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Creating the largest number
CCSS.Math:
Sal arranges digits to make the largest possible number. Created by Sal Khan.
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VictorD
8 days ago
Posted 8 days ago. Direct link to VictorD's post “Arrange the digits 2, 6, ...”
Arrange the digits 2, 6, 0, and 1 so that you create the highest possible four-digit number. So the way I like to think about it is, if I'm trying to create as large of a number as possible, I want to put the largest numbers in the largest place value. So if it's a four-digit number-- so it's one, two, three, four-digit number-- whatever I put here, this is going to represent thousands. Whatever I put here is going to represent hundreds. Whatever I put here represents tens. And whatever I put here represents ones. So I want to maximize the number of thousands I have. For example, the largest number here is 6. I could make it 6,000. I could make it 600. I could make it 60, or I could make it 6. Well if I want as large a number as possible, I'm going to make it 6,000. Notice, if I put any other number in that place value-- if I put a 0 there, I would have no thousands. If I put 2 there, I'd only have 2,000. If I put 1 there, I'd only have 1,000. 6,000 is definitely going to be bigger than any of the numbers that could be constructed with the 2, 0, or 1 in the thousands place. Now the exact same logic, we want the next largest number in the hundreds place. So the next largest number here is a 2. So I'm going to put a 2 right over here. I'd rather have two hundreds than zero hundreds or one hundreds. That's going to make it bigger. Then, same exact idea-- we want the next largest number in the tens place. I'd rather have one 10 than zero 10. And then we're just left with the 0. So we're just going to put the 0 right over here. So we can make 6,210. If I wanted to make the smallest possible four-digit number, then I would rearrange this, so I have the smallest possible number in the thousands and the largest possible number in the ones. So the smallest possible number I could create is-- I'm going to be careful-- 0, 1, 2, 6. So the smallest possible number, if I just switch this around, would be 126 that I could construct out of these digits. But this is what they asked for. So we'll give 6,210.
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2:10Video transcript
Arrange the digits
2, 6, 0, and 1 so that you create the highest
possible four-digit number. So the way I like
to think about it is, if I'm trying to create as
large of a number as possible, I want to put the largest
numbers in the largest place value. So if it's a four-digit number--
so it's one, two, three, four-digit number--
whatever I put here, this is going to
represent thousands. Whatever I put here is
going to represent hundreds. Whatever I put here
represents tens. And whatever I put
here represents ones. So I want to maximize the
number of thousands I have. For example, the largest
number here is 6. I could make it 6,000. I could make it 600. I could make it 60,
or I could make it 6. Well if I want as large
a number as possible, I'm going to make it 6,000. Notice, if I put any other
number in that place value-- if I put a 0 there, I
would have no thousands. If I put 2 there,
I'd only have 2,000. If I put 1 there,
I'd only have 1,000. 6,000 is definitely
going to be bigger than any of the numbers
that could be constructed with the 2, 0, or 1 in
the thousands place. Now the exact same logic, we
want the next largest number in the hundreds place. So the next largest
number here is a 2. So I'm going to put
a 2 right over here. I'd rather have two hundreds
than zero hundreds or one hundreds. That's going to make it bigger. Then, same exact idea--
we want the next largest number in the tens place. I'd rather have one
10 than zero 10. And then we're just
left with the 0. So we're just going to
put the 0 right over here. So we can make 6,210. If I wanted to make the smallest
possible four-digit number, then I would
rearrange this, so I have the smallest possible
number in the thousands and the largest possible
number in the ones. So the smallest possible
number I could create is-- I'm going to be
careful-- 0, 1, 2, 6. So the smallest possible number,
if I just switch this around, would be 126 that I could
construct out of these digits. But this is what they asked for. So we'll give 6,210.