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Byvoorbeeld, die rasionale getal 5 6 kan in desimale notasie geskryf word as 0 , 8 3 ˙ en soortgelyk kan die desimale getal 0,25 soos volg as 'n rasionale getal geskryf word: 1 4 .

Notasie vir repeterende desimale

Jy kan 'n kol oor die herhalende desimale aanbring om aan te dui dat die desimaal repeterend is.

Omskakeling tussen terminerende desimale getalle en rasionale getalle

'n Desimale getal het 'n heeltallige deel en 'n breukdeel. Byvoorbeeld 10 , 589 het 'n heeltallige deel van 10 en 'n breukdeel van 0 , 589 omdat 10 + 0 , 589 = 10 , 589 . Die breukdeel kan geskryf word as 'n rasionale getal, m.a.w. met 'n teller en 'n noemer wat heelgetalle is.

Elke syfer na die desimale komma is 'n breuk met 'n noemer wat 'n vermeerderende mag van 10 is. Byvoorbeeld:

  • 1 10 is 0 , 1
  • 1 100 is 0 , 01

Dit beteken dat:

10 , 589 = 10 + 5 10 + 8 100 + 9 1000 = 10 589 1000 = 10589 1000

Breuke

  1. Skryf die volgende as breuke:
    (a) 0 , 1 (b) 0 , 12 (c) 0 , 58 (d) 0 , 2589

Omskakeling tussen repeterende desimale breuke en rasionale getalle

Wanneer die desimaal repeterend is, is daar 'n bietjie meer werk nodig om die breukdeel van die desimale getal as 'n breuk te skryf. Ons sal verduidelik aan die hand van 'n voorbeeld.

Indien ons 0 , 3 ˙ in die vorm a b wil skryf (waar a en b heelgetalle is), sal ons soos volg te werk gaan:

x = 0 , 33333 ... 10 x = 3 , 33333 ... vermenigvuldig met 10 aan beide kante 9 x = 3 (trek die tweede verg. van die eerste verg. af) x = 3 9 = 1 3

Nog 'n voorbeeld sou wees om 5 , 4 ˙ 3 ˙ 2 ˙ as 'n rasionale breuk te skryf.

x = 5 , 432432432 ... 1000 x = 5432 , 432432432 ... vermenigvuldig met 1 000 aan beide kante 999 x = 5427 (trek die tweede verg. van die eerste verg. af) x = 5427 999 = 201 37

In die eerste voorbeeld is die desimaal vermenigvuldig met 10 en in die tweede voorbeeld is dit vermenigvuldig met 1000. Dit is omdat daar in die eerste voorbeeld slegs een repeterende syfer (nl. 3) was, terwyl die tweede voorbeeld drie repeterende syfers (nl. 432) gehad het.

In die algemeen, as jy een repeterende syfer het, vermenigvuldig jy met 10. As jy twee repeterende syfers het, vermenigvuldig jy met 100. Met drie syfers vermenigvuldig jy met 1000. Kan jy al die patroon raaksien?

Die aantal nulle is dieselfde as die aantal repeterende syfers.

Nie alle desimale getalle kan as rasionale getalle geskryf word nie. Hoekom nie? Irrasionale desimale getalle soos 2 = 1 , 4142135 . . . kan nie geskryf word met 'n heeltallige teller en noemer nie, omdat daar geen patroon van repeterende syfers is nie. Jy behoort egter, so ver moontlik, eerder rasionale getalle of breuke as desimale getalle te gebruik.

Repeterende desimale notasie

  1. Skryf die volgende in repeterende (herhalende) desimale notasie:
    1. 0 , 11111111 ...
    2. 0 , 1212121212 ...
    3. 0 , 123123123123 ...
    4. 0 , 11414541454145 ...
  2. Skryf die volgende in repeterende desimale notasie:
    1. 2 3
    2. 1 3 11
    3. 4 5 6
    4. 2 1 9
  3. Skryf die volgende in breukvorm:
    1. 0 , 633 3 ˙
    2. 5 , 3131 31 ¯
    3. 0 , 99999 9 ˙

Opsomming

  1. Reële getalle is óf rasionaal óf irrasionaal.
  2. 'n Rasionale getal is enige getal wat geskryf kan word as a b waar a en b heelgetalle is en b 0
  3. Die volgende is rasionale getalle:
    1. Breuke waarvan beide die teller en die noemer heeltallig is
    2. Heelgetalle
    3. Desimale getalle wat eindig
    4. Desimale getalle wat repeteer

Oefeninge

  1. Indien a 'n heelgetal is, b 'n heelgetal is en c irrasionaal is, watter van die volgende is rasionaal?
    1. 5 6
    2. a 3
    3. b 2
    4. 1 c
  2. Skryf elkeen van die volgende as 'n onegte breuk:
    1. 0 , 5
    2. 0 , 12
    3. 0 , 6
    4. 1 , 59
    5. 12 , 27 7 ˙
  3. Wys dat die desimaal 3 , 21 1 ˙ 8 ˙ 'n rasionale getal is.
  4. Druk 0 , 7 8 ˙ as 'n breuk a b uit waar a , b Z (wys alle stappe).

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
hey
Giriraj
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
ya I also want to know the raman spectra
Bhagvanji
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, 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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