1Types Of Numbers- Lecture Note of Mathematics Conversion Program.pdf

Mathematics Slides

1. Chapter 01
Types of Numbers
T. G. M. Madushani
B.Sc. ( Industrial Mathematics –Rajarata) 1

2. Content
•Natural numbers
•Whole numbers
•Integers
•Fractions
•Rational numbers
•Irrational numbers
•Real numbers
•Prime number
•Composite number 2

3. NaturalNumbers
Themostfamiliarnumbersarethenatural.Naturalnumbersor
countingnumbersarethemostbasictypeofnumberswhichyou
learnedforthefirsttimeasatoddler.Theystartfrom1andgoto
infinity,i.e.1,2,3,4,5,6,andsoon.Theyarealsocalledpositive
integers.Inthesetform,theycanbewrittenas{1,2,3,4,5,…}.
NaturalnumbersarerepresentedbythesymbolN.
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4. Whole Numbers
Wholenumbersarethesetofnaturalnumbers,including
zero.Thismeanstheystartfrom0andgoupto1,2,3,and
soon,i.e.{0,1,2,3,4,5,…}.Wholenumbersare
representedbythesymbolW
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5. Integers
Integersarethesetofallwholenumbersandthenegativesof
naturalnumbers.Theycontainallthenumberswhichlie
betweennegativeinfinityandpositiveinfinity.Theycanbe
positive,zero,ornegative,butcannotbewrittenindecimalor
fraction.Integerscanbewritteninsetformas{…,-3,-2,-1,0,1,
2,3,…}.Wecansaythatallwholenumbersandnatural
numbersareintegers,butnotallintegersarenaturalnumbers
orwholenumbers.IntegersarerepresentedbythesymbolZ.
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6. Fractions
Afractionrepresentspartsofawholepiece.Itcanbewritteninthe
forma/b,wherebothaandbarewholenumbersandbcanneverbe
equalto0.Allfractionsarerationalnumbers,butnotallrationalnumbers
arefractions.Fractionsarefurtherreducedtoproperandimproper
fractions.Improperfractionsareonesinwhichthenumeratorisgreater
thanthedenominatorwhiletheoppositeistrueinproperfunctions,i.e.
denominatorisgreaterthannumerator.Examplesofproperfractionsare
3/7and99/101,while7/3and101/99areimproperfractions.This
meanstheimproperfractionsarealwaysgreaterthan1.Allterminating
decimalsandrepeatingdecimalscanbewrittenasfractions.The
terminatingdecimal1.25canbewrittenas125/100=5/4.Arepeating
decimal0.3333canbewrittenas1/3.
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7. Rational Numbers
Rationalnumbersareoneswhichcanbewritteninfractionform.The
word“rational”isderivedfromtheword,“ratio”,asrationalnumbersare
theratiosofthetwointegers.Forexample,0.7isarationalnumber
becauseitcanbewrittenas7/10.Otherexamplesofrationalnumbers
are-1/3,2/5,99/100,1.57,etc.Considerarationalnumberp/q,
wherepandqaretwointegers.Here,thenumeratorpcanbeanyinteger
(positiveornegative),butthedenominatorqcanneverbe0,asthe
fractionisundefinedthen.Also,ifq=1,thenthefractionisaninteger.
RationalnumbersarerepresentedbythesymbolQ.
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8. Irrational numbers
Irrationalnumbersarethosewhichcannotbewritteninfraction
form,i.e.,theycannotbewrittenastheratioofthetwointegers.
Afewexamplesofirrationalnumbersare√2,√5,…,π,andsoon.
Youcanseethatthedigitsinirrationalnumberscontinuefor
infinitywithnorepeatingpattern.Irrationalnumbersare
representedbythesymbol??????
′
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9. Real numbers
Realnumbersarethesetofallrationalandirrationalnumbers.
Thisincludesallthenumberswhichcanbewritteninthe
decimalform.Allintegersarerealnumbers,butnotallreal
numbersareintegers.Realnumbersincludealltheintegers,
wholenumbers,fractions,repeatingdecimals,terminating
decimals,andsoon.Realnumbersarerepresentedbythe
symbolR.
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10. Prime Numbers
Primenumbersarethepositiveintegershavingonlytwo
factors,1andtheintegeritself.Forexample,factorsof6are1,2,3
and6,whicharefourfactorsintotal.Butfactorsof7areonly1
and7,totallytwo.Hence,7isaprimenumberbut6isnot,
insteaditisacompositenumber.
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11. CompositeNumbers
Inmath,compositenumberscanbedefinedasthewhole
numbersthathavemorethantwofactors.Wholenumbers
thatarenotprimearecompositenumbers,becausetheyare
divisiblebymorethantwonumbers.
Butalwaysrememberthat1isneitherprimenor
composite.
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12. Questions
1.What are the five rational numbers between 1
and 2?
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13. 2.Show that 0.3333… = 0 3, can be expressed in
the form of rational number, i.e.p/q.
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14. 3.Write the following in decimal form and mention
what expansion it is. (hint: terminating or repeating)
i.36/100
ii.1/11
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15. Summary
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16. Thank You
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