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.