Place Value of Numbers up to One
In this video, we’re going to learn
how to write numbers up to one million in standard, word, unit, and expanded
forms. We’re also going to learn how to
state the value of any digit in these numbers. Now, because this video is all
about the place value of large numbers, let’s start by reminding ourselves of how
place value works.
The digit with the smallest value
in a whole number is the ones digit; that’s on the right here. And we can have anything from zero
ones all the way up to nine ones. But if we have 10 ones, we need to
start thinking about the next column along because we know that as we move across
the places of a number from right to left, each new column on the left is worth 10
times as much. So, from tens, we go to
hundreds. 10 100s are worth 1,000. Don’t forget when we write a number
that includes thousands, we usually partition it from the hundreds, tens, and
ones. And the symbol that we’ll use to
partition it in this video is a comma; it just makes numbers easier to read.
Now, if you have place value blocks
in your classroom, probably the largest block you’ll have is a thousands cube like
this. But that doesn’t mean we can’t
still have fun, imagining what larger place value blocks might look like. The next place to the left is worth
10 times 1,000. It’s the ten thousands column. And if there was such a thing as a
ten thousands place value block, it would be the same as ten thousands cubes piled
on top of each other, something like this. Well, you can see why they don’t
make them, can’t you? It’d be a bit silly to have
something this big around the classroom?
So, this is as far as we’ve
probably got with place value. But in this video, we’re going to
look at the next column along. What do you think 10 lots of 10,000
would be worth? Well, 10 times 10 is 100. So, 10 times 10,000 must be
100,000. You can picture taking 10 of those
imaginary 10,000 towers and putting them together. You’d make a really big place value
block like this. It would be made up of 100
thousands cubes. And each one of these, of course,
is worth 1000 ones. Although making up imaginary place
value blocks is just a bit of fun, it does give us an idea of how large these
numbers actually are.
Now, in this video, we’re just
going to be concentrating on six-digit numbers like this. But it’s worth just mentioning the
next column along. What do you think 10 lots of
100,000 is worth? Well, we know 10 times 100 is
1,000. So, you might think the next column
along is going to be worth 1,000 thousands. And in a way, you’d be right. But 1,000 thousands is a bit of a
mouthful. So, instead we give the name for
1,000 thousands a million. And just to give you an idea of
what a million might look like, here’s an idea. It’s not a sort of place value
block you’d want to use, is it?
So, if we started from a six-digit
number like this, 999,996, and we counted on in ones, our ones digit would slowly
change, going up by one each time until we reached 999,999. And one more than this is one
million. We move to the next column
along. And just quickly, to help us read
one million, which is a one followed by six zeros, we use a second comma. This time it separates the millions
from the three digits that represent a number of thousands, hundred thousands, ten
thousands, and thousands. Now although it’s been important to
think about what a million is, in this video, we’re only gonna be thinking about
numbers that go up to a million. So, really, the largest column
we’re going to be looking at is the hundred thousands column.
Let’s begin then by putting six
digits into our grid to make a six-digit number. We can write the six-digit number
that these digits represent in a few different ways. The most common way to represent a
number like this would be to use digits, the same digits that we can see in the
place value grid. And if we were to do this, we’d
need to write the digits two, five, five — and then in between the thousands and the
hundreds digit, we write a little comma to separate them – a six, a seven, and then
the eight. This is writing the number in
digits or standard form.
Another way that we could represent
this number is in words. How would we say or write this
number in words? Well, this is where that comma
helps us. To begin with, we can read the
number of thousands that we have and then read the last three digits as if they were
a normal three-digit number. Our number is 255,678. Now, each of the six places in our
six-digit number is worth a different place value unit. Another way to represent our number
is to say how many of each unit we’ve got: two hundred thousands, five ten
thousands, five thousands, six hundreds, seven tens, and eight ones. And by describing our number in
terms of how many place value units we’ve got, we call this unit form.
Finally, we can write six-digit
numbers in expanded form. This is where we split up our
number to show it as an addition. We’ve got two hundred
thousands. This digit has a value of
200,000. There’s a five in the ten thousands
place, which is worth 50,000. The five in the thousands place has
a value of 5,000. And then the remaining three digits
are worth 600, 70, and eight. So, 200,000 plus 50,000 plus 5,000
plus 600 plus 70 plus eight is the same as 255,678.
Four different ways to represent
the same six-digit number. And there are lots of other ways we
could have modeled this number too, like using an abacus or using place value
counters. Let’s have a go at answering some
questions where we have to represent six-digit numbers in different ways.
Write down the number given in the
figure in digits.
In the figure or the picture that
we can see in front of us, there’s an abacus. And we know that an abacus is a way
of representing numbers. Each set of beads, and in this case
they’re all different-colored beads, represents a different place value column in
the number. We can see that there are six
different sets of beads here, so we know that it’s a six-digit number. And on this abacus, each place
value is labeled, which is really helpful for us.
In the hundred thousands place,
there’s one bead. So, that’s 100,000. Then, we’ve got six beads in the
ten thousands place, these have a value of 60,000, and then another six beads in the
thousands place, or as it’s labeled here the one thousands place. So altogether, the number of
thousands in our number is 166,000. And if we’re representing this part
of our number using digits, we’d write a one, a six, and a six, followed by a comma,
which is to separate the thousands from the next part of our number, the hundreds,
the tens, and the ones. There are two beads in the hundreds
place, these have a value of 200, three beads in the tens place, so they have a
value of 30, and we’ve got five ones. So, the last part of our number
reads 235. So, we just need to make sure that
we write our two, our three, and our five after that comma.
We’ve used what we know about place
value to read this abacus and write the number that it shows in digits. The number is one hundred sixty-six
thousand two hundred thirty-five. And we write it in digits as
one-six-six-two-three-five. And we’ve used a comma to separate
the thousands from the hundreds, tens, and ones.
Write five hundred sixty-nine
thousand eight hundred thirty-two in expanded form.
In this question, we’ve been given
a number in words, but we’re asked to write it a different way in expanded form. Now, when we write a number in
expanded form, we split it up according to the value of each of its digits. And we write the number as an
addition. So, if we want to think about what
each of the digits are worth in our number, let’s write it in digits. And let’s use a place value grid to
Now, the first part of our number
says five hundred, but we know that this isn’t just five hundred. This is part of a number of
thousands. It’s 500,000. So, we’re going to need to write
the digit five in the hundred thousands place. And the whole of our thousands are
569,000. The rest of the number is 832. So, that’s the number 569,832
written in digits. But now we need to expand it out,
split it up, and write it as an addition.
The five in our number has a value
of 500,000. The six in the 10 thousands place
is worth 60,000. Then, we’ve got a nine in the
thousands place, which, of course, is worth 9,000, an eight in the hundreds place,
which is worth 800, a three in the tens place, and this three is worth 30, and then
two ones are worth two. And if we show these six parts as
an addition, this is the number in expanded form. We can write the number 569,832 in
expanded form as 500,000 plus 60,000 plus 9,000 plus 800 plus 30 plus two.
Here’s another six-digit number,
994,647. If we want to think about the value
of the digits in this number, there are two things we can consider. Firstly, we can think about the
place value of a digit. When we’re asked this, we just want
to know what place that digit is in. So, for example, the place value of
the digit six in this number is hundreds. It’s in the hundreds place.
The other thing we can ask is the
value of a digit. This time, we need to say what the
digit is worth. Now, there are two digit nines in
our number, but the value of this particular digit nine is 90,000 because it’s in
the ten thousands place. Do you remember, at the start of
the video, we talked about how the next column to the left of a column is worth 10
times as much? Well, because both our digit nines
are written next to each other. We can say that the nine in the
hundred thousands place is worth 10 times as much as the nine in the ten thousands
place. There are two fours in our number
too, but this time there are two columns apart. So, we know that the four in the
thousands place has a value not 10 times greater, but 100 times greater than the
four in the tens place.
Let’s try answering a question now
where we have to use what we’ve learned about place value.
What is the place value of the
digit six in 631,049?
In this question, we’re given a
six-digit number, and it was read for us in the question 631,049. Now, each of these digits is in a
different place. And we’re asked what is the place
value of the digit six in this number. Let’s sketch a place value table to
help us. It’s going to need six columns, one
for each digit. Let’s write them in. Six-three-one-zero-four-nine. So, we’ve got a six-digit number,
and our question is all about the digit six in this number. What is its place value?
Well, as we’ve seen already, this
is a six-digit number. So, it starts with hundred
thousands digit. And as we read our number from left
to right, six is the first digit; it’s in the hundred thousands place. The place value of the digit six in
the number 631,049 is hundred thousands.
So, what have we learned in this
video? We’ve learned how to write numbers
up to one million in standard, word, unit, and expanded forms. We also learned how to state the
value of each digit.