Video: Comparing Five-Digit Numbers

In this video, we will learn how to compare whole numbers within 100,000 by considering the place value of each digit.

16:47

Video Transcript

Comparing Five-Digit Numbers

In this video, we’re going to learn how to compare whole numbers with up to five digits. And we’re going to do this by thinking carefully about the place value of each digit.

The Penguins are a world famous rock band, and they’ve recently put out two new records. There’s what they like to call the Blue Album. And it might seem like a funny name for a record, but this one’s called the White Album. Now both of these records are quite popular. We can tell this because underneath the picture of each record, we can see that total sales. And each of these is a five-digit number. The Penguins must have a lot of fans. Let’s read each number. The Blue Album has sold 63,152 copies, and the White Album has sold 63,125 copies. But which record is most popular; which has sold more?

To find the answer, we need to compare these two five-digit numbers and find out which is larger. Now, we know that when we compare two numbers, we need to look at the digits that make them up, and we need to look from one number to the other. At the moment, our two numbers are side by side. Now, we could compare them by looking across from one to the other. But there’s a much better way. By writing each of our numbers in a place value grid, we’ll be able to compare the value of each digit from ten thousands to thousands, hundreds, tens, and then ones. If we want to compare the place value of digits, looking up and down is much easier than looking across.

To begin with then, let’s complete the total sales for the Blue Album, and we said that this’s sold 63,152, and the total sales for the White Album, 63,125. Lots are similar digits there, aren’t there? Now, if we’re going to compare these two numbers together, which digit are we going to start with? Shall we start by comparing the ones digit and then work our way from right to left? Or shall we begin with the ten thousands digits and work from left to right? Well, we know from our experience comparing smaller numbers that we always begin with the digits that are worth the most. And the digits that have the largest place value in these two numbers are the ten thousands digits.

So, we’re going to start with this column and work our way from left to right by looking at our numbers place by place or column by column, it’s almost like we don’t need to worry about the rest of the number. We just need to focus on the one column we’re looking at. So, let’s cover up all the other digits and just focus on the ten thousands digits.

Now, we can see straightaway that both numbers contain a six in the ten thousands place. We can’t separate out one number as being larger than the other, can we? They’re both clearly sixty something thousand and something. So, what do we do? We move on to the next column along. The number 63,152 has a three in the thousands place. Oh, but so does the number 63,125. Both our numbers are sixty-three thousand and something. We still can’t separate them out and see which is larger.

On to the hundreds digits. Both numbers have a one in the hundreds place. So far, they’re exactly the same. But thankfully, as soon as we get to the tens digit, we can see a difference. The Blue Album has sold 63,152. So, in the tens place, there is a digit five. And the White Album has sold 63,125. So, this has the digit two in the tens place.

We’ve worked our way along the number, comparing the place value of each digit from those that are worth the most to those that are worth the least. And now that we’ve found two digits that are different, we can compare the numbers. It really doesn’t matter what the ones digits are. Because the first number has five tens and the second number has two tens, we can tell the first number is larger. 63,152 is greater than 63,125. And that’s how we know out of these two records, the Blue Album has sold more.

Let’s have a go now at answering some questions where we have to compare numbers together and we’ll use a place value grid each time to help us.

Use the symbol for is less than, is equal to, or is greater than to compare the numbers on each pair of cards. 23,099, what, 23,851; 11,273, what, 9,768; and then finally 25,938 plus 1,000, what, 26,819 plus 100.

In this question, we’re given three pairs of cards, and we’re told that we need to compare the numbers on each pair. Let’s start with the first two numbers. How are we going to compare these? Well, we know that to compare two numbers means to look at the digits in those numbers and their place value. And a good way of doing this is using a place value grid. Let’s sketch one for these numbers by writing both numbers in the grid on top of each other. We can compare them digit by digit.

So, our first number has a digit two in the ten thousands place, three in the thousands place. It has zero hundreds, nine tens, and nine ones. It’s 23,099. The number on the second card also has five digits, and some of these digits are very similar. There’s a two in the ten thousands place, a three in the thousands place. This particular number has an eight in the hundreds place, a five in the tens place, and a one in the ones place.

Now that we’ve recorded both of our numbers in a place value grid, it is going to be a lot easier to compare them digit by digit and. To do this, we need to begin with the digits that have the largest value. These are the digits that have the most effect on the number. In other words, we need to start by looking at the ten thousands place. Both our numbers have the digit two in this place, so we can’t separate one number as being larger than the other just by looking at this digit. We’re going to need to carry on and look at the next digit alone. If we compare the two digits in the thousands place, we can see that these are the same too. We still can’t separate out our numbers.

We’re going to have to compare the hundreds digits. Thankfully, we can see that these are different. And so, we now can tell which of our numbers is larger. The number on the first card has a zero in the hundreds place, and the number on the second card has an eight in the hundreds place. And it doesn’t matter about the tens and ones. We know which of our numbers is larger just by looking at the hundreds digit. Our second number is greater than the first. But of course, when we compare two numbers, we read them across from left to right. So, we need to use the less than symbol. 23,099 is less than 23,851.

Now, let’s compare our second pair of cards. Now, we could use a place value grid again to compare these numbers, but can you see something interesting about them? They both have a different number of digits. This is going to make them really quick to compare. In fact, we don’t really need to use the place value grid. Our first number has five digits, so the highest value digit is a ten thousands digit. But our second number only has four digits. So, the highest value digit is only worth thousands.

A whole number with five digits is always going to be larger than a whole number with four digits. So, as we read our numbers from left to right, we’re going to need to use the symbol is greater than. 11,273 is greater than 9,768. And if we complete our place value grid, we can see that the first number has a one in the ten thousands place. But our second number doesn’t have anything.

Now, let’s compare our final pair of cards. These are interesting because each one has an addition written on it. For us to compare these values, we’re going to need to find the total on each card. On our first card, we have 25,938 plus 1,000. Now, what happens if we add 1,000 to a number? Well, there’s a change to the thousands digit. The number 25,938 has a five in the thousands place. But if we add one more 1,000, that five is going to become a six. So, the value of our first card is 26,938.

The addition on our second card is 26,819 plus 100. And we know when we add 100 to a number, it’s the hundreds digit that changes. 26,819 has the digit eight in the hundreds place. But if we add one more 100, our number will contain nine hundreds. So, the value of this particular card is 26,919. This time, both of our values have the same number of digits. So, we’re going to need that place value grid again.

Starting with the place that has the largest value, we can see that both numbers have a two in the ten thousands place, so we can’t separate them out yet. If we compare the thousands digit, these are the same, so will a hundreds digit. But we can see that that the tens digit are different. And this helps us now to compare the two numbers. 26,938 has a three in the tens place, and 26,919 only has a one in the tens place. That’s how we know the value on the first card is greater than the value on the second.

We’ve used place value grids and also in the second example our knowledge of the number of digits to help us compare the numbers on these pairs of cards. 23,099 is less than 23,851. 11,273 is greater than 9,768. And the value of 25,938 plus 1,000 is greater than the value of 26,819 plus 100.

Fill in the blank using the symbol for greater than, less than, or equal to. Forty-five thousand six hundred fifty-eight what forty-five thousand two hundred fifty-eight.

In this question, we’re given two numbers to compare. Now, usually, when we compare numbers, we might look at each digit one by one, see what they’re worth. But in this particular question, our numbers have been written in words. How are we going to compare them? Well, one way to find the answer might be to draw a place value grid and to actually write each number in digits. Our first number is 45,658, and our second number is quite similar, 45,258. Because our numbers are so similar, as well as comparing them using the place value grid, we could actually compare the words together. Let’s do both at the same time.

When we compare two numbers together, we know that we always start by comparing the digit with the greatest value. And as these are two five-digit numbers, that digit is in the ten thousands place. Both numbers have a four in the ten thousands place. So, we need to go on and look at the thousands place. But they have the same digit here, too. And if we compare our numbers written in words, we can see this. Both numbers begin with forty-five thousand.

We’re going to need to compare the next digit along. That’s the hundreds digit. Our first number has a six in the hundreds place, but our second number has a two. And we can see this difference if we compare the numbers in words. Our first number is forty-five six hundred and something, but our second number is forty-five two hundred and something. It doesn’t matter about the rest of the number. We can compare these two numbers together, just using the hundreds digits. Six is greater than two. So, we know 45,658 is greater than 45,258. The correct symbol to use in between these two numbers to compare them is greater than.

Now, so far, we’ve had a go at comparing five-digit numbers using place value grids. But we can also compare a pair of numbers using a number line. We can estimate where each one belongs. Let’s have a go at comparing two numbers where we use this method.

Is 21,442 less than, equal to, or greater than 21,942?

In this question, we’ve got two five-digit numbers to compare. But did you notice something about these numbers as we read them? They both begin with the same number of thousand, 21,000. It’s only the last part of each number that’s different. This means the numbers must be quite close together. We could use a number line to help compare them.

If both numbers are twenty-one thousand and something, they must come somewhere between 21,000 and 22,000 on a number line. When we’re using a number line like this is always helpful to mark the midway point. And that’s 21,500. So, where does our first number belong on this number line? Where would you put 21,442? Well, twenty-one thousand four hundred and something is just less than 21,500, our midway point. We could estimate that this number is about here.

Now, where does our second number belong? Again, the digit we need to be looking at is the hundreds digit. We know that the ten thousands and the thousands digits are the same. This number is twenty-one thousand nine hundred and something. This is very close to 22,000, isn’t it? And now, we can use our number line to answer the question. We can see that 21,442 is less than 21,942. The correct answer to this question is to use the symbol that represents less than.

What have we learned in this video? We’ve learned how to compare numbers with up to five digits by thinking about the place value of each digit.

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