Types of numbers | Assessment Resource Banks

Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …} Whole Numbers (W). Skiptomaincontent YouarehereHome Typesofnumbers AlexNeill,2016 Asmathematicsteachers,weneedtoknowaboutthedifferenttypesofnumbersthatwearedealingwith. Therearenumberslike1,2,3,...etc., oneslike0.33333...,oroneslike5/7. Weintroducestudentstothesegradually,andeachnewtypecomeswithitsownuses,anditsownchallenges.Themaintypesofnumbersusedinschoolmathematicsarelistedbelow: NaturalNumbers(N),(alsocalledpositiveintegers,countingnumbers,ornaturalnumbers); Theyarethenumbers{1,2,3,4,5,…} WholeNumbers(W).Thisisthesetof naturalnumbers,pluszero,i.e.,{0,1,2,3,4,5,…}. Integers(Z).Thisisthesetofallwholenumbersplusallthenegatives(oropposites)ofthenaturalnumbers,i.e.,{…,⁻2,⁻1,0,1,2,…} Rationalnumbers(Q).Thisisallthefractionswherethetopandbottomnumbersareintegers;e.g.,1/2,3/4,7/2,⁻4/3,4/1[Note:Thedenominatorcannotbe0,butthenumeratorcanbe]. Realnumbers(R),(alsocalledmeasuringnumbersormeasurementnumbers).Thisincludesallnumbersthatcanbewrittenasadecimal.Thisincludesfractionswrittenindecimalforme.g.,0.5,0.752.35,⁻0.073,0.3333,or2.142857.Italsoincludesalltheirrationalnumberssuchasπ,√2etc.Everyrealnumbercorrespondstoapointonthenumberline. Studentsgenerallystartwiththecountingnumbers(N). Theyarethenintroducedto0,andthisgivesthemthewholenumbers(W). Theintegersareavoidedinitially,eventhoughsimplesubtractioncouldleadtonegativenumbers(e.g.,3–4=⁻1). Simpleunitfractionsarethenextgroupofnumbersthataremeti.e.,{1/2,1/3,1/4,1/5...},thenotherfractions(e.g.,3/4,4/9,7/2,3/100,­­⁻1/2etc.)whichareknownastherationalnumbers(Q). Wenextmoveontodecimalnumbers(suchas0.3, 0.32,⁻2.7).Thesecanbecalleddecimalfractions,becausetheycanbewritteninafractionalform(e.g.,3/10,32/100,⁻27/10). Theseexpandtotherealnumbers(R),whichincludeirrationalnumberssuchasπ,√2.Anirrationalnumbercannotberepresentedasafraction(i.e.,arationalnumber).πcanberepresentedwithnumerals,i.e.,3.14159265...;howeverthedigitsgooninfinitelybutthereisnopatterntothem. Discreteandcontinuousnumbers Theabovetypesofnumberscanbesplitupintodiscreteorcontinuousnumbers. Thefirstfouroftheabove(N,W,ZandQ)arereferredtoasdiscrete.Thismeansthattheyareseparateanddistinctentities.Infacteachofthesesetsis countable.Thelastset,(R),cannotbecounted.Thisisbecausetheyarecontinuous.Betweenanytworealnumbers,howeverclosetheymaybe,thereareinfinitelymorerealnumbers.   Formoreclickonhttps://en.wikipedia.org/wiki/Continuous_and_discrete_variablesoronTypesofdata:Statistics.Athigherlevelsofsecondaryandtertiaryeducationdiscretemathematics,isoftenmorechallengingthanthemathematicsofcontinuousfunctions.Withcontinuousfunctions,asmallchangeintheinputvariableleadstoasmallchangeintheoutputvariable.Smooth,continuousfunctionsleadontomostofthefunctionsstudentsmeetatsecondaryschool,includingcalculusattheseniorsecondaryschoollevel.    Constructingnumbers Thenumberswemeetatschoolaregenerallyrepresentedbyusingcombinationsoftennumbersymbols(alsocallednumeralsordigits)plusthesymbols".","+",and"–"(e.g.,5,27,35.8,⁻4)Thetennumbersymbolsweuseare: 1  2  3  4  5  6  7  8  9  aswellas0.   Allofthesesymbolsalsorepresentthenumbersone,two,three,...uptonine;aswellaszero.0isitselfanumber,andaveryimportantone.Itiscalledzero,nil,noughtetc.Itisalsoaplace-holder.Itisfirstusedinthissenseinthenumberten(10).The0denotesthatthereisnothingintheunitsplace,andthereforedistinguishes10from1.Theconceptofplaceholderisbestinterpretedastherebeingzero(0)oftheunitsintheplacewherethe0is.Forexample,in1025therearezerohundreds.Studentsneedtomeetthenumber0beforetheymeetthenumber10.