or the value of this digit so
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I'll say the position of each digit in a
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number but we need to know it as oh
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that's the number of tens I add with a
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number of thousands so that's what we'll
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get into in just a second so the
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position of each digit
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in a number
Place Value
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so we get a whole lot of play studies
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going on here
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can you tell me if this is a whole
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number what's the very first place value
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that we do one yeah so we had some ones
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going on how many ones do we have in
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this case that this number says there
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are nine ones so here our very first
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place value is our ones so we move one
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over what's the next place value to the
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left of the ones would have got there
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yeah okay that's great
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says we have five tens here now which is
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five tens fifty that's always say 59
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that's the way this thing works what's
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the next button place value what do you
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think by the way if you're having
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trouble reading then the very back
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there's a lot of seats up here for you
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to move to if you want so hundreds is
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the next one what's the next one to the
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left
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so we have our ones move over to get our
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tens then we have our hundreds we've got
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our thousands what's to the left of
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thousand thousand I'm going to
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abbreviate ten thousand ten thousands
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what happens if we go one with someone
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over on my right hand side this is my
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right okay so some over here what's the
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next place value that we have great
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hundred thou okay
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what happens after we get out of the
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hundred thousands where do we go we have
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ones tens hundreds thousands ten
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thousands hundred thousands is here
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what's this one million you would think
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so right but we have another word for
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that every every triplet has its own
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little pattern we have thousands ten
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thousands hundred thousands then we're
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going to have this is where we all want
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to be right along millions billions ten
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ten millions 100 millions what's the
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next one
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billion if folks that mattered do you
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think it ever ends no do we end in this
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number it means biggest number we get
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they go to forgetting add more so we got
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millions we know that one this is gonna
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be ten millions this one's going to be
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hundred millions this one's going to be
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billions
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can you name me what this one what the
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eight would be if this is billions
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what's this great this would be utterly
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plentiful under a hundred billion a
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billion and then we would have trillion
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trillion if you think this is a big
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number our deficit is in the tens of
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trillions of dollars right now it's one
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moon it's this big it's one more place
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value so we have trillions which is a
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tremendous amount of money if they took
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our national debt and we had that money
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somehow and they spread it between all
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of us we'd be the wealthiest people who
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would be it's a B so crazy like a
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billion dollars to drop in the bucket to
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a trillion in a sane amount of money
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it's huge
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okay so trillions it doesn't end there
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you can go ten trillion under trillion
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quadrillion ten quadrillion hundred
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quadrillion kwinto you have insisted
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sextillion octillion when you keep going
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and going going and never ever ever ends
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there's a lot of big numbers out there
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but my point today and this is that
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every single digit in here has a
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specific name it tells you how many of
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each place value have how many how many
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of each of value you have here how many
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thousands do we have we have one
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thousand how many ten thousands do we
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have it zero ten thousands but we have
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two hundred thousands this right here
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this is the fundamental of when we use
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this with expanded form the fundamental
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of addition because when we add we use
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this information
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maybe not explicitly but I'll show you
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how to use it implicitly in our audition
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also we kind of need to know how to
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write these as words and say them
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appropriately so if I gave you the
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number in this one could you write that
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out in English like we'll go back and
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forth between writing it and write it as
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a number for instance what I'm talking
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about we say this one is 54 we'd say it
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54 yeah okay how do you say this one 678
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you know a lot well no a lot of people
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say 678 m I'm going to kind of get you
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away from that because that word and
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that word and actually means a decimal e
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I spelled wrong oh no I was going to be
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this I'm a bad Spiller I just if I go so
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I'm gonna put the decimal before that I
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would maybe like out sorry this is just
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a little indicator and this is what I'm
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talking about right before we're not
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suggestible yet good call so if we said
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678 it would imply to someone writing
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that number down that would it be like
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678 hundredths like 600 point seven
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eight we don't want to say things like
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that so the only time we ever use and is
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if we're doing with the decimal let me
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show you who I'm talking about if we do
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this number the appropriate way we would
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say that is 93 we don't say the nine
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forever say 93 that's weird how we say
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that when we consider this to be one
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number of thousands we have 93 thousand
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two hundred five said it with me
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great we're not 205 because that and
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would imply a decimal would say 205 it's
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going to be kind of weird to get away
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from that but that's really the way
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people say the numbers let's practice
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let's practice one more we're going to
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do the place values for these things
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then we'll try to say out loud we'll
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talk a little bit more about that so one
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one six seven
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now I'm an a secret place values first
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of all to make sure you really have a
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handle on this okay don't answer right
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away I'm gonna give everyone about five
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seconds to think about it so right now
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in your head I want you to think about
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don't say it think about what is this
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place value right there don't say it out
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loud just think about it we're talking
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about the seven do you have it um what
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is that tender yet how about the three
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great can you tell me how about this
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this six of you so the way we would say
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this we consider this to be a triplet
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we'd say 679 million because this was
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the millions right 679 million four
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hundred thirty what 125 done do you
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think and go back and forth between
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saying then writing them and the numbers
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themselves some people do appreciate and
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feel okay with it so far if you don't
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don't raise your hand but if you're not
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raising them apply that you're not
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getting so stretching before how much
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you'll feel okay about saying these
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looks good okay that's great the last
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thing we're doing this section is a very
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short section we're going to talk about
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expanded form expanded form means we
Expanded Form
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take a number like one of these and we
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write it as the sum what's a sum mean in
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math Maggie if I say s um like some
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what's that mean okay so we're adding
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together to get a total right that sum
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means we're adding we can actually take
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a number unlike number like this and
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write it as a sum of its parts which is
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kind of interesting to leave some new
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addition
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so they span form
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gives us really the basis for addition
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and subtraction but here's what expander
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form looks like here's a normal number
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if I wanted to write expanded form all
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you need to do in order right expanded
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form is know your place values can you
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tell me what place value the four is it
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right now great someone else over here
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tell me what place value that eight is
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in and how about the three and how many
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ones do we have here is expanded form it
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says you take that information and you
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write this as a sum of the number
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followed by the appropriate amount of
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cereals basically we have fourth out you
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said there's there's four in the
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thousands spot right makes we have four
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thousands we could write this as four
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thousand plus then you look at the next
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number they okay what's the next digit
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poets three hundreds we have three
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hundreds right let's add them 300 plus
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go to the next one that's the eight and
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eight tens or eighty very good and we
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have also man on the ones which is hey
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if you add all that up do you suppose
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you get 4382 I detected right there
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caught sure hope so Hannah huh otherwise
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math doesn't make any sense me to stop
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right here but that's expanded form
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means that we can take a number and
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separate each individual digit as a sum
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of its parts
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that's what means we have four thousand
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four thousand three hundred three
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hundred eight tens plus eighty two ones
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we get that too bad
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how many we feel okay with this that's
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all we mean by expanded form you should
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be able to go from expanded form to our
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normal standard notation or standard
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rotation to our expanded form just back
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and forth like that it's really over
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but why it's important is because when
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we get at section 1.3 which we're going
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to do right now this really is how we
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add numbers together we look at place
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value by place value we add place value
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by place value it's kind of cool it's
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all based on sekonic they said expanded
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form we just don't really talk about it
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do you guys have any questions on the
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whole place values issue say the numbers
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or expanded form at all we just did
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section of 1.2 that's pretty painless
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right only like 50 more sections
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together we're almost there
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how does there