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# Introduktion til positionssystemet og pladsværdi

## Video udskrift

Voiceover:Let's say that
you wanna count the days since your last birthday because you just wanna
know how long its 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 can say look there's
been one, two, three days. So one way to think about it is 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 then 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 bunch of days you get here and you're like on well
how many days has it been? Well you just recount everything. You say one, two, three,
four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17 days. So well you know this
number representation it took me 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 to sense
you're counting the days since your last birthday. But at some point you realize every time you wanna know how may days its been to count it is 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. One, two, three, four,
five, six, seven, eight, nine, 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're first trying you might have even called
it something called 37. You would just call it this, this number. This number of days since my birthday. And I say well look. What if there was an easier
way to group the numbers? You know I have 10 fingers on my hands. What if I were to group them into 10s? And then I would say just
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 one, two, three, four, five,
six, seven, eight, nine, 10. So that's a group of 10 right over there. And then you have one, two,
three, four, five, six, seven, eight, nine, 10. So this is another group
of 10 right over here. And then let's see. We have one, two, three,
four, five, six, seven, eight, nine, 10. So that is another group
of 10 right over there. And then finally you have
one, two, three, four, five, six, seven. So you don't get a whole group of 10 so you don't circle em. 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 okay. One group of 10. Two groups of 10. Three groups of 10. Or you can say one, two, three 10s. And so that's essentially 30. And then I have another one, two, three, four, five, six, seven. And so you say oh I have 30 and then seven if you knew to use those
words which we now use. Now this is essentially
what our number system does using the 10 digits we know of. The 10 digits we know of
are zero, one, two, three, four, five, six, seven, eight, nine. Now 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 our
brains to understand it. So here if we want to represent three 10s, we would have put a three in what we would call the 10s place. We would put a three in the 10s place. And then we would put the ones, one, two, three, four, five, six, 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 10s place. And as we'll see you go one more space you go to the 100s space. 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 10s. One, two, three. Three 10s Three groups of 10. And then another set of ones. So we could rewrite this. This is equal to, this
is equal to three 10s three 10s plus, plus seven ones. Or another way to think about it what are the three 10s? Well if use the same number system to represent three 10s you
would write that down as 30. 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. Where even a number like 37 as soon as you just write
scratches on a wall, it becomes pretty hard to read. And you can imagine when you get to much much larger numbers like 1,052 to have to count that
many marks every time. But our number system gives
us a way of dealing with it.