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'n Getal (soos beskryf in die hersieningshoofstuk) is 'n manier om 'n hoeveelheid voor te stel. Die getalle wat op hoërskool gebruik sal word is almal reëel, maar daar is heelwat verskillende maniere om enige gegewe reële getal voor te stel.

Hierdie hoofstuk beskryf rasionale getalle .

Khan academy video oor heelgetalle en rasionale getalle (in engels)

Die oorhoofse beskouing van getalle

Die term "heelgetal" het nie 'n konsekwente definisie nie. Verskillende skrywers gebruik dit op verskillende wyses. Ons gebruik die volgende definisies:

  • natuurlike getalle is (1, 2, 3, ...)
  • telgetalle is (0, 1, 2, 3, ...)
  • heelgetalle is (... -3, -2, -1, 0, 1, 2, 3, ....)


Die volgende getalle is almal rasionaal

10 1 , 21 7 , - 1 - 3 , 10 20 , - 3 6

Jy kan sien dat al die tellers en noemers heelgetalle is.

Rasionale getal

'n Rasionale getal is enige getal wat geskryf kan word as:

a b

waar a en b heelgetalle is en b 0 .

Slegs breuke wat 'n heeltallige teller en noemer het (wat nie 0 is nie), is rasionale getalle.

Dit beteken dat alle heelgetalle rasionaal is, aangesien hulle geskryf kan word met 'n noemer van 1.

Dus is

2 7 , π 20

nie voorbeelde van rasionale getalle nie, want in elke geval is óf die teller óf die noemer nie 'n heelgetal nie.

'n Getal wat nie geskryf word in die vorm van 'n heelgetal gedeel deur 'n heelgetal nie kan nogtans 'n rasionale getal wees. Dit is omdat die vereenvoudigde resultaat wel as 'n kwosiënt van heelgetalle geskryf kan word. Die reël is dat indien 'n getal geskryf kan word as 'n kwosiënt van heelgetalle, dit rasionaal is, selfs al kan dit op 'n manier geskryf word wat nie so 'n kwosiënt is nie. Hier is twee voorbeelde wat dalk nie na rasionale getalle lyk nie, maar nogtans is, omdat daar ekwivalente vorms gevind kan word wat bestaan uit 'n heelgetal gedeel deur 'n heelgetal:

- 1 , 33 - 3 = 133 300 , - 3 6 , 39 = - 300 639 = - 100 213

Rasionale getalle

  1. Indien a 'n heelgetal is, b 'n heelgetal is en c irrasionaal is, watter van die volgende is rasionale getalle?
    (i) 5 6 (ii) a 3 (iii) b 2 (iv) 1 c
  2. Indien a 1 'n rasionale getal is, watter van die volgende is geldige waardes vir a ?
    (i) 1 (ii) - 10 (iii) 2 (iv) 2 , 1

Vorme van rasionale getalle

Alle heelgetalle en heeltallige kwosiënte is rasionaal. Daar is twee bykomende vorme van rasionale getalle.

Ondersoek: desimale getalle

Jy kan die rasionale getal 1 2 skryf as die desimale getal 0,5. Skryf die volgende getalle as desimale getalle:

  1. 1 4
  2. 1 10
  3. 2 5
  4. 1 100
  5. 2 3

Beskou die getalle na die desimale komma. Kom hulle tot 'n einde of gaan hulle voort? Indien hulle voortgaan, is daar 'n herhalende patroon in die getalle?

Jy kan 'n rasionale getal as 'n desimale getal skryf. Twee tipes desimale getalle wat as rasionale getalle geskryf kan word:

  1. Desimale getalle waarvan die nie-nul getalle na die komma tot 'n einde kom of termineer , byvoorbeeld die breuk 4 10 kan geskryf word as 0,4.
  2. Desimale getalle wat 'n nimmereindigende herhalende patroon van getalle na die komma het, byvoorbeeld die breuk 1 3 kan geskryf word as 0 , 3 ˙ . Die dot beteken dat die 3 'e repeteer, m.a.w. 0 , 333 ... = 0 , 3 ˙ .

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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Akash Reply
it is a goid question and i want to know the answer as well
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
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for screen printed electrodes ?
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s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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I'm interested in nanotube
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Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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