Lesson Video: Writing Three-Digit Numbers in Various Forms Mathematics • 2nd Grade

In this video, we will learn how to use place value blocks and tables to write three-digit numbers in expanded, unit, and standard form, and in words.

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Video Transcript

Writing Three-Digit Numbers in Various Forms

In this video, we’re going to learn how to use place-value blocks and tables to write three-digit numbers in expanded, unit, and standard form and also in words. Let’s start off by modeling a three-digit number using these place-value blocks. We’ll take some hundreds, some tens, and some ones. Now, as well as modeling this three-digit number using place-value blocks like this, we can also write it in different ways.

The first way we can write this number is using what we call unit form. This is where we write a number using the place-value units to help. Do you remember what our three place-value units are? We’ve got a number of hundreds, tens, and ones. If we count them, we can see that we have one, two, three hundreds. And we can see one, two, three, four, five tens and one, two, three, four, five, six, seven, eight, nine ones. So when we write a three-digit number in unit form, we just say how many hundreds, tens, and ones there are. We could write this number as three hundreds, five tens, nine ones.

Another way we could write this number is using what we call standard form. This is probably the most common way that we write three-digit numbers because we simply write it using three digits. These place-value arrow cards are going to come in useful later on. But they show our number using digits. By writing a three, a five, and a nine next to each other, we can show a number that has three hundreds, five tens, and nine ones. When something gets expanded, it gets bigger. And what we do when we write a number in expanded form is that instead of writing the number 359 next to each other, we expand this or split it up so that we can see the value of each digit. And we’ve already said that our number is made up of three hundreds, five tens, and nine ones.

But a good way of showing our number in expanded form is to take those place-value arrow cards that we had and to split them up. Now we can see what each digit’s value is. Our three hundreds are worth 300, our five tens have a value of 50, and of course, our nine ones are worth nine. And to show that these three parts come together to make one number, we usually write this as an addition, 300 plus 50 plus nine.

The final way that we can write this number is in words. And remember, words aren’t just a way of writing a number; they’re also how we read the number as well. They’re what we say when we see these three digits. And when we try to read a three-digit number like this in words, we usually look at the hundreds digit by itself first and then read the tens and the ones digits together. If we look at the hundreds digit by itself then, we know we need to write or say the words three hundred. And then if we look at the last two digits as a two-digit number, we can see a five and a nine next to each other, fifty-nine. So we can write or say our number using words as three hundred fifty-nine.

Look at all the different ways we can show the same three-digit number. We could even use place-value tables too. We’re going to try answering some questions now, where we have to practice writing numbers in these different ways. But before we do so, let’s remind ourselves of what we’ve learned. We can model three-digit numbers using place-value blocks. Then, if we write them in unit form, this means using the place-value units of hundreds, tens, and ones to help us. This new number has two hundreds, three tens, and zero ones. So writing the number in unit form two hundreds, three tens, zero ones.

Writing the number in standard form means using digits. This is the way we normally write three-digit numbers. We can use a place-value table to help here. So we have a 2 digit in the hundreds place, a 3 digit in the tens place. And to show that we have zero ones, we have to put a 0 in the ones place too. This is why this number in standard form are the digits 230. Writing the number in expanded form means splitting it up so that we can see each digit’s value. The two is worth 200. We know the three is worth three tens, which have a value of 30. And, of course, the zero is just worth zero. So in expanded form, our number is 200 plus 30 plus zero.

And remember, we can write a number in words by looking at the hundreds digit first and then the tens and ones together. We have a two in the hundreds place, so we can say two hundred. And then if we look at the tens and the ones digits together as a two-digit number, we can see the number thirty. This new number is two hundred thirty. Let’s get on with our questions.

Which number is missing from the expanded form?

In this question, we can see two sets of place-value arrow cards. One is labeled digit form and the other is labeled expanded form. Now, our question asks us which number is missing from the expanded form. And if we look at the arrow cards, we can see that one of them isn’t labeled with a number, is it? So really, what the question’s asking us is, what number belongs on this arrow card? And you know when we started off the video, we said there were two sets of arrow cards. That’s not actually true. What we have in this question is one set of arrow cards because how arrow cards work is that we can take a number of hundreds, tens, and ones. But we can combine the cards together to show the same value in digit form.

So what we’ve got in this question is the same set of arrow cards, but we’re working the other way around. We’re starting off with a number in digit form. Let’s label our arrow cards so they’re the same as the ones at the top. We have a seven in the hundreds place, a nine in the tens place, and a five in the ones place. And, you know, we can read numbers like this by looking at the hundreds digit first and then reading the tens and ones digits together. The hundreds digit is a seven, so that’s 700. And then, if we look at the tens and the ones digits together, we can see a two-digit number, can’t we, 95. So we can read this number as 795. And because our number is a three-digit number, if we want to write it in digit form, we just need three digits ⁠— 7, then 9, then 5, 795.

Now we can also show the same value in expanded form. Now, although using expanded form is to do with splitting up a set of arrow cards, it’s really where we show each digit’s value. We know that the seven in 795 is in the hundreds place, so we know this has a value of 700. And we can see when we split up our arrow cards, that’s why we’ve got the number 700 written on the hundreds card. We’ll come back to the tens digit in a moment because this is where our missing number is. But when we look at the ones place, we can see there’s a five, which has a value of five. Five ones are just worth five, aren’t they? And we can see this number on our arrow cards again. So we can see another way of asking this question now, can’t we? In other words, what’s the nine worth in 795?

Now, it would be very easy to just look at our tens digit and think to ourselves, it’s a nine. We write the numbers 795, so surely the missing number is just nine. Now, that’s an easy mistake to make, but we need to think carefully, where is the nine in our number? It’s in the tens place, isn’t it? So it’s not worth nine; it’s worth nine tens. And we know that nine tens have a value of 90. And if we read our number in expanded form, you can sort of hear that the number is correct. 795 equals 700 plus 90 plus five. A nine in the tens place has a value of 90.

500 plus 70 plus two is the expanded form of 572. We can also write it in words as five hundred seventy-two. What is the written form of the expression 100 plus 20 plus nine?

Before we go on to the actual question part of this question, let’s look at the first couple of sentences because they give us some examples that can help us. Firstly, we’re given an addition, 500 plus 70 plus two. But this is not just any old addition. This addition is a way of showing a three-digit number, and that three-digit number is 572. Now, if we were to make the number 572 using place-value blocks, we know that we’d need five hundreds, seven tens, and, of course, two ones. Now, as well as writing this number in digits as 572 and also in words as five hundred seventy-two, we can show this number in what we call expanded form. An expanded form just means showing what each digit is worth.

Now, if we just looked at our five hundreds on their own and didn’t think about any of the other digits in the number, we’d say that the value of what we can see is 500. And if we just look at the seven tens on their own, we know that seven tens have a value of 70. And finally, two ones are worth two, so we can think of the expanded form of a number of sort of splitting it up into different parts. 500 plus 70 plus two equals 572. Now that we understand this, let’s look at the actual question we’ve got to answer, “What is the written form of the expression 100 plus 20 plus nine?”

This looks like a number in expanded form, doesn’t it, just like our 500 plus 70 plus two. Let’s start by modeling this number using place-value blocks, 100 plus 20, which is the same as two tens, plus nine. Now, we can see this is going to make a three-digit number, can’t we, because we’ve got some hundreds, tens, and ones. And our question asks us, what is the written form of this expression? In other words, how can we write this number in words?

Before we do that, shall we work out what number it actually shows. Let’s use a place-value table to help us. We have one hundreds block, so we’ll write a one in the hundreds place; two tens blocks, so we’ll write a two in the tens place; and nine ones blocks, so we’ll put a nine in the ones place. Now, if our question asked us something like, what is this number written using digits, then we now know what the answer is; it’s 129. But we need to write this number using words. And to do that, we need to read it correctly.

Now we know when we read a three-digit number, we should look at the hundreds digit on its own first and then look at the other two digits together. There’s a one in the hundreds place. And we know already that that’s worth 100. And if we look at the tens and the ones digits together, we can see that they show the number 29. So all we have to do to answer the question is to put these two together and show our number using words. The written form of the expression 100 plus 20 plus nine is one hundred twenty-nine.

Fill in the blanks: 987 equals what hundreds plus what tens plus what ones.

In this question, we need to think about this three-digit number. Can you read it? It’s 987. And if someone was asked, “What parts is the number 987 made up of?,” and they said, “Well, well it’s made up of nine plus eight plus seven,” what would you say to them? Well, hopefully you know that although our number is made up of the digits nine, eight, and seven, they’re not worth nine, eight, and seven, are they? In a three-digit number, the three digits are worth hundreds, tens, and ones.

Can you see the words hundreds, tens, and ones in our answer? Let’s draw a place-value table to help us think about what the hundreds, tens, and ones are in our number. Let’s start by putting the digits of our number in the table, 987. Now we can use this to help us fill in the blanks. How many hundreds do we have? There are nine hundreds in our number, and that’s why if we wanted to split our number into parts, we wouldn’t write nine. We write the value of nine hundreds, which is 900. How many tens are there? We can see the digit eight in the tens column, which shows that our number has eight tens. The eight in 987 isn’t worth eight. It’s worth eight tens or 80. And finally, the digit in the ones place is a seven. Our number has seven ones, and seven ones are just worth seven.

If we look at our part–whole model, this looks a lot better, doesn’t it? 900 and 80 and seven go together to make 987. Let’s read through our completed sentence together. 987 equals nine hundreds plus eight tens plus seven ones. Our missing digits are nine, eight, and seven.

What have we learned in this video? We’ve learned how to show and write three-digit numbers in lots of different ways, using place-value blocks, place-value tables, and in expanded, unit, and standard form and in words.

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