Place Value 3 Place Value 3
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- 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.
- 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.
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