Video: Comparing Three-Digit Numbers

In this video, we will learn how to compare numbers up to 1000 by comparing the number of hundreds, tens, and ones.

17:32

Video Transcript

Comparing Three-Digit Numbers

In this video, we’re going to learn how to compare numbers up to 1000 by comparing the number of hundreds, tens, and ones.

Now there are all sorts of ways we could represent three-digit numbers. Let’s start by comparing some objects. And let’s imagine that in a stationery store, notebooks are sold in big bundles of 100, smaller packs of 10, and also on their own in ones. And let’s imagine there’s this many blue notebooks and there are this many red notebooks. Now we know that we’ve got two three-digit numbers represented here because we’ve got a number of hundreds as well as tens and ones. And if we want to compare the blue notebooks with the red notebooks, these two three-digit numbers, where are we going to start? Should we start by comparing the number of ones, the packs of 10, or the bundles of 100?

When we compare numbers, we’ve got to start somewhere. Now perhaps you know already which part of the number we need to start comparing. It’s the part of the number that has the biggest value. In a way, it’s the part that matters most. Now without doing any counting, just imagine that you’ve been given the job of lifting these notebooks to put them in the back of a van. And let’s imagine that they’re as heavy as they look. So the bundles of 100 are really heavy. The packs of 10 are not really very heavy at all. And the individual notebooks on their own are quite light really. And your boss says to you, do you want to take the blue notebooks or the red notebooks? Which would you choose? Or here’s another question. Which part of the number would you be looking at before you made your decision?

Would you make your decision based on the individual notebooks, the packs of 10, or the bundles of 100? Well, if you don’t fancy doing any heavy lifting, I think you might make your decision based on the number of hundreds, don’t you? And this is a rule we can remember whenever we’re comparing numbers together. We always start by comparing the part of the number that’s worth the most. So let’s start by looking at these hundreds. If we have to, we’ll go into the tens and ones, but we might not have to. If we look at the blue notebooks to begin with, we can see two hundreds bundles. So this number contains two hundreds. It’s going to be 200 and something.

But if we look over at the red notebooks, we can see there’s only one bundle of 100. This number is going to be 100 and something. So straightaway we can say which number’s the greatest, can’t we? We can say that there are more blue notebooks than there are red. Even though we know which number is going to be larger, let’s just quickly look at the rest of each number so we can write them down as three-digit numbers. So the blue notebooks are made up of two 100s, one 10, and three ones. This is the number 213. And then the red notebooks are made up of one hundred, five tens, and five ones. This is the number 155.

By the way, before we move on, look at how if we’d have started by comparing the ones, we might have been tempted to say that there were more red notebooks. Good job we started with the bundle that had the biggest value, isn’t it? 213 is greater than 155.

Now there are lots of different ways to represent three-digit numbers, not just with objects. Let’s generate some random numbers by spinning this spinner. There we are. So our first number is going to be made out of place value counters. Okay, and let’s spin again to generate another number. Our second number needs to be represented in words. Okay, now let’s compare our two numbers together. Do you notice something interesting about our first number? There aren’t any place value counters that represent hundreds, are there? We’ve just got tens and ones. So we can say this is going to be a two-digit number not a three-digit number. And if we look at our number that we’ve modeled using words, we can see that there are some hundreds in it. This is a three-digit number.

So we’re comparing a two-digit number with a three-digit number. Now, as we’ve said already, we always start by comparing the part of the number that has the most value. And in the three-digit number, that’s the number of hundreds that we have. But our first number doesn’t have any hundreds. So we don’t need to count anything. We don’t need to even look at the rest of the number. We know which number’s largest. A number with three digits is always larger than a number with two digits because a number with two digits is less than 100 and a number with three digits is 100 or more. So we could use this symbol in between both of our numbers. And let’s quickly write them using digits to show what we mean. Six 10s and two ones is 62. 62 is less than 221.

Let’s try one more example. Our first number is going to need to be written as a numeral, which means using digits. There we are. And then a number written in expanded form. And if you remember, expanded form means we need to separate out the hundreds, the tens, and the ones and write it as an addition. Here we’ve done it using arrow cards. Right, so let’s compare our numbers, shall we? And once again, we’re going to start with the part of the number that has the greatest value. In this case, it’s the hundreds. Our first number is written as a numeral, which means we’ve used digits to write it. Now to help us remember which digit’s which , shall we label them? Now you might think this is a little bit like a place value grid, isn’t it? But it’s going to help us.

So our first number has a four in the hundreds place, which is worth 400. But if we look at the number of hundreds in our second number, we can see that there’s 400 there too. So we’ve compared the part of the number that’s worth the most, but they’re the same. What we do now? Well, we carry on moving through the number comparing the part of the number with the next highest value, which, of course, is the tens. Our first number has a seven in the tens place. We know that seven 10s are worth 70. But the tens in our second number are also worth 70. When we compare three-digit numbers, we don’t always have to go to the ones, but we do in this case because our hundreds and our tens are exactly the same.

Our first number has two ones, but our second number has four ones. And now finally, we can see which number’s the greatest. It’s the second number. The first number is less than the second. And if we read them both as numbers, 472 is less than 474.

Now in a moment we’re going to answer some questions where we need to practice our skills of comparing numbers. But before we do, here’s a quick game for you to see whether you’ve learned what you need to. Let’s imagine you’ve got six digit cards and we’ve used them to make two three-digit numbers. But at the moment, they’re upside down. Now you could compare these numbers by turning over all six cards. But the aim of the game is to compare these two numbers by turning over as few cards as possible. So your question is this. In which order would you turn over the cards to make sure that you can compare the numbers by turning over as few cards as you need to? Would you turn over each of the cards in the first number and then go through the second if you need to? Or maybe you’d compare each type of digit starting with the ones first and so on. What would you do?

Well, hopefully, if you can put into practice what you’ve learned in the video already, you’d start by comparing the digits that are worth the most, the hundreds digits. And if those two hundreds digits are different, we can answer the question in two moves. We can compare the two numbers without turning over anything else. 600 and something is less than 900 and something. And can you see if we’d have started with the ones digits, it wouldn’t really have told us very much. We know eight ones are larger than one one. And we know five 10s are larger than zero 10s. But it’s not until we see those hundreds that we can really compare these numbers.

Right, let’s have a go at answering those questions then.

Compare 251 and 234. Which number is greater?

In this question, we’re given a pair of three-digit numbers, 251 and 234. And we’re told to compare them. We need to find which number is greater. In other words, which is the largest number? Now underneath the question, we can see a place value grid. And place value grids are really helpful when we’re comparing numbers. Do you know why? It’s because they help us to see numbers in terms of the value of their digits, in this case, the hundreds, the tens, and the ones. Now which digit should we start comparing first? Is this like column addition and we need to start with the ones and move from right to left? Should we start with the hundreds and work from left to right? Or doesn’t it matter?

If we think for a moment about the value of each part of our number, we know that the hundreds are worth a lot more than the tens or ones. And because they’re worth a lot more, we need to start by comparing them. They make the biggest difference to our numbers. So let’s start by comparing the hundreds digits in our numbers. We can see that both of our numbers begin with the digit two. They’re both 200 and something. And because the hundred digits are exactly the same, we can’t separate these numbers. We can’t see which one is greater yet. And so this is why we move along down the number to the place with the next greatest value. And that’s the tens digits.

The number 251 has five 10s, and the number 234 has three 10s. These are different, so they’re gonna help us compare the numbers. We know five 10s are greater than three 10s. And now we can see which number’s greater. It doesn’t matter what the ones show us. We’ve compared the hundreds and they were the same. So we moved on to the tens, and we saw that one lot of ten was greater than the other. 251 is greater than 234. The number that’s greater is 251.

Pick the symbol to compare the numbers. 377 what 731.

In this question, we’re given two numbers to compare. And because we can see that they both have the same number of digits, we can’t just compare them by counting the digits. We need to look at what those digits are. These are both three-digit numbers, so they both contain a number of hundreds, tens, and ones. And we’re told that we need to pick the symbol to compare these numbers. Do you remember which symbols we’re talking about here? Remember that when we use comparison symbols like this, we always read the numbers and the symbols from left to right. And also the widest part of the symbol, the open end, always points towards the larger number. So if we used this symbol, we’re saying that the first number is less than the second or we could say the first number is greater than the second. And if we think they’re both the same, then we’d used this symbol here.

Now, for many of you watching this video, you might already know which number’s the least and which number’s the greatest. You might have even spotted as we read the question, we read those numbers out. But before we go through how to find the answer, think for a moment: How do you know which is the greatest? What did you look for? Which part of the numbers did you look at or listen for as they were read aloud? When we compare two numbers together like this, we always look at the part of the number that’s worth the most first. And in three-digit numbers like this, that means the hundreds digit.

Our first number has a three in the hundreds place. This is worth 300. But our second number has a different digit. It has a seven in the hundreds place worth 700. And because these two digits are different, this is all we need to do to compare the numbers together. We know that three 100s are less than seven 100s. And so a number that’s 300 and something is always going to be less than a number that’s 700 and something, isn’t it? 377 is less than 731. The correct symbol to use to compare these two numbers together is the one that represents less than.

Choose the correct symbol to compare the given numbers. 246 what 264.

Here are two three-digit numbers that we need to compare here. And we need to choose the correct symbol to write in between them to compare them. Do you remember what our three symbols mean? The widest part of these arrow-like symbols always points towards the greater number. So with this symbol, the greater number’s going to come first. This symbol means is greater than. Our second number [symbol] is facing the opposite direction, so we can see the smaller end of the arrow comes first. This helps us remember that the first number is less than the second. And, of course, when there is no wide end or thin end and both lines are exactly the same distance apart, this is the equals sign. And it means that they’re both the same.

Now that we’ve reminded ourselves about the symbols, let’s compare the numbers. Do you remember which part of the number we need to compare first? It’s the part with the greatest value. There’s no point looking at the ones first and deciding that one lot of ones is greater than the other because the number of hundreds might be different. The digits with the greatest value are the hundreds digits. But we can see that both numbers have a two in the hundreds place. They’re both 200 and something. So far, the numbers are equal, aren’t they?

We need to keep comparing, so we need to look at the digit that has the next greatest value. And this is the tens digit. Our first number has a four in the tens place, which is worth 40. And our second number has a six in the tens place, which is worth 60. Now that we’ve got two different digits to look at, we can see straightaway which number is larger and which is smaller. Four 10s are less than six 10s. So our first number is less than our second, and we need to use the less than symbol. Although the number of hundreds in our numbers was the same, the number of tens was different. And we used this to compare our numbers together. 246 is less than 264. And so the correct symbol we need to use to compare the numbers is the one that means is less than.

Which is greater, 91 or 736?

Now perhaps by seeing these numbers or listening to them as they were read out, you could spot which of these two numbers was greater. But stop for a moment and ask yourself, how do you know? What was it about these two numbers that told you which one was greatest. Let’s look at each number for a moment and think about it. Our first number is made up of two digits, a nine and a one. In other words, it’s made up of nine of these, or tens. And, of course, we know it’s made up of one of these, a one. But when we look at our second number, we can see it’s longer, isn’t it? It contains more digits.

As well as a tens digit and a ones digit, this number contains a hundreds digit too. There are seven 100s in this number. Now often when we compare numbers, we might look at the digits, compare the nine 10s with three 10s and so on. But here we’ve got a two-digit number and a three-digit number. And we can see straightaway which number’s greater. It’s the number with more digits. The number with three digits is greater than the number with two digits. The greater number out of 91 and 736 is 736.

What have we learned in this video? We’ve learned how to compare numbers up to 1000 by comparing the number of hundreds, tens, and ones.

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