3.The Set of Rational and Irrational Numbers Together Are Called Realnumbers

CHAPTERNO.1

REALNUMBERS(Weightage10 –11Marks)

BASICCONCEPTS:

1.Rationalnumbersarenumberswhichcanbewrittenintheformof,where both‘p’and‘q’are integersandq≠ 0.

2.Irrationalnumbersare numberswhichcan’tbeexpressintheformof

rationalnumbers.

3.The set of rational and irrational numbers together are called Realnumbers.

4.ThefundamentaltheoremofArithmetic:“Everycompositenumbercanbeexpressedasaproductofprimesandthisfactorizationisunique(apartfromtheorderinwhichtheprimefactorsoccur).

5.H.C.F :Productofthesmallestpowersofeachcommonprimefactorsinthenumbers.

6.L.C.M : Product of the greatest powers of each prime factors in thenumbers.

7.TheproductoftwopositiveintegersisequaltotheproductoftheirL.C.M

andH.C.F.

8.Let x=bearationalnumbers, suchthattheprimefactorizationof“q”isoftheform2n.5m wheren,marenonnegativeintegers. Then‘x’hasa

decimalexpansionwhichterminates

9.If ‘q’isnotintheformof 2n.5mthenthat‘x’hasadecimalexpansionwhichisnon–terminatingrepeating(recurring)

10.(i)a,xaretwopositiveintegersanda≠1and x=an then= n

(ii)Logarithmof anynumbertoagivenbase isthevalueofindextowhichthe basemustbe raisedto getthegivennumber.

11.LAWSOFLOGARITHMS:

i.=+

ii.=-

iii.=m.

iv.=1

v.=0

12.

Rational Numbers(Q)Integers(Z)

WholeNumbers(W)Natural Numbers(N)

IrrationalNumbers

( QI)

Real Numbers (R)

NWZQRR =QQI

SHORTANSWERQUESTIONS(S.A.Q)(2MARKS)

1.FindtheL.C.MandH.C.Fof220and284byapplyingtheprimefactorizationmethod?

2.Withoutactuallyperforminglongdivisionexpressthefollowinginthe

decimalexpression

i.ii.

3.Expandthefollowinglogarithms

ii.

iii.iv.

4.SimplifyeachofthefollowingexpressionaslogN.

i.Log2+log5

ii.Log10+ 2log3–log 2

iii.3log4

iv.2log 3–3log

VERYSHORTANSWERQUESTIONS(V.S.A.Q)(1MARK)

5.Express156asaproductoftheprimefactors.

6.Showonthenumberline.

7.Express0.375inform

8.=xexpress thisinthe powers