Indices. Indices. Curriculum Ready ACMNA: 209, 210, 212,

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Inis Inis Curriulum Ry ACMNA: 09, 0,, 6 www.mtltis.om

Inis INDICES Inis is t plurl or inx. An inx is us to writ prouts o numrs or pronumrls sily. For xmpl is tully sortr wy o writin #. T is t inx. Anotr wor or inx is xponnt. Answr ts qustions, or workin trou t ptr. I us to tink: Wt r inis? (Wt r xponnts?) How r inis us to writ vry lr n vry smll numrs? Wt is sintii nottion? Answr ts qustions, tr workin trou t ptr. But now I tink: Wt r inis? (Wt r xponnts?) How r inis us to writ vry lr n vry smll numrs? Wt is sintii nottion? Wt o I know now tt I in't know or? Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Bsis Inx Nottion Inx nottion is us to writ prout o numr wit itsl in n sir wy. For xmpl: Inx or xponnt or powr # # # 6 Bsi numrl So wn multiplyin numr, sy 6, y itsl 00 tims, it s sir to writ 6 00 inst o 6# 6# 6 #...(00 tims). Bs I t inx is w usully mk it invisil so w writ 7 inst o 7. Ain n Sutrtin wit Inis Two xprssions in inx orm r lik trms i ty v t sm s AND ty v t sm inx. Cn simplii (lik trms) Cnnot simplii (unlik trms) Sm inx Dirnt inis + ^ 8 6 + Sm s Dirnt s Simpliyin lik trms Lik trms 6 + + + 6 + Lik trms Lik trms roup totr ^6 + 6 + ^ + + Simpliy lik trms ^6 + ^ + J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Bsis Multiplition wit Inis Consir t prout # ^ # # ^ # # +. In t prout, t s is t sm n t inis v n totr. In nrl you n pply t ormul or multiplition wit inis: m n m+ n # Sm s A inis Multiplyin trms wit inis 7 + t # 9t # 9 # t # t 6t 6t Coiints multipli sprtly Coiints multipli sprtly REMEMBER A oiint is t numr or t vril in n xprssion. E. T oiint o x is. + + pq # pq # # p # p # q # q p q pq Sm ss roup totr Division wit Inis I w ivi 7 7 7 7 7 7 7 7 7 7 7 7 ' # # # # # # m # # m 7 # 7 7. 7# 7# 7 7# 7# 7 In t ivision, t son inx () s n sutrt rom t irst (). In nrl, pply tis ormul or ivision wit inis: m n m n ' Sm s Sutrt inis Diviin trms wit inis Coiints ivi sprtly 7 7 0y ' y ^0 ' ^y ' y y y 7 Coiints ivi sprtly 6 6 ' 7 ^ ' 7^ ' ^ ' ^ ' 6 Sm ss roup totr Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Qustions Bsis. Writ in xpn orm: 6 9 ^ ` j ` j x xy i. Intiy t s, inx n si numrl o o t ollowin: 0 Bs Bs Bs Inx Inx Inx Bsi numrl Bsi numrl Bsi numrl ` j Bs ^ Bs ^ Bs Inx Inx Inx Bsi numrl Bsi numrl Bsi numrl ^ 6 Bs Bs Inx Inx Bsi numrl Bsi numrl. Intiy t ollowin vlus: Wt is t si numrl o to t inx? Wt is t s o n xprssion wit inx n si numrl 6? Wt woul t inx o n xprssion i t si numrl is 8 n t s is? Wt is t inx in n xprssion wit s 7 n si numrl? J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Bsis. Us lik trms to simpliy t ollowin in inx orm (i possil): + + ^ ^ 7+ 7 + 7 + ^6 + ^ + 6 + ^ ^ + ^ +. Fin t ollowin prouts in simplst inx orm: 6 # # # 7 ^ # ^ ^ # ^ ` j # ` # j ` j q # q 7 x # y# y # x 0 # i 8 6# wv# w # v Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Qustions Bsis 6. Fin t ollowin prouts in simplst inx orm: 8 ' 8 7 ' 7 6 ^ ' ^ 9 m ' m 9 rs ' rs 8 9 6 6' 9 x y 7 6xy i 6 ' 8 J 6 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Knowin Mor Risin Inis to Inis W us wt w know out multiplyin trms wit inis, to in rul or risin inis to inis. Consir or xmpl: 8 ^ # # Noti tt t s rmins t sm n w in t prout o t inis. In nrl, pply t ormul ^ m n mn Sm s Multiply Inis Risin inis to inis ^ # 0 x x x ^ # Mor Inx Lws I prout or rtion is ris to n inx, tn t inx pplis to trm. Brkts wit inis ^ m m m m n m m m ^x x pq ^ p ^q 7x 6pq # 8 6pq x x ` j x 8 ^ m 6 9 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC 7

Inis Knowin Mor T Zro Inx m 0 m m m Tis mns 0 wn! 0 Anytin ris to n inx o 0 is. T zro inx 0 0 0 0 00000 0 0 0 ^ ` ^+ x ^ j 0 0 0 6 + ^6 + ^ ^ 0 # 7 # 7 7 Frtionl Inis Lt s try iur out wt to o wn t inis r rtions, su s For xmpl, onsir : 6 or p 7. Usin t inx lw or multiplition w n sy ^ Fin t squr root o ot sis to otin ^ Simpliy y nllin t inx o wit t squr root For ny, w n sy is t squr root o t numr. In t sm wy is t u root o. Bsilly, or ny n, n is t n t root o. Alwys us t ormul n n Frtionl inis 6 6 6 8 ^ x # 8 # x x J 8 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Knowin Mor Ntiv Inis Lt s s i w n us wt w know to iur out ow to us ntiv inis su s, or x For xmpl: Ntiv inis 0 ^. ` 0 0 0 0 Sin 0 Usin t ivision o inis lw Aorin to t zro inx lw In nrl, or ntiv inis w us t ormul: n n Ntiv inis xmpls 6 t m t t x x ` j ` j 9 ^ ^ ^ In tis xmpl, t minus () is inlu in t inx. In tis xmpl, it is NOT inlu in t inx. Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC 9

Inis Knowin Mor Mor Frtionl Inis Up until now w v only work wit rtionl inis wit numrtor lik or. As ll mtmtiins know, ts r not t only typ o rtions. It is importnt to lrn ow to us rtionl inis wos numrtors r not or xmpl: Usin t risin n inx to n inx lw, w in ^ ^ In nrl, t ormul or rtionl inis is: m m n n m ^ ^n ^ m n n m Mor rtionl inis 7 ^7 ^ 8 7 6 6 ^ 6 6 6 6 00xy 6 ^ 8^00xy B 8 ^ 00 xy ^0xy 000xy 6 9 ` 8 j ` 8 j 6 J 0 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Knowin Mor. Us t lw or risin inis to inis to rwrit t ollowin in simplst inx orm: ^ 6 ^ 6 7 8 ^ 0 ^ x ^ 6 ^. Us inx lws to rwrit t ollowin in simplst inx orm: ^x ^t ^xy ^p q 0 ^ 7 ^u ^ 7 xy ^ i ^ j ^pqr 7. Us inx lws to rwrit t ollowin in simplst inx orm: ` j x y o x m y x y o ` j xy m y Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Qustions Knowin Mor. Us t zro inx lw to simpliy t ollowin: 0 67 0 ^6 0 ^ 0 0 ^ 0 ^# 0 0 0 0 # i 0 ^ 7 0 j 6p 0 k 0 # x l # x 0. Simpliy t ollowin xprssions usin t lw or ntiv inis: 0 ^ ^ p 7 i 6p j ^6p k 7 0x ' 0x l 7 6 0 0pq' 0pq 6. Us rtionl inis to writ t ollowin in sur orm: 7 0 n 6 6 q 7 x mn 6 mn 6 ^ i 7 J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Knowin Mor 7. Writ t ollowin in inx nottion: 8 x 0 0 x y x 8. Writ t ollowin in simplst positiv inx nottion: ^ 8 ` j w # w ^7 # ^7 6 p ' p 7 x # x y ' y ^ pq 7 0 i 0 x # ` # 0 # x j j ^6 ' 6 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Usin Our Knowl Ar, Volum n Sur Ar Inx nottion n ppli to msurmnt, to in xprssions or ts msurmnts or to solv prolms. Fin n xprssion or trinl wit t ollowin imnsions: x An xprssion or t r o tis trinl is x Ar # ^Bs# ^Hit # x# x # # # x# x x ` ^ j Tis is t pln or swimmin pool: y 6y y I t volum o t swimmin pool nnot x Stp : Dtrmin n xprssion or t volum: Volum ^lnt# ^rt# ^it 6y# y# y y Stp : St t xprssion qul to 768 n solv or y: 768m wt is t mximum vlu or y? y 768 y y 6 y 6 Divi ot sis y Fin t u root o ot sis J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Usin Our Knowl. A rpt ns to put own on st or n upomin onrt. Tr is only 90 m o rpt vill or t st wi s t ollowin sp: Fin t vlu o x to nsur ll t rpt is us. x x x. A nw uilin is in uilt ntirly out o lss (inluin t roo, xluin t loor). T sp o t uilin is isply low. I tr is only 6 60m o lss vill, tn wt is t mximum prmissil vlu o p to nsur tr is nou lss or t ntir uilin? p p p Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Qustions Usin Our Knowl. In n ropln, t pssnr in s imnsions: k k 6k k Bor lit, t in must ill wit oxyn. Writ n xprssion or t volum o oxyn rquir or ropln in trms o k. I prtiulr irlin rquirs omin volum o 60 000 m o oxyn or 0 roplns, tn solv or k. J 6 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Usin Our Knowl Sintii Nottion or Lr Numrs (Grtr Tn ) Sintii nottion pplis inx nottion to lp writ vry lr n vry smll numrs in n sy wy. For xmpl, 000 0 0 0 0 # # Som xmpls r: 000 # 0 00 000. # 0 8 000 000 8. # 0 6 7 Tis my sm silly or numrs tis smll ut it is rtinly lpul or lr numrs su s # 0 0 or # 0 00 Not tt 8 000 000 is not writtn s 8 0 6 #. Sintii nottion rquirs t irst numr to twn 0 n 0 (so on o,,,..., 9). Sintii nottion or lr numrs For lr numrs (rtr tn ) t inx o 0 is t numr o iits twn t irst iit n t iml point. 7 6 First iit 8000000. 0 8. # 0 7 Diml point Btwm n 0 Sintii Nottion or Smll Numrs (Lss Tn ) Sintii nottion is writtn s (numr twn 0 n 0) (inx o 0), t only irn or smll numrs is tt t inx is ntiv. Som xmpls r: 0.0 0 00 # 0 0.007 7 7 # 0 ^7. # 0# 0.7 # 0 0 000 Ain t nswr is not writtn s 7 # 0 sin t irst numr is rquir to twn 0 n 0. Sintii nottion or smll numrs For smll numrs (lss tn ) t inx is t ntiv vlu o t mount o iits tr t iml point up to n inluin t irst nonzro iit. Diml point 0.007.7 # 0 First nonzro iit Btwm n 0 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC 7

Inis Usin Our Knowl Sintii Nottion Mks Clultions Esir Usin sintii nottion 000 000 0000 000 # 0000 000 ' 00 7 8 ^. # 0 # ^. # 0 7 8. #. # 0 # 0 7+ 8 0. # 0 0. # 0 ^0. # 0 # 0 6 0. # 0 (Rmmr t irst numr must twn n 0) ^. # 0 ' ^# 0 8. # 0 # 0 8. # 0 0 8 0. # 0 0. # 0 ^# 0 # 0 # 0 6 8 6 (Rmmr t irst numr must twn n 0) 0.000 0.00 # 0.0000 ' 0.000000009 ^. # 0 # ^# 0. # # 0 # 0 8.86 # 0 7 886. # 0 (Rmmr t irst numr must twn n 0) 9 ^. # 0 ' ^9# 0. # 0 9 9# 0. # 0 9 9 0 ^9 0.# 0 + 9 0.# 0 0.# 0 ^# 0 # 0 # 0 (Rmmr t irst numr must twn n 0) 0. 0000096 96# 0 ^96 ^0 8 8 # 0 ^. # 0 # 0. # 0 (Rmmr t irst numr must twn n 0) J 8 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Usin Our Knowl. Rprsnt t ollowin lr numrs usin sintii nottion: 000 780 000 00 000 97 80 000. 000 000 000. Rprsnt t ollowin smll numrs usin sintii nottion: 0.006 0.0007 0. 0.0000000000 0.000000076 0.0088 6. Rprsnt t ollowin numrs in sintii nottion: Twlv tousnts Two million, tr unr tousn Four unr n twnty millionts Nin illion, iv unr n sixty svn million 7. Rwrit t ollowin in norml numrs: 0. # 0 6 6. 98 # 0 87. 7 # 0 8 0.097 # 0 7 00067. # 0 9 00000. # 0 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC 9

Inis Qustions Usin Our Knowl 8. Evlut t ollowin prouts usin sintii nottion: 7 8 ^# 0 # ^7# 0 ^. # 0 # ^8. # 0 7 ^ ^ 6. 0 ^. 0 ^. # 0 #. # 0 # # # 0 ^ ^. ^6. # 0 #. # 0 7 6# 0 # ^# 0 9. Evlut t ollowin quotints usin sintii nottion: 8 7 ^6# 0 ' ^# 0 ^96. # 0 ' ^. # 0 8. # 0 '. # 0 ^ ^ ^7. # 0 ' ^6# 0 ^6. # 0 ' ^8# 0 6 ^. # 0 ' ^9# 0 J 0 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Usin Our Knowl 0. Evlut t ollowin usin sintii nottion: 6 # 0 00# 0 00 6 # 0 6 # 0 0. 0 ^ # 8 0 ^ #. Evlut t ollowin usin sintii nottion: 0 000# 60 000 ' 9000 0 000 78 ' 0.6 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Tinkin Mor Comprin Sintii Nottion Arrn t ollowin numrs in snin orr:. # 0 6.7 # 0. # 0 6.6 # 0 8. # 0 Stp : Arrn y inx 6.7 # 0. # 0. # 0. # 0 6.6 # 0 8 Stp : Arrn y numr in inx 6.7 # 0. # 0. # 0. # 0 6.6 # 0 8 Sm inx Arrn t ollowin numrs in snin orr: 9. # 0 8. # 0 7. # 0 6. # 0 8. # 0 Stp : Arrn y inx 7. # 0.9 # 0 8. # 0 8. # 0 6. # 0 Stp : Arrn y numr in inx 7. # 0 8. # 0.9 # 0 8. # 0 6. # 0 Sm inx Prixs or Inis o 0 W ll know tt tr r 000 m in km. T prix kilo tully mns 000 or 0. So wn w sy kilomtr w mn # 0 mtrs, or wn w sy kilorms w mn 0 # rms. T prix milli in millimtrs mns 0 (or 0.00). So wn w sy istn is mm, w mn # 0 m (or 0.00 m). Som otr prixs r: Smll numr Lr numr Prix Inx Arvition pio 0 p nno 0 9 n miro 0 6 μ milli 0 m to 0 kilo 0 k m 0 6 M i 0 9 G tr 0 T Wn w sy o tryt (T), tis mns 0 # yts o mmory. J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Tinkin Mor. Arrn t ollowin in snin orr: # 0. # 0 7 7# 0 6.# 0 7.# 0 6 # 0.# 0.# 0 # 0 # 0 7.# 0 6# 0 7.# 0 # 0. Complt t ollowin tl: Msurmnt Prix Inx Smll or Lr Numr Expn Form 00 M M 0 6 Lr 00 000 000 6 nm Nno 97 μm 60 p 0 0 Lr 00 m 000000 C 0.00000000 m T mss o t Ert is stimt to.98 0 # k. Writ tis vlu in trrms (T). T istn rom t Ert to t Sun is stimt t.96 0 # m. Writ tis in Gimtrs (Gm). T r o n ltron is.609 0 9 # Couloms (C). Writ tis in pioouloms (pc). Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Tinkin Evn Mor Finin Missin Trms Fin in o t ollowin xmpls: Finin t missin trm in prout To otin y itsl, ivi ot sis y vrytin otr tn : 7 # # 7 7 Finin t missin trm in prout To otin y itsl, ivi ot sis y vrytin otr tn : # vw vw # vw vw vw vw v w vw Finin t missin numrtor in quotint To otin y itsl, multiply ot sis y t nomintor unr : 6 # 6 # 6 # 8 J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Tinkin Evn Mor Finin Missin Trms Finin t missin nomintor in quotint To otin y itsl, swp t nomintor wit t trm on t otr si o t quls sin: 8 8 6 7 8 Finin t missin vlu in sur To otin y itsl, ris ot sis to t inx wi will nl t sur wy: ^ ^ 6 8 Finin t missin vlu in n inx To otin y itsl, in t squr root o ot sis to nl t squr wy (ssum is positiv). ^ ^ 8 9 8 9 6 (Rmmr t squr root is positiv y onvntion) Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Qustions Tinkin Evn Mor. Fin t vlu o in t ollowin prouts: r # r # 8 6 8 mn # mn # 8 xyz 0yzx 6 8 6 7 # pqr # 6p qr 8 7 6 0 6 9 # # # # J 6 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Qustions Tinkin Evn Mor. Fin t vlu o in t ollowin quotints: 0y 6 y 6 9tu tu 6pq 6pq 8 8 0 ' xy z ' 6x y. Fin t vlu o in t ollowin: xy z 8 9 ^ 6p q ^ 6m n p Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC 7

Inis Qustions Tinkin Evn Mor. Qustions to tink out: Explin t irn twn ^# n #. Wt is t irn twn ^ 0 n 0? Wt is t irn twn 6 n 0 6 #? For ny numr, os 0 xist? I so tn wt is its vlu, i not tn wy not? Dos 0 xist? I so tn wt is its vlu, i not tn wy not? 0 Is tr vlu or so tt x # x? Do 6 0 n 6 0 v irnt vlus? Wt r t vlus o x n y i ^ 8 6? y x J 8 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Answrs Bsis: Bsis:. #. 6 6# 6# 6# 6 9 9# 9# 9 ^ # # ` j # # # # Bs Inx Bsi numrl Bs Inx 6 Bsi numrl 6 ` j ` # # # j ` j ` j ` j. 6 x x# x ( so s is ) xy x# x# x# y# y# y (Inx is ) i # # # # # (Inx is ). Bs 0. ^ ^ Inx Bsi numrl 0 Bs Inx ^ ^ + ^6 ^ + 7^ + 7 7 + ^ Bsi numrl 9 Bs Inx Bsi numrl 6 Bs. 9 ^ 0 9 ` j xy 8 ^ 7 q 0 0 Inx Bsi numrl 8 i 8wv 6 Bs 6. 8 7 7 6 Inx Bsi numrl 9 Bs Inx ^ 7 7 ` j rs 9xy Bsi numrl i 8 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC 9

Inis Answrs Knowin Mor:. 0 6.. 6 6 0 x 0 x 8 t xy p 0 q 0 u Knowin Mor: i 6 7 n 7 q 6 x m n 6 mn 6 6 7 0 8 8 6 0 ^ x y 7. 8 x i 0 0 6 8 j p q r 0. x y x y 8 6 x y 9 x 8 8. 0 x x y 6 9 w 7. p y 0 x i i 0 x j j 6 k l Usin Our Knowl:. 00. x 7m 7 7. p 9m 6 7 p 6. Totlvolum k m 8k i k 6 j p 6p x l pq.. # 0 78. # 0 J 0 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

Inis Answrs Usin Our Knowl: Tinkin Mor:. 0. # 0 6 978. # 0 7.. # 0 0. # 0 0 #,. 0 6 #, 7 0 6 #,.# 0 7,. # 0 7. 6. # 0 7. # 0. 0 #, 0 #, 0 #,.# 0, # 0 0 # 0 76. # 0 8 88. # 0 7. 0 #, 7. 0 #,, 6# 0, # 0 6. 7. 8. 9.. # 0. # 0 0. # 0 7 698. # 0 877. # 0 97. # 0 6.7 # 0. # 0. # 0 6 967. # 0 9 8. # 0 6. # 0. # 0 7. # 0. # 0 8. # 0 9 # 0 # 0 # 0 6. # 0 8 8# 0 6 6# 0. Expn Form Smll or Lr Numr Msurmnt Prix Inx 00 M M 0 6 Lr 00 000 000 6 nm Nno 0 9 Smll 0.000 000 06m 97 μm miro 0 6 Smll 0.000 097 m 60 p pio 0 Smll 0.000 000 000 6 m to 0 Lr 00 m M C m 0 6 Lr 000 000 C nm nno 0 9 Smll 0.000 000 00 m 0. 8# 0 6 0 # 0 # 0. # 0 0 6. # 0 0 98. # 0 T 96. # 0 Gm 609. 0 7 pc #. 6. # 0 0 # 0. # 0. # 0 Mtltis 00% 00% Inis P Lrnin J SERIES TOPIC

Inis Answrs Tinkin Evn Mor: Tinkin Evn Mor:. r mn 6 x z pqr. Ys, tr is vlu or tt mks 0 x # x. T vlu is 7x 6 No, t two trms o not v irnt vlus; ty r ot qul to. x n y. 0y tu 8 8 6p 9 q 0 9xyz 7. 6x yz 7 9 p q 7 m np. T irst is uin (risin to t inx o ) t prout o n, tt is. T son is tkin t prout o n u, tt is 6 9 #. T irst is risin t prout o n to t inx o zro, tt is ^. 0 T son is multiplyin y 0, tt is 0 #. T irst is sort n wy o writin # # # # #, wi is qul to 096. T son is sort n wy o writin # 0# 0# 0# 0# 0# 0, wi is qul to 000000. W n usully writ ny sur lik n s n 0 But i w o tis wit w woul t 0 n so on. Sin w n t ivi numr 0 y zro it tlls us tt os not xist. 0 000 J 00% Inis SERIES TOPIC Mtltis 00% P Lrnin

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