00:03
Okay, let's look at this number and they're asking is it rational or irrational? okay, what's a rational number? rational number.
00:13
My handwriting's not working today.
00:19
Rational number.
00:22
It's a number that we can write like this.
00:24
We write it looks like a fraction or it can look like a fraction and p and q are integers.
00:35
And if you don't remember integers or are...
00:37
The negative and positive whole number than zero so negative three negative two we'll put some dots over here negative one zero one two okay so if we want to show that something's a rational number we have to find two integers that we can write as a ratio and that gives us this decimal here okay so let's i'm gonna clear i'm gonna clear my drawings and we're gonna look at this so if you notice look at this number right here.
01:11
If you notice, there is no decimal place.
01:16
It stops.
01:20
Okay.
01:23
My writing may or may not get better.
01:25
Who knows? it stops right there.
01:29
If it continued, it would have dot, dot, dot.
01:33
Let's also look here.
01:35
6 -9 -7 -8 -9 -9 -7 -8 -9 -9 -7 -8.
01:43
Well even if we said okay if we said okay starting here we've got some sort of repeating part then we could we could even then and if it kept going even then we could find we could find a decimal like a fraction with integer numbers so what we would he do well one thing we could do is we could do is we could find a decimal like a fraction with integer numbers.
02:19
Could say hmm let's let x equal 0 .697 899 and then 7 899 etc let's assume for a moment let's assume for a moment that it keeps going because it because this stops here it's immediately rational because terminating decimals all i need to let me just list this i'm just gonna let me just tell you it show you something when i'm thinking out loud.
03:00
If this stops here, all i have to do is ignore the zero and put a one and then how many, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, fourteen, fifteen, sixteen, sixteen, seventeen, seventeen, seventeen, seventeen, sixteen, seventeen, fraction if you if you ignore this zero for a second that fraction is represents the decimal if it stops right here and so you say oh yeah that's totally a hundred percent rational let's assume though that it keeps going okay so what i'm gonna do is i need to move it one two three four so i'm gonna have one two three four five six and let me just let me just make sure i got that right oh my brain so you all have those days where it's just like i'm trying to do some math but my brain is just like not is not is not doing it right okay so here we go let's do this point six nine actually i don't need to yeah well six nine eight is that gonna line up okay, so what i need to do is this.
05:05
Hold on.
05:09
I need to get it so that this, this bit, lines up with this bit.
05:15
So i need to move it over.
05:17
One, two, three, four spaces.
05:20
Okay, so i need to, let's erase that.
05:24
And i'm going to try to move it over one, two, three, four spaces...