Question Video: Use Place Value to Compare Numbers Up to 100000 Mathematics

Use <, =, or > to compare the numbers on each pair of cards. 23,099 _ 23,851. 11,273 _ 9,768. 25,938 + 1,000 _ 26,819 + 100

06:52

Video Transcript

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.

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