# Lesson Video: Writing Five-Digit Numbers in Various Forms Mathematics

In this video, we will learn how to write five-digit numbers in digit, word, and expanded forms.

16:22

### Video Transcript

Writing Five-Digit Numbers in Various Forms

In this video, we’re going to learn how to write five-digit numbers using digits, words, as well as in unit and expanded form. If we’re going to write five-digit numbers in different ways, we’re going to need to understand what each of those digits is worth. So let’s quickly go over our knowledge of place value.

The digit with the smallest value in a five-digit number is the ones digit, over here on the right. Now, in this column, we can show anywhere between zero ones up to nine ones. But this column only holds one digit. So as soon as we get to 10 ones, we need to regroup them because 10 ones are exactly the same as one 10. Again, our tens column can fit anywhere between zero and nine 10s. But as soon as we get to 10 10s, we move along to the next column again and regroup because 10 10s are the same as one 100. And we can use this idea of each new place to the left being worth 10 times as much as the last one as we move along through the columns. We know that 10 100s are the same as one 1,000. These are the place value columns in a four-digit number.

But what do you think the value of our fifth place is going to be? Because we know how place value works, we know that it’s going to have a value of 10 1,000s. And 10 1,000s have the same value as one lot of 10,000. This is the new column that we’re gonna be thinking about in this video. Five-digit numbers contain a number of ten thousands, thousands, hundreds, tens, and ones.

Now, if you remember what you’ve learned about your work with four-digit numbers, you’ll remember that when we write larger and larger numbers, we don’t just write long strings of digits. We often group them in threes to make them easier to read. The hundreds, tens, and ones digits are in a group of three. We call this the ones group. And we did say the thousands digit is in a group of its own, but now we’ve got a new digit to add to this. Both the ten thousands and thousands digits are in the next group along.

And while sometimes you might see a little gap between the thousands and the hundreds digits to show these groups, in this video, we’re going to be using commas. It really helps us to say five-digit numbers aloud because as soon as we see that comma, we can say thousand. So this number here, for example, is 10,360.

Now, before we move on, you may be wondering why we’ve just used place value counters and not place value blocks when we’ve done so much work with them till now. Well, it’s because as we work with larger and larger place values, we need larger and larger blocks. We’d need 10 of these 1,000s cubes to make some sort of a rod. This is what a 10,000s rod might look like. It’s really too big to use. And we’ve learned enough about place value so far to understand what ten thousands are. We don’t need to visualize them like this. And so, in this video, we’ll just be using place value counters if we have to.

To understand all the different ways we can write five-digit numbers, we’re going to need a five-digit number. So let’s model one out of counters. Let’s have five 10,000s, two 1,000s, seven 100s, four 10s, and nine ones. The first way that we could write our five-digit number is by recording all these place value units that we can see. As we’ve just said, we’ve got five 10,000s, two 1,000s, seven 100s, four 10s, and nine ones. By recording the number of ten thousands, thousands, hundreds, tens, and ones that we have, we’ve written our number in what we call unit form. It’s a way of showing all the different place value units that make up our number.

How else could we represent this five-digit number? If we’re looking for the quickest way to show a five-digit number, we don’t want to be modeling it with lots of different place value counters or even writing it in unit form. The quickest thing we can do is simply to write four digits. There are five 10,000s, so we need to write the digit five in the ten thousands place, two 1,000s. Now we’re about to move on to our hundreds. Remember what we said about separating our thousands and hundreds digits? That’s right, a comma.

We have seven 100s, so the digit seven goes in the hundreds place, then four 10s and nine ones. To write our number using digits, we just need to write five-two-seven-four-nine. But that’s not how we’d say this number if we saw it. How would we say or write this number in words?

Well, this is where that comma comes in useful. Because we did say that our ten thousands and thousands digits are read as a number of thousands. When we get to the comma, we say thousands. To the left of the comma then, we have the digits five and two, five 10,000s and two 1,000s. Put them together and we’ve got 52,000. Then we just read the hundreds, tens, and ones as if we were reading a three-digit number. Our number in words is fifty-two thousand seven hundred forty-nine.

Now, in this video, there’s one more way of representing five-digit numbers that we’re going to look at. And this is expanded form. When something expands, it grows; it gets bigger. And when we write a number in expanded form, we separate it out into each of its parts. Instead of writing it using five digits, we expand it out and write down what each of those digits is worth. And we write the number as an addition.

A good way to show this is using arrow cards. Here’s our number modeled out of arrow cards all put together. But then we can expand this out and pull out each individual arrow card and see what they’re worth. As we’ve said already, the five digit is in the ten thousands place. This is the same as five lots of 10,000. 10,000, 20,000, 30,000, 40,000, 50,000. The digit two is in the thousands place. This has a value of 2,000. The seven digit has a value of 700. Four in the tens place is worth 40. And of course nine ones are simply worth nine.

So using expanded form, we’d say our number as an addition, adding all these parts together. It’s worth 50,000 plus 2,000 plus 700 plus 40 plus nine. So if we include our place value model that we started with, we’ve written a five-digit number in five different ways. And we don’t even have to stop there. We could even use something like an abacus to show our number.

Let’s have a go at answering some questions now where we have to read and write five-digit numbers in different ways.

Write eighty thousand nine hundred twenty-seven in digits.

There are lots of ways to represent numbers. And in this question, we’re given a number that’s been written in words: eighty thousand nine hundred twenty-seven. And we’re asked to write this number a different way, in digits. How many digits do you think we’ll need? Or perhaps a better question is, which part of our number should we look at to work out how many digits we’ll need?

Just like any number, as we read it in words, we can see that the place value units get less and less. So, for example, the last number we say, which is the seven in 27, this actually has the smallest place value. This isn’t really a lot of help to us to work out how many digits we’re going to need. But if we look at the other end of our number, that’s the first part that we say, we can see a different story, 80,000. This is the part of the number with the largest place value.

Now, because we can see the word thousand, it might look like we’re talking about the thousands column here. Is this a four-digit number? Well, when we look how many thousands we need, it’s 80,000. We’re going to need five digits to show our number. Let’s draw a place value grid to show this.

If our number was 8,927, then we’d need to write the digit eight in the thousands place. Then it would be a four-digit number we’d be talking about. But we need to show 80,000. And so the digit eight needs to go in the ten thousands place. Eight lots of 10,000 are the same as 80,000. And notice that our number doesn’t say 81,000 or 85,000. It just says 80,000. So we need to put a zero in the thousands place.

Now we’re just left with the hundreds, tens, and ones, and we need to show 927. Well, we know how to do this, don’t we? That’s a nine in the hundreds place, a two in the tens place that represents 20, and a seven in the ones place. And the only other thing that’s useful to remember as we write our five-digit number is that it’s helpful to put a comma after the thousands digit and before the hundreds digit. It’s just a way of separating out the thousands, and it helps us to read the number quickly, 80,927.

We used a place value grid to show that this number contains eight 10,000s, zero 1,000s, nine 100s, two 10s, and seven ones. We can write the number using the digits eight-zero-nine-two-seven.

Write this number in words.

In this question, we’re given a five-digit number. And it’s a good job it wasn’t read to you as we read the question. Then you’d know how to write this number in words straight away. But so far, all we’ve got is this number written in digits.

To work out how to write it in words, we’re going to need to think about the place value of each of these digits. What are they worth? Let’s try modeling our number using place value counters. Let’s start with the lowest-value digit first. So we’re going to need one one, six 10s, six 100s, eight 1,000s, and our largest-value digit, six lots of 10,000. So how would we read this number?

To begin with, what are six lots of 10,000 worth? 10,000, 20,000, 30,000, 40,000, 50,000, 60,000. Let’s make a note of this, 60,000. But wait a moment! We’ve got some more thousands. There’s an eight in the thousands place. Our number isn’t just 60,000; it’s 68,000. Perhaps you noticed a little comma in the number in the question. This comma appears between the thousands and the hundreds digits, and it’s a way of separating out the thousands. So when we see this comma, we can look at it and say thousand, sixty-eight thousand.

Now we just need to say the last three digits. We’ve got a six in the hundreds place, so that’s six hundred, six 10s, which are worth 60, and then our one one. Because we read our last two digits as a two-digit number, we say sixty-one. Perhaps you knew how to write this number without even using the place value counters to help. A five-digit number that’s written 68,661 is written in words sixty-eight thousand six hundred sixty-one.

What is 10,000 plus 2,000 plus 50 plus five in standard form?

In this question, we’re given what looks like an addition, but this is more than an addition. This is a number that’s been written for us in what we call expanded form. Expanded form is a way of writing a number as an addition by showing the value of each of its digits. So we can see with the number that’s being talked about here we’ve got a digit that’s worth 10,000. There’s going to be another digit that’s worth 2,000, one that’s worth 50, and then a digit that’s worth five.

Now, we’re asked to write this number in standard form, in other words, the way that we usually write a number using digits. Because there are four parts to our addition, do you think it’s gonna be a four-digit number? Well, if we look closely, we can see that there’s one type of digit missing. Did you spot it?

Let’s use a place value grid to help us see which one. The first number in this addition is 10,000. So we need to use a digit that represents this value. To show 10,000, we need to write the digit one in the ten thousands place. One lot of 10,000 is 10,000. The next number in our addition is 2,000. So which digit do you think our number has in it and where should we write it?

Well, for a digit to be worth 2,000, it needs to be the digit two and it needs to appear in the thousands place. Our next number is 50. How would we represent 50 in our place value grid? 50 is the same as five 10s. So we need to write the digit five in the tens place. Can you see what’s happened here? We haven’t been given a number of hundreds. We still need to show that there’s an empty hundreds place though, and so we can use zero as a placeholder. And that’s why even though we’ve been given four parts to our addition, it’s actually a five-digit number. We just don’t have any hundreds. Finally then, we need to add five. And to show five in our number, we just write five in the ones place.

We recognized that the addition in the question was a number written in expanded form. To write this number in standard form, we thought carefully about how to create these values by writing digits in the right places. The number is 12,055. And we write this in standard form by writing the digits one-two-a comma-zero-five-five.

What have we learned in this video? We’ve learned how to write five-digit numbers using digits, words, and in unit and expanded forms.

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