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Creating the largest number

Sal arranges digits to make the largest possible number. Created by Sal Khan.

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Video 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.