Decomposing whole numbers
Narrator says 'I have 14 100s here' when the number is 14 thousands, and says 14,000 plus seven ones gives '14,000' (should be 14,007). Interventions use the correct values.
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Sal works out which description matches the number 14,070. He turns each description into a number by adding its parts with place values lined up: 14 thousands and 7 tens make 14,070, while 14 thousands and 7 ones make 14,007 and 14 hundreds and 7 tens make 1,470.
You'll be able to
- turn a description like '14 thousands and 7 tens' into a number.
- explain why 14 hundreds is the same as 1 thousand and 4 hundreds.
- check which description matches a number by lining up place values.
Key words
- place value
- The value a digit has because of where it sits in a number, like ones, tens, hundreds or thousands.
- tens place
- The second spot from the right in a whole number; a 7 there means 7 tens, or 70.
- decompose
- To break a number into parts, like 14,070 = 14,000 + 70.
Transcript
- [Narrator] We are asked which answer choice describes the number, and I'm not gonna say it 'cause that might be a hint. This number right over here. So pause this video and have a go at that before we do this together. Okay, now let's do this together. There's a couple of ways we could do it.
We could try to express this number in words, or we could look at these words here and express them as a number and see which one matches up. Well, I'm gonna go with the second way because they're saying things in not always the most standard way. I have 14 100s here.
And you normally wouldn't say, well, sometimes you might say it that way, but let's just try to break it out here. So if I have 14 1,000s as this choice A says, that would be 14 and then 1,000s, and then two, that I'm adding seven 10s. So seven 10s is what? Well, it's seven in the 10s place and zero ones.
Or another way to think about it, it's 70. So if I took 14,000 plus 70, what is it going to be? And I could do this here if I wanna line up the place values, 14,070. Well, I have no ones, I have seven 10s, I have no 100s. I have four 1000s and I have one 10,000.
I have 14,070, which is exactly the number that they have over here. So we luckily stumbled on, or we looked at choice A and it was actually the choice that describes this number. But let's look at the other ones and see why that doesn't make sense. The second choice here still has the 14,000s.
So it still has this part right over here, but they say seven ones. So if you were to add 14,000 and then have seven ones, you'd get 14,000. And then you would add those seven ones in the ones place. So you would get that. And then the last one, the sum of 14 100s and seven 10s.
Well, they have the seven 10s part, which we already said is the same thing as 70. But what does 1,400 look like? Well, 1,400. Let me do this in a new color, maybe purple, 1,400. That is one way to think about it is you could go to the, let's look at our place value here.
If this is ones, this is 10s, this is 100s. You could say you have 14 of these 100s. Or another way to think about it is you have four 100s and a 1,000. Or another way of saying a 1,000 is 1,000. That's the 1000's place. So 1400 looks like this. So if you were to add 1,400 and 70, you would get 1,470, not what they originally asked us about.
So we can feel very good about choice A.
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