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## Topic A: Multiplicative patterns on the place value chart

## Video transcript

- [Instructor] What we're
going to do in this video is refresh our understanding
of place value but we're going to dig a little bit
deeper and think about place value in the context of decimals. So just as a refresher
if I have the number 973, this should be review for you. We already know that this
rightmost space right over here, this is the ones place and if
we move one space to the left of that, this is the tens place. Notice we went from ones
to tens, tens are ten times as much as ones. And then we move one
space to the left of that, we go to the we multiply by tens again. We get to the hundreds space
and so this nine doesn't just represent nine, it represents
nine hundred or we could write that as 900. Similarly the seven doesn't
just represent seven, it represents seven tens or 70. This three represents three
ones, so it actually does represent three. But as I promised we're
now going to extend our understanding and what we
do is we put a decimal here which you've probably
seen before at the right and the reason why we even
need a decimal is to really tell us where our ones place is. We say okay if we go right
to the left of the decimal that's going to be our one
space because once we start introducing decimals we can
introduce as many spaces as we want to the right of the decimal. And so let's think about
those a little bit. If when we went from hundreds
to tens, notice we divided by ten, when we go from tens
to ones, notice you divide by ten. So what do you think this
place over here is going to be called? Well what happens if you
take one divided by ten? Well then you get a tenth
so as you might imagine this is the tenths place. And then if you were to
go one place to the right of that, what would this place be? Well it'd be tenths divided
by ten or 1/10 of a tenth, so this would be a
hundredth, hundredths place. And then if you were to
go one space to the right we could keep doing this
forever, but if we were to go one space to the right of
that, what would it be? Well a hundredth divided by
ten or 1/10 of a hundredth is a thousandth, thousandth space. And so for example if I
were to extend this number instead of if just being 973,
if I were to write 973.526, what do these numbers
these digits represent? This five doesn't just
represent five, it represents five tenths or another
way of writing five tenths you could write it like this
0.5 you just have a five in the tenths place. Or you could write it as five tenths. This two I think you
get where this is going, this doesn't just represent
two, it represents two hundredths I'm just going
to make it very explicit in this video, so it's
very clear two hundredths. Another way to write that
is you just write a two in the hundredths place. So we're going one two spaces
to the right of the decimal or you could write it as two
over 100, two hundredths. And so for kicks, pause
the video what are all the different ways of
representing this six? What does this six represent? Well this is six thousandths,
six thousandths, thousandths, there you go. I could also write that as
zero point, let's see it's the tenths place,
hundredths place, and then in the thousandths place I
have six or I could write this as six over 1000, six thousandths. So big picture place value we
can keep going to the right of the decimal and we can
start representing things that are I guess you
could say more precise.