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Regrouping whole number place values

CCSS Math: 4.NBT.A.2

Video transcript

- [Voiceover] Five thousands equals how many hundreds? There's probably a few ways we could take this on, but maybe let's start by thinking about these five thousands. Five thousands is 1,000, five times. So let's think about each of those thousands, each of those five thousands. In 1,000, how many hundreds are in 1,000? 1,000 equals how many hundreds? Well let's see, let's count by hundreds until we get to 1,000, and I'll keep a little tally mark so we can keep count of how many hundreds it takes us to get to 1,000. 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000. So it took 10 hundreds, to get to 1,000. So 1,000 is 10 hundreds. So what would 5,000 be? 5,000 is five times as many thousands. So we're also gonna have five times as many hundreds. So five thousands will equal five times 10 hundreds, because we have 5,000 this time, so we have five times 10 hundreds, or five times 10. Five times 10 is 50. So 5,000 equals 50 hundreds. Another way we could think about this is place value, so let's do that. Let's look at a place value chart. Here we have a place value chart and if we fill in five under thousands we can see that we have three empty spaces. We have no hundreds, no tens and no ones, So we need to fill those in with zeros, or 5,000. Again, it's 5,000. Writing the word thousands essentially replaced those three zeros. Five thousands is the same as five with three zeros behind it, and now we want to change these five thousands to be hundreds. Well when we read this place value chart, when we read five, when we stopped here, five is the last number we read and then we read the place value above it, thousands. So for hundreds we'll do the same thing up until the hundreds. We'll read the place value chart until the place value we want and then the place value. So five thousands is the same as 50 hundreds. Five thousands is equal to 50 hundreds, and we don't have to include these last zeros on the end because just like thousands implied three zeros, hundreds, by saying hundreds we've essentially implied that these zeros are there. So five thousands is equal to 50 hundreds. We weren't asked about tens but we could look here and figure it out, I bet. Tens I would say, is 500 10s. We'd read up through the tens and then the tens place because 10s have one zero after them. That zero is implied when you say 10, and then finally, if we went all the way to the end, we could also say that this number is equal to 5,000 ones. So any of those, five thousands, 50 hundreds, 500 tens or 5,000 ones, are equivalent. They're all equal to each other, but the one we were asked about was hundreds. So five thousands equal 50 hundreds. Here's another one. 30 tens equals how many hundreds? So this time we're looking at tens and hundreds. So let's think about how tens and hundreds relate. How many tens are in 100? How many tens are in 100 and we could write one hundred, the word or the number in 100. Well to figure that out if we don't know already, we can count tens. We can count by 10s and see how many 10s it takes us to get to a hundred. One ten is 10, 20, 30, 40, 50 60, 70, 80, 90, 100. So we got to a hundred and it took us 10 tens. There are 10 tens in 100. So if there's 10 tens in 100 how many hundreds are in 30 tens? Well to get from 10 tens to 30 tens, that's three times as many tens, so we'll also have three times as many hundreds, or three hundreds. 30 tens is three sets of 10 tens. 10 tens are a hundred. So another way to think of that is 30 tens is three sets of hundreds, or three hundreds. We could also think about this in terms of place value. Here we have this tens and we know that tens can be represented by a zero. So instead of 30 10s, we could simply write a 30 with a zero on the end, that zero for tens, and then over here, equal to, we have hundreds and hundreds can be represented by two zeros. So to make these equivalent, what number will need to fill in this spot? And the answer again, is a three like we already saw up top. So 30 10s is equal to three hundreds.