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(male narrator) So up until now, we've been converting
to and from bases that were less than 10--
like base 5 and base 7.
But there are, in fact, bases that are bigger than 10.
Uh...the trick with them is that
when you start listing out values--
like let's say, we wanted to do base 12--
we would need symbols that go all the way up to 11.
So...there we go.
There are symbols that go up to 11... [laughs]
Uh...and then...and then this would be a base 12 system,
so if you were to see the number...1-2,
that would be two 1s, and this would mean one...12.
And so in base 10, that would correspond to the number 14.
So 12...this is 1-2 base 12 corresponds to-to our number 14.
If we were to see the number, uh...let's say, T3...
that would mean three 1s and...ten 12s.
Right?
Because remember, T was representing 10,
so that would be 120 plus 3.
This corresponds to 123 base 10.
Now...most of the time,
we're not gonna write things like T and E
to represent these numbers,
and instead, we're gonna write things like...
10...3, as a way of representing this same number.
And we'll use commas to separate the places.
Uh...now there are some systems
that do go beyond 9 with other symbols.
Uh...one of them is using computers
called the "hexadecimal system," which is base 16,
and they use the letters A through F,
uh...to capture the numbers 10 through 15.
So...uh...that we can work with bases bigger than 10,
and in fact, that becomes necessary
if we're gonna start talking about the Mayan number system,
uh...which is base 20.
So the Mayan number system
uses dots and lines to represent numbers.
Uh...so a dot corresponds with a 1.
A line corresponds with a 5, and then they come in groupings.
And so we go... we can say 1.
There's 2...there's 3... there's 4,
and then naturally 5 would come next.
If we wanted to represent the number 6,
we would use a line and one dot.
If we wanted to represent the number 10,
we would use two lines.
The number...uh...the number 18 would be three lines,
and that's 15, 16, 17, 18 and three dots.
Now interestingly, though, once we get up to 20,
the idea is...ahhh... drawing four lines
is too many lines to draw.
And so this is where we get into our new place value.
Uh...and so for... in the Mayan number system,
instead of writing numbers next to each other like we do--
like we write this--
they write their numbers on top of each other
with the bottom one being the-the lowest place value...
uh...so it would be the 1s.
Uh...so the bottom one is-is the 1s.
The next value up is the 20s.
The next value up is the 20-squareds--
or in other words, the 400s.
So if we saw, let's say, this number...here...
this would mean two 20-squareds, two 20s,
and what is that, five, six...six 1s.
And we would combine those together
to find out the-the value of this number.
In this case, that would be 846, uh...in our usual base 10.
Now it's important to note here
that this number can go up to, say, 18 here
within...18 or 19, within any of these place values.