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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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  • aqualine sapling style avatar for user ( ͡° ͜ʖ ͡°)
    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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    (3 votes)
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  • blobby green style avatar for user hil29261
    what do you mean creating the largest possible number?
    (3 votes)
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  • blobby green style avatar for user gonzalez-hollidayzac
    10000000000000 times 2000000000000
    (3 votes)
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  • blobby green style avatar for user letlhohonolo18
    The digits 1 to 7 are used to create a four-digit code to enter a locked room. How many different codes are possible if the digits may not be repeated and the code must be an even number greater than 5000?
    (2 votes)
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  • aqualine ultimate style avatar for user petersjw
    at he give away the answer
    (2 votes)
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  • mr pink red style avatar for user HaileyT
    how can you put 300,99 together?
    (2 votes)
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  • starky tree style avatar for user Brianne
    what collor is the sky?
    (2 votes)
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  • leafers ultimate style avatar for user 💖💕❤Grace❤💕💖
    Hi,
    Can you guys tell me what i should do when there is two number which is the same what should i do.please.^^
    (1 vote)
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  • duskpin sapling style avatar for user Alina
    so it the highest form of 3219 9321?
    (1 vote)
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  • winston baby style avatar for user ztaylor.stu
    How do i get a bigger bigger number?
    (1 vote)
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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.