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let's say that you want to count the days since your last birthday because you just want to know how long it's been and so one day after your birthday you put a mark on a wall then the next day you put another mark on the wall the day after that you put another mark on the wall so out that day you say well how many days has it been well you could say look there's it's been one to three days so one way to think about it is this this set of symbols right over here represents the number three but then you keep going the fourth day you put another mark fifth day you put another mark and you keep going like that day after day each day you add another mark and this is actually the earliest way the most basic way of representing numbers the number is represented by the number of marks so after a bunch of days you get here you're like oh well how many days has it been well you just recount everything you say 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 days say well you know this number representation it took me a little bit of time to realize that this is 17 but it seems to be working so you just keep going day after day after day after day you just keep marking off the days on your wall just essentially counting the days since your last birthday but at some point you realize every time you want to know how many days it's been to count it it's a little bit painful and not only that is this is taking up a lot of space on your wall you wish that there was an easier way to represent whatever number this is so first of all let's just think about what number this actually is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 so you wish that there was a better way to represent this number which we now call 37 and maybe when you were first trying you might not even called it something called 37 you would just call it this this number this number of days since my birthday I said well look what if there was an easy way to group the numbers you know I have 10 fingers on my hands what if I were to group them into tens and then I would to say how many groups of 10 I have and then how many ones do I have left over maybe that would be an easier way to represent to represent this quantity here and so let's do that so 1 2 3 4 5 6 7 8 9 10 so that's a group of 10 right over there and then you have 1 2 3 4 5 6 7 8 9 10 so this is another group of 10 right over here and then let's see we have 1 2 3 4 5 6 7 8 9 10 so that is another group of 10 right over there and then finally you have 1 2 3 4 5 6 7 so you don't get a whole group of 10 so you don't circle them so just by doing this very simple thing now all of a sudden it's much easier to realize how many days have passed you don't have to count everything you just have to say ok one group of 10 two groups of 10 three groups of 10 or you could say 1 2 3 tens and so that's essentially 30 and then I have another 1 2 3 4 5 6 7 and so you say I have 30 and then 7 if you if you new to use those words which we now use and this is essentially what our number system does using the 10 digits we know of the 10 digits we know of are 0 1 2 3 4 5 6 7 8 9 and what our number system allows us to do is using only these 10 digits we can essentially represent any number we want in a very quick way a very easy way for brains to understand it so here if we want to represent 3 tens we would have put a 3 and what we would call the tens place we would put a 3 in the tens place and then we would put the ones 1 2 3 4 5 6 seven we'd put the seven in the ones place and so how do you know which place is which well the first place starting from the right the first place is the ones place and then you go one space to the left of it you get to the tens place and as we'll see you go one more space you go to the hundreds place but we'll cover that in a future video so this essentially tells us the exact same thing this tells us the exact same thing as this does right over here this tells us three tens one two three three tens three groups of ten and then another seven ones so we could rewrite this this is equal to this is equal to three tens three tens plus plus seven ones or another way to think about it what are three tens well if we use the same number system to represent three tens you would write that down as thirty and then seven ones once again if you use our same number system you would represent that as seven so these are all different ways of representing 37 and hopefully this allows you to appreciate how neat our number system is well even a number like 37 as soon as you just write scratches on the wall it becomes pretty hard to read and you can imagine when you get to much much larger numbers like a thousand and fifty-two to have to count that many marks every time but our number system gives us a way of dealing with it