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## 4th grade

### Course: 4th grade > Unit 1

Lesson 6: Comparing multi-digit numbers# Comparing whole number place values

CCSS.Math:

Sal compares whole numbers written in expanded form, written form, and number form. Created by Sal Khan.

## Want to join the conversation?

- so 7907 is lessthanthe ader number(5 votes)
- jackie, you are correct, 7907
**is less than**7970.

One way to show that something is*"less than"*something else (in mathematics) is to use the "`<`

" symbol. So, as Sal explains at1:07, when you use the "`<`

" symbol you are saying that the number on the left of the symbol is*"less than"*the number on the right. This means that you would write the comparison as:`7907 < 7970`

(20 votes)

- Who else thought this was really ez(11 votes)
**Me**. I thought that.(2 votes)

- What is the difference between natural numbers and whole numbers? My 3rd Grade teacher only uses the word "natural numbers" but the title says " Comparing whole number place values" .(5 votes)
- How about negative numbers ? Is -1 a whole number ?(4 votes)

- what tools would you use to help you figure out the answer?(4 votes)
- Can math get harder than: place value when multiplying and dividing by 10.(3 votes)
- Yes, math can get harder than this. There’s multi-digit multiplication (by numbers other than just 10), multi-digit division (by numbers other than just 10), operations with fractions, operations with decimals, percents, conversion between fractions & decimals & percents, exponents & roots, operations with signed numbers (positives and negatives), pre-algebra, algebra 1 & 2, geometry (which could have proofs), trigonometry, probability & statistics, pre-calculus, calculus, and much more! There is always something new and interesting to learn in math.

Have a blessed, wonderful day!(3 votes)

- every negitive number is a whole number.(2 votes)
- Negative numbers are not considered whole numbers, just the counting numbers 0, 1, 2, … If you want to include the negatives of the counting numbers, you have to say they are integers. There are also negative numbers which are not integers such as -1.5.(4 votes)

- hello whats up yo(3 votes)
- Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand. You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000. I don't know if that helps you or not. And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is just equal to 7. So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I'll scroll to the right a little bit. So either of these could be considered expanded form.Write 14,897 in expanded form. Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits. So we have 14,000. I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form. So let's think about what place each of these digits are in. This right here, the 7, is in the ones place. The 9 is in the tens place. This literally represents 9 tens, and we're going to see this in a second. This literally represents 7 ones. The 8 is in the hundreds place. The 4 is in the thousands place. It literally represents 4,000. And then the 1 is in the ten-thousands place. And you see, every time you move to the left, you move one place to the left, you're multiplying by 10. Ones place, tens place, hundreds place, thousands place, ten-thousands place. Now let's think about what that really means. If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up. Actually, let me start at the other end. Let me start with what the 7 represents. The 7 literally represents 7 ones. Or another way to think about it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let's think about the 9. That's why I'm doing it from the right, so that the arrows don't have to cross each other. So what does the 9 represent? It represents 9 tens. You could literally imagine you have 9 actual tens. You could have a 10, plus a 10, plus a 10. Do that nine times. That's literally what it represents: 9 actual tens. 9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it. So let me write all the different ways to think about it. It represents all of these things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents-- we see it's in the hundreds place. It represents 8 hundreds. Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800. That 8 literally represents 8 hundreds, 800. And then the 4. I think you get the idea here. This represents the thousands place. It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000. 4,000 is the same thing as 4 thousands. Add it up. And then finally, we have this 1, which is sitting in the ten-thousands place,W(3 votes)
- Sal, would you ever become a math teacher?(1 vote)
- my grandson and I need help, the no. is 2,358. We have a box that asks for the unknown no. blank + Blank = what and then below it another set of the same thing. How do we do this?(1 vote)

- 55789 is greater than 368(1 vote)

## Video transcript

Compare the expressions on both
sides of the question marks. So on the left-hand side of the
question mark, I have 7,907. So, it's 7,000 plus
900 plus 7, which is going to be the
same thing as 7,907. Now let's compare
that to what we have on the right-hand
side of the question mark. On the right-hand side, we have
7,000 plus 970, which is 7,970. Or if we wanted
to expand it out, we could write that as
7,000 plus 900 plus 70, and then we have 0 ones. So if we compare place
value by place value, we have 7,000 in either case. So the thousands
place is the same. We have the same
number of hundreds. We have 9 hundreds. But here we have no
tens, and we have a 7. And here we have no
ones, and we have 70. And clearly, 70
is greater than 7. So the number on
the right is greater than the number on the left,
or the number on the left is less than the
number on the right. I always remember
the less than symbol because it points to the
smaller number, or either of these symbols point
to the smaller number. So this right over here
would mean greater than. You have the larger
number on the left. This is less than. You have the smaller
number on the left. So we would go with less than. This is less than that.