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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
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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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