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Inleiding

'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, ....)

Definisie

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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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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