Ee E-YA74 1 Number Systems Fastrack« Revision ) > Matra Numbers et of cuntog numba. Meth2 3.45.9 holo umbers (use of natura numbers W234 503 Angers (etl whole umbers nd egative Bebe h 8-2-1 Zoed > Rational Numbers (Q): Numbers which can be eapessedinthe orm 2. where pand gare Integers and a0 (recur Lae 2bosnosinsesttomet ashen number Fae@"«s9.then 2 benonteim rumbirt ae sad tobe eqeaen f amertor > teratoma Numbers Nudes whch Real Numbers (Sz onthe nunéer ln. Aso eer point nthe nunber > Radial sign: Suppese a> Obe area number and n Bexpoccuetegee Then tn roo a dines 1 Ho=b, FP cand >0.Thesymbol "ued tn Gis le, oF scaled he radkal lan where 9 andere krow os inde and radar respectively wedge BOOSTER osu 26,0+50)-ernchnteed bbe postive elPn ye = shame on eY * pumbetsandaand necro panes hen rues hen A mint rah pg eds, 8S Paar Qy Practice Exercise 2G Mattipe roca avtion 08. Arana unberbetnecn (Fw 1 peyton sneer ‘ & Steartmber Anat mamber gaa ftw! posive integer which + not Oh bey eteentere ‘perfect square, then the value of Ja is: 6. ener ona oriravonl QL, Whichofthe lowing santrvatinal number? 08 Bene yon nub he = Miretaseerta @ fatto d bisa iafoainanias iz. Whatisthedcinanrm of 201 04 Tesum oft alan! umber b 2 soe an ge 18 Thee F199 other 2a & few pad gee integrand 206 8. What i the deci veprsemation of an 3 : Seg emi awed sehr bier ‘eco eo bra 7. A toa numer betwen Sa 9 O18, =F et1 then tional number betwen and 5: an cai aaa 2119007 Thesinpldvate FE AB EE oe ete 01m treo ten + equ ce os as 19,1 Va taneaten (22=! oq gan ue 21 Thesimplied orm of 922, IF sequal (24 iL pontine el oumber and? = 11 then an ot aut Drecton (Nos. 25-2; Inte flowing gosto, Reasen Choos the cared opto “ (025, Amertion (A: Rational numbering between Reason (Rl Rational umber ying between | | | | | | | | | | | | | | | | ' on u(2}(2) | | | | | | | ' | | | | | | | | Som Eye (926, Assertion (A): 6527 terminating decimal a recurring decimal number st of digi is ‘peated peridlcaly 21 Astin (A) The rtlonaising factor of i a Reason (8): If he product of tw0 ieatonat ‘he atoning itr a the ote {928 Anton (A: The implied form of 7 «7 Reason (Ry a> Oe eal number nd pond ‘heraionl numbers Thea d =a (G28. Auertion (A) The sum of fo fealonl Resto (The of wo lea members 2 Flin the Blanks 22eauesns (930. the predut or quotient ofa noe 270 raional {G81 The tonal numbers whose mamestor and denominator both ate ego Or they are ‘edetlot cq te clled ronal (938 IF the deco representation of « sumber | non terminating nonrepeating. tho the fumberie aan number 32 Yer wequtta QM 1ra=3 and b= 5 the ale of a+ willbe ) TuefFalse tyoe ovestions wv (296. the square roots of pon integer arelvaye (936, Every point on the number ine of the oem Frere mia patra umber. 57 the mamber (3-V5)3+)i5 an ieatonat 38 For ration dng the denominator of the hiplyand vie by 30-14-45 hen symbol Vie sal to bea Sie)Som Eye 9. since F144 ond YB=1.792 Therefore the rtonal umber between JF and 2 ana etna ou ig crt ube at wae dial rie otertnentot BE dea-ane( BoA) 1 BTU == rotainting nn oun-0-B) erasing te lca ratons romo oe 4a nrmmoase ER AEE ia a 45 een ae CtSETI EY TRICK a ((erbieino-» — ie ne (Gl canter? 10? ea pi) Nem ae bteosias b - &-G BiePee” EY Q1 The ratinating factor of YE +5 ee a) BG 4 5 +5) Q Accrtiog to Vinal explanation, the Ht ass 3. According 10 San eplanton, the 2-Bide= 07 - WF? simpcaton ot BF) hh 4, Adon off rain mbes °@ Case Study Based Questions Len sag ter of SH) case study 1 Se cee cies 3 iain gy . a He mie senna & By rationalisation the denominator homecerand 6 (E+ NKVE af) by sng the idetiy BD asm atati Ae . = él so Boobie Bien atone WatEe on” EY | i ! | 1 tural number ¢ 8. Sinn, Be L782and oS #2236 i 1 amen | 1 Case study 2 Hence, rational number 5 lies between I 1 the nui aurter line 60 | 1 nme | | Amonberet teem 2 ide atin ees | uber, ig #0 and pan a nego. nl | | | | ! i | | | | | | 1 : \ | ua | j oe ae | ! f ’ | ! ota , oy | ! a | | ational a | 1 : a= 01 waar evne \ ! 12 | | es i | | ee | Vee eae on | | | | | THDeae ee <6 ee? ae 0) § erin -——Belutions} ———- ‘cot deine sh de by 200, we gst 131, 2 Se.opon scone (a) from (2h we 9 crease Mo Rabi LBs Raa ee ‘ae ys ws ayig arb bye her = FRICTTEEYS =24345=30 sho lame shout raloral amben, imo G2 atye fos tend teat 4 Find prods of 0 ren ne Creo ana O= ME acTN eye Solutions} + 95 redsieateeat(*) (94 tx =0.000216 then inde value (0. 5: Simpy 40! 2 Weta xeB=3 vate a ial oa Compare ts woget Bet EF toy nonstate wel 4 ono cm ce ey teat: a wilh) as ronda aie eanben Then Q2 i 3 arational umber or (2. Find rational umber between led oe! 3. Comer he follwing deal amber ito anda oss coors 4. waite he nl nome 2 ei 8. Calle the value of 25 inthe form of 2, where pand arategerand 0. 6. Write the two rational sumbers bevesn Bends, O1. Find heal o 218" 6, Sie1. Simpy (72+ /800~ 8 (98. simply 3+ 513-5) by sing dentin 19. Wat the ating factor oF 010. Simpy 5+ QL. Wee the simpli vale of 2 nt, inde auc of (bs = (ste) 018. Simpy (29+ (5° + 43°F Short Answer Tyse-| Questions S QL ie a0 1 atonal sarber? ity your (92. tgser threw racona numbers burween $ and 3 98. Cassy the following numbers as rtlonal or ‘natlonal with jae (4 oro. form, where py 4 ae Qe baron Tin Integers and g 20, 95. Find two tration numbers betwen and 6. 1 Y--2236 then find the approsimate veloc “% qs (8. Fndthevalucofaad i 242/2, duck what ti lori byt. 9. Fx=1¢4F then find he vate of (x—4) 010. Taking 2 = 1414 and x « 3.14 evaluate pl three places decimal 1 Simply that $81 ~ 6 +1553 + VBS ow and b = 3, then find the valoe of a BY 13. show that 222) Pee Pe OU, Simply SESE SH 0 3 GY Short Answer yee: ovestons (1. Find sc rational numbers between and 4 02, Baps 055 Informa 2, whrpand ge img ang = 3, Plaate 5276 + /a=3/8, (04, Rationale the denominator of as Yaree en 4/3~ 0/2, fad evalu 7. Show how /can be represented om the (8. Locate YF the numbering 08, Represent JES oo the number ne 0, sip 2 au ints (3) (3) Ab 0 brtuate 6/799 25 18 Wate V4, 15, 6 ascending oder grxaxoy Pant _ ou 5. Show a G) Long Answer tysc ves 1 Gretworat in rien i onal ubePn ye (2, Epes 137+ 05 sea traction inthe simplest Z EET LEH 8 hog prove that fee Vera= ema’ et (08 Lets be etoal sey be atonal 657d aprs gues cherega0 eceailyHrtona? Jetty your anever by ig savage (4, Prove that : 0 Find he ale of 4 yt, 5. Find wand if aig as0F "ay NEG UE gs ise we isris au. 96, simply 223253 cts rena TNE gua, tg 2 be RH, and ab 0, find the ani fen find the mice of leat ° + 13, 65-29". 2500, thn find he ale of oe 3 9 035 = Sie * eneoea ton su 1h 5 2+ 8)0-)= 7 -WP sat= lett sands, aa Fearn 10+ oF Hand. fn 10124124. ta nn terminating curing short answer Types Questions ay 1. Yes 24 ational uma {eminaing non securing daca runbac Zeocanse womindas $b Sry Face itn ronal nonber vhichareiathefemot Zwhewpandaae 4 tat lexeges and ga (PICee EPA 16. en (5=2236 of 3 Ratoaisog te der ont a 328 a 9. Gren x= 1 ae 196 SPIE eritonaisicn ams Short Answer Type! Questions awaSom Eye Baa woo 838 meee 3985 a (34 242)? + (3-242)? - a4 2/218-242) a rome a ~ os 94 8412V2 +9 +8 12V2-407- v2" N= Ai = 5-8 ara}SETI EY night angi AONB ure Pytagors OF = Ora tenes ne segment OC repesents Fon the ear (Ok 3 units on a number lne Dato 8 = VES ree poet orcas EE awaLang Answer Type Questions Raton Hee ita tox 1322 a ‘gn, mtehog 9 2 by 1. we get TN eye Es FRatonaling the denomintor of ach pt a, AaB Hal. n3 orate as TRICK. awa 8) 95) O55. Asp ay =A ei 20+3+6/i5 22043-6155, ey BoasisePee EPA | i ae 2 eat) : qo esaecaenepae | eases wage | | tyr oda | 285 eee i | (atontang econo eat | | 1 . avian i 1 = = 32 fe “i ! i Siemens = cea 1 jae Ae 9. We have ' ton TTT TE ! Ses wh Bek Lie | Sree aie Saena ! 1 7. Given, x: oa ! ' vragen wn bo HE | | mien s42-2410_7=2440 I Bea New (ob)! ab = (222000, 2=2/10 | nat aunt | | ates a) (5a | ee apap i "eB a cape (223022340) \ | 1 "Yprale=aiptariema ; ! ' i i 17119TN eye aro? ase +2aent - ° ae Ftd t 2 =a zB Chapter Test ‘Multiple cholee Questions Ronen (a> 0b areal number and p and sbecatioal qumbers then @ = ad? (OL Actions umber between ad 1 > ae 4, Asertion (A): The sum of te Iain ’ ae unten 2-T and 2+VIT cao! 2, Mheratonalienion ator ef +7 i = aii-s Fillinthe Blanks ‘Assertion and Reason Type Questions QS. AF the decimal repreentation of = umber Diectons @ Nos 5) hn oe i smetemiotig eonrepeing ten te teen Moth Atrion ard Aesson (ae tye @b Thorac ot YO)” i 58 an TE BAN ua faeg © eaton fe not the conect expanatan af Q7. The product of (S~V) and (54F)te alan 3, Asetion (Athen frm of 8. For ratlonaling the denominator of the shipy and divide by 3. expreion Fem aaTN eye case study Based Questions Very Short Answer Type Questions (98 Ia clsraom, ne dy # mah teacher ght stents of as IX soot he aunber sys, QD Simpy 708+ VIR aoe QUL Wit the spied valu of nit A numerator 290i aration oor fsa umber, wish canbe rp a Short Answer Type: Questions O12. Find two eatin! oumbers between O18, Pedi valeot and SB aa ra Short Answer Types Questions QUE. Show how 9 can be vepesnted on the (0) Finda rational mmberbetneen Sand ame (Fld he eal mumber of ais metsct(2) (2) 28 . Long Answer Type Question Wet the tonal form f 33. (uy teu? mtd rect! OM Sgt ah