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Lesson Video: Ordering Four-Digit Numbers Mathematics

In this video, we will learn how to order four-digit numbers by comparing thousands, hundreds, tens, and ones.

17:36

Video Transcript

Ordering Four-Digit Numbers

In this video, we will learn how to order four-digit numbers by comparing thousands, hundreds, tens, and ones.

Here’s a set of zero to nine digit cards and a place value table. Let’s choose four different digit cards and place them into the table. Let’s start by placing our three digit in the thousands column. Our hundreds digit is a five, our tens digit is an eight, and our ones digit is a six. The position of each of these digit cards tells us the digit’s value. The three digit is in the thousands column. We can model this using three 1,000 place value counters. The three digit in our number is worth 3,000. The hundreds digit is a five. The five is worth 500. There are eight 10s, and we know that eight 10s are worth 80. The six digit in our number is worth six ones.

Can you say the number that we’ve made? It’s 3,586. We would write our four-digit number like this. Did you notice we separated the thousands and the rest of the number using a comma? This helps us to read the number correctly. We know we have an amount of thousands, followed by the rest of the number. We’re going to use our knowledge of place value to help us order four-digit numbers from greatest to least or from least to greatest. To do this, we’re going to have to look very carefully at the value of each of the digits.

A group of friends are doing a project about dinosaurs. They’ve researched the mass of dinosaurs and made this table. Now they want to order the dinosaurs from lightest to heaviest. Let’s write the mass of each dinosaur into our place value table. This will help us to compare the value of the digits. Tyrannosaurus has a mass of 6,350 kilograms. The mass of Plateosaurus is 1,814 kilograms. The mass of Albertosaurus is 2,722 kilograms. And the mass of Ceratosaurus is 1,361 kilograms.

Remember, we’re trying to order the mass of the dinosaurs from lightest to heaviest. Which digits should we compare first? To find the dinosaur which weighs the least, we need to find the mass with the least amount of thousands. Plateosaurus and Ceratosaurus both have a one digit in the thousands column. So we know that one of these two dinosaurs weighs the least. To help us find out which one, we’re going to need to move into the hundreds column. Which of our two numbers is worth more? 1,814 has eight 100s, and 1,361 has three 100s. We know that three is less than eight, so three 100s are worth less than eight 100s. So we know the dinosaur which weighs the least is Ceratosaurus with a mass of 1,361 kilograms, followed by Plateosaurus with a mass of 1,814 kilograms.

Now we just need to compare 6,350 with 2,722. Both of these four-digit numbers have a different thousands digit. 6,350 has six 1,000s. 2,722 only has two 1,000s. So 2,722 kilograms is less than 6,350 kilograms. The dinosaur which weighs the least is Ceratosaurus, followed by Plateosaurus, Albertosaurus, and the heaviest dinosaur is Tyrannosaurus. We compared the mass of each dinosaur, and we ordered them from lightest to heaviest. To do this, we had to compare the value of thousands and the hundreds. Sometimes when we’re comparing numbers, we also have to compare the tens and ones.

So far, we’ve learned that when we’re comparing four-digit numbers, we’re comparing numbers which have a thousands, hundreds, tens, and ones digit. When we compare four-digit numbers, we need to compare the thousands, hundreds, tens, and ones. Let’s practice what we’ve learned so far by answering some questions.

Order the following numbers from greatest to least.

In this question, we’re shown three four-digit numbers, and we have to order these numbers from the greatest to the least. Let’s use a place value table to help us compare our three four-digit numbers. Our first number has three 1,000s, four 100s, no 10s, and eight ones. This is the number 3,408. Our second number also has three 1,000s. It has five 100s, four 10s, and no ones. It’s the number 3,540. Our final four-digit number also has three 1,000s. It has three 100s, eight 10s, and no ones.

We’re looking for the greatest number. We could start by comparing the thousands digits. But that’s not going to help us very much because each of our numbers has three 1,000s. Let’s move into the hundreds column. Which of our numbers has the most amount of hundreds, four 100s, five 100s, or three 100s? Five 100s are worth more than four 100s or three 100s, so the greatest number is 3,540. Which of our two remaining numbers is the greatest, 3,408 or 3,380? We already know that both numbers have the same amount of thousands. So again, we’re going to have to compare the hundreds digits. And we know that four 100s are worth more than three 100s. 3,408 is greater than 3,380.

We’ve ordered the numbers from greatest to least. The correct order is 3,540, 3,408, and 3,380.

Order the following numbers from least to greatest.

In this question, we’re comparing three four-digit numbers. We have to order these three numbers from the least to the greatest. Let’s compare our numbers using the place value chart. Our first four-digit number has one 1,000, no 100s, nine 10s, and no ones. The number is 1,090. Our second four-digit number also has one 1,000. It has one 100, nine 10s, and no ones. And our third four-digit number also has one 1,000. It has no 100s, no 10s, and nine ones.

Which of our three four-digit numbers is worth the least? Let’s start by comparing the thousands digits. Each of our numbers has the same amount of thousands. They all have a one digit in the thousands column, so we need to compare the hundreds digits. The number 1,090 has no 100s, and the number 1,009 also has no 100s. But 1,190 has one 100, so we know this is the greatest number. Let’s cross that number out. Now we can compare our two remaining numbers. We need to compare the tens digit. 1,090 has nine 10s, and 1,009 has no tens, so we know 1,090 is worth more than 1,009.

We compared the value of the thousands, hundreds, and tens digits and ordered the numbers from least to greatest. The correct order is 1,009, 1,090, and 1,190.

Fill in the blank: 2,415 is less than what, which is less than 2,561, which is less than 2,678. Is the missing number 2,574, 2,387, 2,487, or 2,450?

In this question, we have to find the correct number to place in between the numbers 2,415 and 2,561. Our number is greater than 2,415 but less than 2,561. Let’s use our place value table to help us find the number between 2,415 and 2,561. Let’s start by looking at our first number, 2,574. Each of our numbers has a two in the thousands place. Each number is worth 2,000 and something. We’re going to need to compare the hundreds digits.

Our first number has four 100s, and the others have five 100s. We know that five 100s are worth more than four 100s, so this could be the number we’re looking for. But we’re going to need to compare the tens digits. 2,574 has two 1,000s, five 100s, and seven 10s. 2,561 has two 1,000s, five 100s, and six 10s. The number we’re looking for has to be worth less than 2,561. So this can’t be the number we’re looking for because seven 10s are worth more than six 10s, not less.

Let’s try a second number, 2,387. Again, each of our numbers has the same amount of thousands. 2,415 has four 100s, and 2,387 only has three 100s. We’re looking for a number which is greater than 2,415, and we know that three 100s are worth less than four 100s. So this is not the number we’re looking for either. Is 2,487 greater than 2,415? Both of these numbers have two 1,000s, and both numbers have four 100s. Let’s compare the tens digits. 2,415 has one 10. 2,487 has eight 10s. Eight 10s are worth more than one 10, and eight 10s are worth more than six 10s. But 2,561 has five 100s, so it’s worth more than 2,487. This could be the number we’re looking for. 2,415 is less than 2,487, which is less than 2,561. The missing number is 2,487.

Rearrange the digits of the number 7,013 to get a 4-digit number that’s as close as possible to 1,000.

This question is all about place value of four-digit numbers. We’re given a four-digit number, which is 7,013. And we’re told to rearrange the digits to make a four-digit number that’s as close to 1,000 as possible. To help us answer this question, we can use a place value table and some digit cards. We’ve got a seven digit in the thousands place, a zero digit in the hundreds place, a one digit in the tens place, and a three digit in the ones place. We have to rearrange these digits to make a number which is as close as possible to the number 1,000. We could start by putting our one digit in the thousands column.

Which of our three remaining digits should we place in the hundreds column? Which has the least value, seven 100s, no 100s, or three 100s? It’s no 100s, so we can place the zero digit in the hundreds place. So far, we’ve got one 1,000, no 100s, and we still have two more digits to place into the place value table. Which digit should we place in the tens column? Which is worth less? Three 10s are less than seven 10s, which means we need to put our seven digit in the ones place. We rearranged the digits of the number 7,013 to get a four-digit number that’s as close as possible to 1,000. The number we made is 1,037.

What have we learned in this video? We’ve learned how to order four-digit numbers by comparing thousands, hundreds, tens, and ones.

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