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Wiskunde

Graad 9

Getalle

Module 1

Getalle – waar kom hulle vandaan?

KLASWERK

1. Ons noem die versameling natuurlike getalle N , en ons skryf die versameling so neer: N = { 1 ; 2 ; 3 ; . . . }

1.1 As jy enige twee natuurlike getalle bymekaartel, is jou antwoord altyd weer ’n natuurlike getal? Hoe sal jy te werk gaan om iemand te oortuig dat dit wel so is?

1.2 Vermenigvuldig enige twee natuurlike getalle. Is die antwoord ook altyd ’n natuurlike getal?

1.3 Trek nou enige natuurlike getal van enige ander natuurlike getal af. Beskryf al die moontlike soorte antwoorde wat jy kan verwag. Probeer neerskryf hoekom dit gebeur.

2. Om voorsiening te maak vir die antwoorde wat jy in 3.1 teëgekom het, moet ons die getallestelsel uitbrei na die heelgetalle, wat die natuurlike getalle insluit. Hulle word voorgestel deur die simbool Z en hier is een manier om hulle neer te skryf: Z = { 0 ; ±1 ; ±2 ; ±3 ; . . . }

2.1 Voltooi die volgende definisies deur neer te skryf wat in die hakies moet kom:

  • Telgetalle N 0 = {.........................}
  • Heel getalle Z = {.........................} op ’n tweede manier!

3. As jy enige heelgetal deur enige ander heelgetal (behalwe 0) deel, kry jy altyd weer ’n heelgetal?Om voorsiening te maak vir hierdie antwoorde, moet ons die getallestelsel weer uitbrei; hierdie keer na die rasionale getalle:

3.1 Q (rasionale getalle) is al die getalle wat geskryf kan word in die vorm a b size 12{ { { size 11{a}} over { size 11{b}} } } {} waar a en b heeltallig is, en b nie ’n nul is nie. Verduidelik baie mooi waarom b nie nul mag wees nie.

4. Q ` (irrasionale getalle) is al die getalle wat nie as ’n breuk geskryf kan word nie, en dus nie in Q is nie. As ’n mens Q en Q ` saamvoeg dan kry jy die reële getalle, R .

4.1 Skryf neer wat jy dink in die versameling R ` is. Ons noem hulle nie-reëel.

einde van KLASWERK

Knoopskrif is dikwels in die antieke tyd in verskeie wêrelddele gebruik. Dit was ’n manier om goed, veral getalle, te onthou deur knope te maak in ’n tou. Die gebruike wissel vanaf eenvoudige stelsels waar een knop een item voorgestel het, tot ingewikkelde maniere om van plekwaardes gebruik te maak. Deur verskillende kleure tou te gebruik, kan meer as een stelsel getalle saam voorgestel word. Die Inkas se naam vir hierdie stelsel was quipu .

HUISWERKOPDRAG

1. Die tabel bevat nie ’n nul nie. Hoe belangrik is dit dat ons ’n nul moet hê? Dink aan al die goed wat ons nie sal kan doen sonder ’n nul nie.

2. Vind uit wat die naam is vir die versameling getalle wat jy sal kry as jy R en R ` saamvoeg. Kan jy enigiets meer van hulle sê?

3. Ontwerp jou eie stel natuurlike getalsimbole soos dié in die vorige tabelle. Vul hulle in en wys hoe jy enige getal kan skryf met jou simbole. Dink nou nuwe tekens uit om + en – en × en  te vervang, en maak dan ’n paar sommetjies om jou werk duidelik te maak.

einde van HUISWERKOPDRAG

VERRYKINGSOPDRAG

Maak kennis met rasionale getalle

  • Bevestig die volgende antwoorde op jou eie sakrekenaar:
  • Onthou om die berekenings in die regte volgorde te doen.
  1. 2 + 3  100 + 1 + 1  10 = 3,013

Is 3,013 ’n rasionale getal? Ja, want ons kan so maak:

3,013 = 3 1 + 13 1 000 size 12{ { { size 11{3}} over { size 11{1}} } + { { size 11{"13"}} over { size 11{"1 000"}} } } {} = 3 000 1 000 + 13 1 000 size 12{ { { size 11{"3 000"}} over { size 11{"1 000"}} } + { { size 11{"13"}} over { size 11{"1 000"}} } } {} = 3 000 + 13 1 000 size 12{ { { size 11{"3 000"+"13"}} over { size 11{"1 000"}} } } {} = 3 013 1 000 size 12{ { { size 11{"3 013"}} over { size 11{"1 000"}} } } {}

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, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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