Writing whole numbers in expanded form
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Writing a number in 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.