- [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.