Creating the largest number

arrange the digits two six zero and one so that you create the highest possible four-digit number so the way I like to think about it is I want to if I'm trying to create as large of a number as possible I want to put the largest digits in the largest or 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 six I could make it six thousand I could make it six hundred I could make it sixty or I could make it six well if I want to as large number of a possible as possible I'm going to make it six six thousand notice if I put any other number in that place value if I put zero there I'd have no thousands if I put two there I'd only have two thousand I put one there only have one thousand six thousand is definitely going to be bigger than any of the numbers that could be constructed with the two zero or one 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 two so I'm going to put a 2 right over here I'd rather have two hundredths than zero hundreds or 100s 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 1/10 then zero ten and then we're just left with the zero so we're just going to put the zero right over here so we can make 6210 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 zero six I'm going to be careful zero one zero one two six 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 have 6210