Lesson Video: Place Value of Three-Digit Numbers Mathematics • 2nd Grade

Video Transcript

Place Value of Three-Digit Numbers

In this video, we’re going to learn how to recognize numbers from a model of hundreds, tens, and ones. And we’re also going to learn how to state the place value of digits in a three-digit number. Let’s make a three-digit number out of place value blocks. To make our number, we’re going to need three different types of blocks: some hundreds, some tens, and some ones. Let’s take three hundreds, five tens, and we’ll have eight ones. What number have we made? We’ve got three hundreds blocks. So we know that these have a value of 300. Our five tens are worth 10, 20, 30, 40, 50. And of course, our eight ones are worth eight. So we’ve made the number 358.

Now, how can we write the number 358 using digits, like this? Can you see what we’ve done here? We’ve written the numbers 300, 50, and eight all in a long row. This isn’t correct though. It’s not how numbers work. A number that contains hundreds, tens, and ones only needs three digits. Remember the title of this video, Place Value of Three-Digit Numbers. We only need a digit to represent the number of hundreds, one to represent the number of tens, and one for the ones.

Now, we have three hundreds, five tens, and eight ones. So we can write the number 358 using the digits three, five, and eight. This is where these place value arrow cards come in really useful. When they’re split up like this, we can see the value of each digit. We have 300, 50, and eight. But if we push them together, we can see how to write the number using three digits. Three hundreds, five tens, and eight ones are 358.

Now, it’s really important that we understand the value of each digit when we’re working with three-digit numbers. Which of these digits is worth the most? Well, if we took these three cards and put them anywhere on the page, all we can see are the digits two, four, and nine separately. And of course, we’d say nine is the largest digit, isn’t it? But as soon as we put these digits together to make a three-digit number, the position or the place of each digit really matters.

Imagine for a moment that you’ve seen this lady. But the position or the place that you’ve seen her is sitting next to you on the bus with her shopping on her lap. You probably wouldn’t think she was a queen, would you? She looks like a queen, but she’s not in the right place or position. But if you saw her on a golden throne, there’s a different story. Now, her position tells you that she probably is the queen.

So to find out which of our three digits is worth the most, we don’t just look at the digits, but we look at what position they’re in. Out of the digits two, four, and nine, nine is the largest digit. But where is it in the number? It’s sitting in the ones place, isn’t it? Its value is nine ones. Now, on its own, the digit four is less than nine. But in this number, it’s sitting in the tens place. It has a value of four tens or 40.

So is the digit four worth the most? No, because although the digit two looks like the smallest digit if we looked at it on its own, it’s the king or queen of our number, isn’t it? We’ve put it in the most important position. It’s in the hundreds place. And so our tiny little digit two has a value of 200.

To find the digit with the largest value in this number, we need to look at the place that has the largest value. So we can say that in the number 249, the digit that’s worth the most is the two. The lowest, the largest digit on its own, the digit that’s worth the least in this number, is the nine, nine ones.

Let’s try answering some questions now where we have to think carefully about the place value of three-digit numbers. And remember, it’s all about the position we put our digits in.

Using a place value grid, we can figure out the value of each digit. To find the value of the three in 435, I can write the digits into the grid: four hundreds, three tens, five ones. The three is in the tens column. So I know the three has the value of three tens, which is the same as 30.

Use a grid to help you find the value of the six in 126.

We’re given a three-digit number in this problem, aren’t we? It’s the number 126. And of course, it’s made up out of the digits one, two, and six. Now, we’re being asked to find the value of the six in this number. What is this six digit worth? But we know that the value of a digit in a three-digit number depends on where it is in the number. Its position really matters.

Let’s draw a grid to help us, exactly the same as the one we’ve just looked at. As it’s a three-digit number, we’re going to need three columns for our hundreds, tens, and ones. And to help us remember what each one of these is worth, we could pop a hundreds block in the hundreds place, a tens block in the tens place, and a one in the ones place. Now, we can write our three-digit number in the grid, 126.

Rather than having just one block in each column, should we try to make the number? We already have one hundred, so that can stay the same. But we’ll put in one more tens so that we’ve got two tens. And five more ones will give us six ones. By using that place value grid to help us, we can see where the digit six is. It’s in the ones place, isn’t it? And because it’s in this position, we know what the six is worth. The value of the six in 126 is six ones.

Select the number that has a two in the hundreds place.

We’re given four numbers as possible answers to this question. Can you see? They’re all made up of three digits. And our job is to select or to choose the number that has the digit two in the hundreds place. Now, we know that the digits in three-digit numbers like this all have a different value. If we read each number from left to right, the digits are worth hundreds, tens, and ones.

Let’s look at the first number to begin with. It’s made up of a six followed by a two and then a three. This number has a two in it. But when we look at our grid, we can see that the two is in the tens place. This isn’t the number we’re looking for, is it? The digit two has a value of two tens or 20. And we read this number as 623.

Our second number starts off with a seven. So that’s a seven in the hundreds place. We can see straight away that this isn’t the number we’re looking for, is it? It has five tens. And this number also includes a digit two. But this time, it’s in the ones place. In this number, the digit two has a value of just two. And we’d read this number as 752.

Now, this next number is the number we’re looking for. But can you see why? Maybe if we write it on our grid, you’ll be able to see. We have two in the hundreds place. The rest of the number has a four in the tens place, which is the same as 40, and a five in the ones place, 245. This is the number that has a two in the hundreds place. And if we just check the last number, we can see this contains two twos. But neither of them are in the hundreds place, are they? We know that when we read a three-digit number from left to right, the first digit we see is the hundreds place. And the only one of these numbers that has a two in the hundreds place is 245.

Find the value of the nine in the number 192.

We’re given a three-digit number in this question. And it’s made up of the digits one, nine, and two. Now, we know that a digit’s position in a number gives it its value. And in this question, we’re thinking about the digit nine. It’s in the middle of our number, isn’t it? But what’s its value? Let’s use a place value grid to help us.

We know that three-digit numbers are made up of hundreds, tens, and ones. Now, our number, which is made up of a one and nine and a two, has a one in the hundreds place and nine in the tens place and the digit two in the ones place. We could also use place value equipment to model this number: one hundred, nine tens, and two ones.

Now, if we want to think about the digit nine in our number, we need to think about the middle column, don’t we? The nine is worth nine tens. Now, what’s the value of this? 10, 20, 30, 40, 50, 60, 70, 80, 90. We read our number as 192. And because the digit nine is in the tens place, we know that it has a value of 90.

In which of the following numbers does the digit nine have the smallest value?

What do you notice about the four numbers that we’re given in this problem? Well, you might notice that they’re all made up of three digits. They’re all three-digit numbers. But if we look more closely, what else can we see? They’re all made up of the same three digits, aren’t they? They all contain a one, a nine, and a two. And you know, we could make some of these numbers by taking digit cards that have a one, a nine, and a two on them and just swapping them around. Here’s our second number, our third number, and our last number.

So we can see that all four possible answers contain a one, a nine, and a two. But it’s the nine that we really want to be thinking about because our question asks us, in which of the numbers does the digit nine have the smallest value? And to be able to answer this question, we need to think about what the value of each place in a three-digit number is worth.

Now, we know that the digits in a three-digit number are worth hundreds, tens, and ones. Here’s a hundred. This is what a ten looks like. And here’s a one. Now, if we look at our four numbers, we can see that the digit nine sometimes appears in the hundreds place, sometimes in the middle of the number, which is the tens place, and sometimes in the ones place. Now, which is the smallest value, hundreds, tens, or ones?

Well, we know it’s the ones, don’t we? This is the digit on the right of the number. And can you see which of our numbers has a nine in the ones place? The number where the digit nine has a smallest value is this number here. It’s 129. We know that the smallest value place in a three-digit number is the ones place. And so we were looking for the number that had nine in the ones place. Instead of being worth 900 or 90, the nine in this number is just worth nine. The digit nine has the smallest value in the number 129.

What have we learned in this video? We’ve learned how to recognize numbers from a model of hundreds, tens, and ones. We’ve also learned how to recognize the place value of digits.