Writing Four-Digit Numbers in Various Forms
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 100.
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 own?
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 digits.
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 our number.
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 two answers.
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.