00:01
All right, today we're going to talk about the difference between rational and irrational number.
00:05
We're going to start with the first number, which is 0 .75, and we have to determine whether that is a rational number.
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And in order to determine that, we have to know what a rational number is.
00:20
And a rational number is any number that can be represented as a ratio or fraction of two numbers or two integers.
00:29
Okay.
00:29
Now in order to determine whether 0 .75 is a rational number, we need to be able to change it to a fraction.
00:37
If we can change it to a fraction or a ratio, then it is a rational number.
00:42
In order to do that, you're going to take, you'll notice that the 5 is in the 100th place.
00:47
So it's 0 .75, 7 is in the 10, 5 is in the 100th.
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Since the 5 digit is in the 100th, you're going to say it is 75th, 100th, and you're going to divide it by a 0 .5 .5.
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100.
01:00
It's in the 100th place, so we're going to divide it by 100.
01:03
Okay? so we're able to change this number 0 .75 into a fraction, which is 75 over 100.
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In order to simplify this fraction, you're going to divide the numerator and the denominator by 25, and you'll get 3 over 4.
01:23
So we're able to take 0 .75 and change it into a fraction.
01:29
Therefore, 0 .75 is a 3 .75 is a 3 .5.
01:31
So we are able to take 0 .75 is a rational number.
01:35
It's a rational number.
01:36
Okay.
01:38
The next problem they give you, the next number they give you is 0 .2, 2, 3, and it has a bar on the top, which means the 3 is repeated, and only the 3 is repeated.
01:50
So that's the same as saying 0 .2, 2, 3, and then the 3 goes on.
01:58
The 3 continues.
01:59
Now, in order to determine whether this number, 0 .223 repeated, can be turned into a fraction, or is it rational, we need to be able to change it to a fraction.
02:12
There is a way to change this to a fraction.
02:14
What we're going to do is we're going to take this 0 .223 with a bar, and we're going to change it to an equation.
02:22
So we're going to take this number and we're going to put x in front of it.
02:26
So x equals 0 .2, 2, 3, and you know that the number continues.
02:34
Okay? in order to solve this, what you're going to do is you're going to multiply it by 10.
02:42
You're going to multiply it by 10 because you want the decimals to line up when you're doing this equation.
02:48
You want your decimals to line up, so you're going to multiply x by 10.
02:53
So if i take x and i multiply it by 10, you'll get it...