Writing Four-Digit Numbers in
In this lesson, we’re going to
learn how to write four-digit numbers in digit, word, and expanded forms. To help us write four-digit numbers
in different ways, we need to understand what each digit is worth. So, let’s begin at the beginning
and start with our knowledge of place value.
The place in a four-digit number
that has the smallest value is the ones place. We know we can have anywhere
between zero and nine ones. But as soon as we get to 10 ones,
we have to start thinking of the next place along. And that’s the tens place. And again, we can go anywhere from
zero 10s up to nine 10s. But as soon as we get to 10 10s, we
start to think about the next place. 10 10s are worth the same as
And we know that a number that just
contains hundreds, tens, and ones is a three-digit number. But in this video, we’re thinking
about four-digit numbers, so we need to think about the next place along. Do you remember what this one’s
worth? We can show anywhere between zero
and nine 100s, but we know that 10 100s are worth 1000. And so, the first thing we can say
about the numbers that we’re going to be looking at in this video is that they’re
all going to contain a number of thousands, hundreds, tens, and ones.
And before we move on, there’s
something else that’s going to help us in this video, particularly when we’re
writing four-digit numbers using digits. And that’s it is we learn about
larger and larger numbers with more and more digits. If we just write them as they are,
we could just end up with a long string of digits. And then it becomes quite difficult
to work out what each digit’s worth and how to read the number. So instead, what we try to do is
think of our digits in groups of three. Our first group of three are our
hundreds, tens, and ones. And so far, that’s all we’ve had to
think about with numbers.
But now, we’re starting to think
about four-digit numbers. We’ve moved in to the next group of
three digits. We’ll come back to this idea later
on, but for now we can just remember that our hundreds, tens, and ones are part of a
group together. We could call this our ones
group. And our thousands are part of the
next group along. And this is our thousands
group. We’ll see how this affect how we
write numbers later on. But to begin with, let’s use some
place value blocks to model a four-digit number.
Here we are. Let’s write down how many of each
type of place value block we’ve got. We have three 1000s. Our hundreds blocks are grouped in
twos. So, we can see two, four, six,
eight 100s. We’ve got four 10s and three
ones. And you know by writing down the
exact number of thousands, hundreds, tens, and ones that we’ve got, we’ve written
our number in what we call unit form. We’ve said how many of each place
value unit we’ve got: three 1000s, eight 100s, four 10s, and three ones.
How else can we show this
four-digit number? The quickest way for us to show a
four-digit number is not to get out our place value blocks and put them all out on
the table, or even to write it in unit form. The quickest thing we can do is
just to write four digits: a three in the thousands place, an eight in the hundreds
place, a four in the tens place, and a three in the ones place. Now, we could just write our
four-digit number like this. But you remember what we said a few
moments ago about having a long string of digits that can be difficult to read. Do you remember how we talked about
grouping our digits in threes and how our thousands digit is in a group on its
Well, we can show this when writing
four-digit numbers using digits. Sometimes, you might see a number
written with a small gap between the thousands and the hundreds digits. Can you see that by doing this, the
hundreds, tens, and ones digits are in a little group on their own, aren’t they? But another way to do this, and
this is what we’re going to be doing in this video, is to put a comma in between the
thousands and the hundreds digits.
So far then, we’ve represented our
four-digit number using a place value model in unit form and also in digit form. But you know we haven’t tried
saying this number yet. How can we use words to represent
our number? We can see a three in the thousands
place, so that’s three thousand. We know we have eight 100s, so we
can just say eight hundred. And then, as usual, we can look at
the last two digits together and read them as a two-digit number. We have four 10s, which are worth
40, and three ones. So that’s forty-three. And we can say the whole number as
three thousand eight hundred forty-three.
Now, in this video, we’re also
going to look at one more way to represent a four-digit number. And we call this using expanded
form. We can take our number using
digits: three eight four three. And we can expand how we think of
it by looking at each part separately. We can partition it or split it up
into 3000, 800, 40, and three. And if we want to express our
number in expanded form, we need to write these four parts as an addition. Because 3000 plus 800 plus 40 plus
three is exactly the same as 3843. We’ve just expanded it out to show
each part as an addition.
So, in this introduction, we’ve
looked at five different ways to show four-digit numbers. But there are lots more. We could’ve used place value
counters or even an abacus. How well do you think you can read
and write four-digit numbers in these different ways? Let’s practice what we’ve learned
by answering some questions.
Write the number shown in
We can write and show numbers in
lots of different ways. The picture shows a number modeled
using an abacus, and we’re told to write the number that it shows in digits. So, let’s begin by looking at our
abacus. What can we tell about the number
that we need to write? Firstly, we can see that underneath
our abacus, there are some letters, and these label the different place values of
We already know that O stands for
ones, T stands for tens, and the letter H is for hundreds. But in this question, we’re moving
on to a fourth place. The letters Th stand for
thousands. And because our number has four
places, thousands, hundreds, tens, and ones, we know that we’re going to need four
digits to show it. Let’s count how many beads are
representing each place.
There are one, two 1000s. So, we’re going to need to use the
digit two in the thousands place. Then there are one, two, three,
four 100s. So, we need to write the digit four
in the hundreds place. There are one, two, three, four,
five, six 10s. And there are two ones. Our number is 2462. Now, we could just write our four
digits in a row like this. But as we learn about larger and
larger numbers, writing digits in a string like this can make it harder for us to
see what each one’s worth. And that’s why we can think of our
digits in groups of three.
We’ve got our hundreds, tens, and
ones on the end. And we can think of our thousands
as being part of a new group. And that’s why we can write our
digits with a small gap in between the thousands and the hundreds digit or, as we’re
going to do here, we could put a comma. And whenever we see that comma, it
helps us remember that the digit before it is the thousands digit. We’ve written the number shown on
the abacus using four digits. We recognize the number as 2462,
and we can write this number as two comma four six two.
Write this number in words.
Normally, when we’re going through
these questions, we read out the question exactly as it’s written so that we
understand what it’s asking us. But did you notice? As this question was read aloud, we
didn’t read the number. We just said write this number in
words. This is because if we’d have read
the number aloud, we’d have given the answer before we started. This question is all about writing
a number in words. So, let’s spend some time having a
look at this number and thinking about how we can say and write it in words.
Firstly, we can see that our number
has four digits. And so we know it has a number of
thousands, hundreds, tens, and ones. And to help us write this number in
words, we need to think about what each digit is worth, where it belongs in the
number. The nine digit is in the thousands
place; that’s worth 9000. The digit two is in the hundreds
place, so that’s worth 200. The digit seven comes next; that’s
in the tens place. And seven 10s are worth 70. And then the digit five is in the
ones place. Our number is 9275.
Can you see where each part of our
number comes from? In this question, we were given a
four-digit number made out of the digits nine two seven five. We’ve used our knowledge of place
value to help write the number in words. We can write this number as nine
thousand two hundred seventy-five.
Write the following number in
expanded form: 1384 equals what. 4000 plus 800 plus 30 plus one,
1000 plus 300 plus 80 plus four, 1000 plus 300 plus 40 plus eight, or 3000 plus 100
plus 80 plus four.
We know that we can express numbers
in lots of different ways. In this question, we’re given a
four-digit number. And the way that it’s written in
the question we’d say is it’s in digit form. We’ve just got those four digits
written: one three eight four. And our question asks us to write
this number in a different way. We need to write it in expanded
form. We know when something expands, it
gets bigger or it opens up. And if we want to write a number in
expanded form, we need to take that number and open it up into its different
parts. A four-digit number is made up of
thousands, hundreds, tens, and ones. And so we need to split up our
four-digit number into four parts.
We could sketch a part–whole model
to help us here. Perhaps, we ought to call it a
part, part, part, part–whole model. To begin with, let’s write our
whole number, 1384. Let’s begin by looking at our first
digit, one. Is it worth one, 10, 100, or
1000? Well, if we think of the four
places that make up a four-digit number, we know that the first digit is the number
of thousands that we have. And if there’s a one in the
thousands place, this has a value of 1000.
Now, if we pause for a moment to
look at our possible answers, we can see that they are four different additions. They show a number of thousands
added to a number of hundreds plus a number of tens and a number of ones. Now, as we’ve seen already, the
thousands digit in our number is one, and this has a value of 1000. So, can you see which answers might
be correct here? It’s not the first addition because
that begins with 4000. And we know it’s not the last
edition either; that begins with 3000. But it could be either of the other
Let’s carry on splitting up our
four-digit number. And we’re on to the second digit,
three. Now, this digit is in the hundreds
place, and three 100s have a value of 300. But can you see if we go back to
our two possible answers, both of them show 300 being added. In fact, the only difference
between them is the number of tens that are being added and the number of ones. So, let’s finish off expanding the
tens and ones in our number. In the tens place, we have the
digit eight. And we know that eight 10s have a
value of 80. And then, finally, in the ones
place we have the digit four.
And so, by looking at our
part–whole model, we can say that the number 1384 can be split into 1000, 300, 80,
and four. And so we can see the answer. We’ve expanded a four-digit number
into its thousands, hundreds, tens, and ones. And we’ve written these as an
addition, just the same as writing the number in expanded form. 1384 is the same as 1000 plus 300
plus 80 plus four.
This number is written in unit
form: two 1000s, four 100s, eight ones. Write the number using digits.
In this question, we’re given a
number that’s been written for us in unit form. In other words, it’s been written
in such a way that we can see the different place value units. It tells us how many thousands we
have, how many hundreds, and so on. Now, when we normally see a number,
we don’t usually see it written in unit form. We would normally write a number
using digits; it’s the quickest way to write numbers. And this question asks us to write
this number using digits.
So, when we look at the different
place value units that make up our number, we can see that it’s made from two 1000s,
four 100s, and eight ones. So, that’s a three-digit number,
isn’t it? What do you think? How many digits are in our
number? Well, it is true that there are
only three place value units that are mentioned: thousands, hundreds, and ones. But if our number contains
thousands, it has to be a four-digit number. We need to show digits to represent
the thousands, hundreds, tens, and ones. Even though there aren’t any 10s to
show, we need to use a zero as a placeholder to show that there are no 10s.
So, let’s go through the different
parts to our number. It has two 1000s, four 100s. We know it has zero 10s. We don’t mention those, but we know
there aren’t any. And it has eight ones. So, we can write our number using
these digits. We can write a little comma between
the thousands and the hundreds digit just to separate out our thousands. It makes it a lot easier to
read. The number that’s written in unit
form as two thousands, four hundreds, eight ones is the number 2408. And we can write this number using
digits: two comma four zero eight.
So, what have we learned in this
video? We’ve learned how to write
four-digit numbers in digit, word, unit, and expanded forms.