Regrouping whole number place values | Math | 4th grade | Khan Academy

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 one thousand five times, so let's think about each of those thousands. Each of those five thousands in one thousand, how many hundreds are in one thousand? One thousand equals how many hundreds? Well, let's see. Let's count by hundreds until we get to a thousand, and I'll keep a little tally mark so we can keep count of how many hundreds it takes us to get to a thousand.

One hundred, two hundred, three hundred, four hundred, five hundred, six hundred, seven hundred, eight hundred, nine hundred, one thousand. So it took 10 hundreds to get to a thousand. So, 1,000 is 10 hundreds. So what would five thousand be? Well, five thousand is five times as many thousands, so we're also going to have five times as many hundreds. So, five thousands will equal five times ten hundreds because we have five thousand this time.

So we have five times ten hundreds, or five times ten. Five times ten is fifty, so five thousand equals fifty 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 5 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. So, five thousand again, it's five thousand. 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 fifty hundreds. Five thousand is equal to fifty 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 two zeros are there.

So five thousands is equal to fifty hundreds. We weren't asked about tens, but we could look here and figure it out. I bet tens we would say is 500 tens. We'd read up through the tens, and then the tens place, because tens have one zero after them. That zero is implied when you say ten.

And then finally, if we went all the way to the end, we could also say that this number is equal to five thousand ones. So any of those five thousands: fifty hundreds, five hundred tens, or five thousand ones are equivalent. They're all equal to each other. But the one we were asked about was hundreds, so five thousands equals fifty hundreds.

Here's another one: thirty 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 one hundred? How many tens are in one hundred? And we could write one hundred, the word, or the number in one hundred.

Well, to figure that out, if we don't know already, we can count tens. We can count by tens and see how many tens it takes us to get to a hundred. One ten is ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, one hundred. So we got to 100, and it took us 10 tens. There are 10 tens in 100. So if there's 10 tens in one hundred, how many hundreds are in thirty tens?

Well, to get from ten tens to thirty tens, that's three times as many tens, so we'll also have three times as many hundreds, or three hundreds. Thirty tens is three sets of ten tens. Ten tens are a hundred. So another way to think of that is thirty 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 thirty tens, we could simply write a thirty with a zero on the end. That's 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 thirty tens is equal to three hundreds.