Rational and Irrational Numbers - By tecmath
Transcript
00:0-1 | Good day and welcome to the Tech mouth channel . | |
00:02 | What we're gonna be having to look at in this | |
00:03 | video is a very quick description of the difference between | |
00:06 | rational and irrational numbers . So rational numbers . These | |
00:10 | are numbers which can be expressed as fractions in the | |
00:12 | form of say the algebraic expression A over B . | |
00:17 | Um , but both of these images be is not | |
00:20 | allowed to be equal to zero . Okay , because | |
00:22 | that wouldn't lead to very happy times , dividing any | |
00:24 | number by zero . Doesn't look very happy times . | |
00:27 | So An example , this might be saying something like | |
00:30 | you can have a number like 2/3 or you can | |
00:33 | have a number say like a quarter or you can | |
00:36 | even have say a number like three which could be | |
00:40 | expressed instead is 3/1 . So it's also going into | |
00:46 | this year that pretty much the one of the things | |
00:49 | that that's the definition of it , but probably the | |
00:52 | feature which is really really defining for these also Is | |
00:56 | the decimals that come out here . So obviously three | |
00:59 | doesn't have any decimals . Okay . It has zero | |
01:01 | but for all intents and person doesn't have it doesn't | |
01:05 | have zeros but rational numbers also other have so terminating | |
01:13 | Decimals . Okay , so something like here where it | |
01:16 | terminates and it's 0.25 and it stops there or it | |
01:20 | could actually have recurring decimals like this one here is | |
01:23 | 0.6666666 . And it Rikers itself . Okay . Or | |
01:28 | even say something if it was like a number which | |
01:30 | was 0.24-4-4 where it Rikers and Rikers so it has | |
01:35 | these repeating sequences and rational numbers have this irrational numbers | |
01:40 | on the other hand don't have this um so irrational | |
01:43 | numbers now . So irrational numbers basically end up , | |
01:48 | you don't have , you have these an infinite number | |
01:51 | of non recurring decimals . When you get these there | |
01:55 | these Are easily seen . Would say something like this | |
01:59 | number here . The square root of two . Okay | |
02:02 | , um so if you would have worked this out | |
02:04 | on a calculator , you'd see this , you get | |
02:06 | this number of say zero . Uh actually you wouldn't | |
02:11 | get zero point , you'd actually hit you get this | |
02:13 | , you get one , I would forward four uh | |
02:19 | 2136 No , I don't know that off the top | |
02:21 | of my head . I'm looking down at something at | |
02:23 | the moment as I do this because it's quite a | |
02:26 | quite a difficult one to get . You're gonna notice | |
02:28 | there's no repeat here . In fact this could keep | |
02:31 | being worked out and it would not actually ever repeat | |
02:34 | itself . So this is known as an irrational number | |
02:38 | . Okay , so quite often it's actually left . | |
02:42 | This will be the answer . Um which is the | |
02:45 | exact form which is called a certain yeah . Okay | |
02:48 | . And this is going to be looking at search | |
02:50 | ads in future videos . Okay , so the exact | |
02:53 | form of these of an irrational number is called a | |
02:57 | surge here . So just one last thing , a | |
03:01 | couple of other irrational numbers , you probably fairly um | |
03:05 | aware of paul has an irrational number , no matter | |
03:08 | how much you work it out . 3.1415 la la | |
03:11 | la la la la la . You end up with | |
03:14 | these non repeating decimal uh expressions . Okay , is | |
03:19 | also one as well . Okay , so hopefully that | |
03:23 | explained rational numbers versus irrational numbers . Um so that's | |
03:28 | the major definition and the difference between them . It's | |
03:31 | also the reason that we do get into third . | |
03:33 | So we can actually get these exact expressions because irrational | |
03:37 | numbers don't have an exact expression . So we can | |
03:39 | always leave This one here is an exact expression . | |
03:42 | We can call it .66 , and we can say | |
03:44 | that there and people know that what exactly will be | |
03:47 | forever on afterwards . Um Where is this one here | |
03:51 | ? You should keep writing this and you'd never actually | |
03:53 | fully be able to define it . So in fact | |
03:56 | , we often leave the exact value as I said | |
03:59 | , okay , hopefully that explain a few things and | |
04:02 | we'll see you next time , Okay ? |
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