H SERIES. Decimals. Decimals. Curriculum Ready ACMNA: 103, 128, 129, 130, 152, 154,

Transcription

1 Dimls H SERIES Dimls Curriulum Ry ACMNA: 0, 8, 9, 0,,,

2 Copyriht 009 P Lrnin. All rihts rsrv. First ition print 009 in Austrli. A tlou ror or this ook is vill rom P Lrnin Lt. ISBN Ownrship o ontnt Th mtrils in this rsour, inluin without limittion ll inormtion, txt, rphis, vrtismnts, nms, loos n tr mrks (Contnt) r prott y opyriht, tr mrk n othr intlltul proprty lws unlss xprssly init othrwis. You must not moiy, opy, rprou, rpulish or istriut this Contnt in ny wy xpt s xprssly provi or in ths Gnrl Conitions or with our xprss prior writtn onsnt. Copyriht Copyriht in this rsour is own or lins y us. Othr thn or th purposs o, n sujt to th onitions prsri unr, th Copyriht At 98 (Cth) n similr lisltion whih pplis in your lotion, n xpt s xprssly uthoris y ths Gnrl Conitions, you my not in ny orm or y ny mns: pt, rprou, stor, istriut, print, isply, prorm, pulish or rt rivtiv works rom ny prt o this rsour; or ommrilis ny inormtion, prouts or srvis otin rom ny prt o this rsour. Whr opyriht lisltion in lotion inlus rmunrt shm to prmit utionl institutions to opy or print ny prt o th rsour, w will lim or rmunrtion unr tht shm whr workshts r print or photoopi y thrs or us y stunts, n whr thrs irt stunts to print or photoopy workshts or us y stunts t shool. A worksht is p o lrnin, sin or stunt to writ on usin n ink pn or pnil. This my l to n inrs in th s or utionl institutions to prtiipt in th rlvnt shm. Pulish P Lrnin Lt For mor opis o this ook, ontt us t: Dsin P Lrnin Lt Althouh vry prution hs n tkn in th prprtion o this ook, th pulishr n uthors ssum no rsponsiility or rrors or omissions. Nithr is ny liility ssum or ms rsultin rom th us o this inormtion ontin hrin.

3 Dimls llow us to mor urt with our lultions n msurmnts. Bus most o us hv tn inrs, it is thouht tht this is th rson th iml systm is s roun th numr 0! So w n think o imls s in rtions with powrs o 0 in th nomintor. Writ in this sp EVERYTHING you lry know out imls. Giv this o! Q To mk rk-rn olour pint, you n mix yllow n lu tothr, usin xtly 0. (hl) s muh yllow s you o lu. How muh rk-rn pint will you mk i you us ll o th. ml o lu pint you hv? Work throuh th ook or rt wy to o this Mthltis Dimls P Lrnin Lt H SERIES TOPIC

4 How os it work? Dimls Pl vlu o imls Dimls rprsnt prts o whol numr or ojt. # Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0 # 000 on thousnth th iml pl: ' 0 # on tn thousnth t... # ' 0 ' 00 Tnths Hunrths Thousnths Tn thousnths W H O L E D E C I M A ' 000 ' ' ' Hunr thousnths Millionths Tn Millionths L ' A th to th nm or iml pl vlus Writ th pl vlu o h iit in th numr.70 Multiply y multipls o 0 Divi y multipls o 0 Expn orms Pl vlus... # hunr... # 0 0 tns (or sixty) Intr prts... # ons (or iv)... ' 0 or ` # 0 j ' 00 or 7 ` # 00 j ' 000 or 0 ` # 000 j... ' or ` # j tnths 7 hunrths 0 thousnths tn thousnths st iml pl n iml pl r iml pl th iml pl H Dimls SERIES TOPIC Mthltis P Lrnin Lt

5 How os it work? Your Turn Dimls Pl vlu o imls Writ th iml tht rprsnts ths: hunrths 9 tnths tn thousnth 0.0 Alwys put zro in ront (ll lin zro) whn thr r no whol numrs thousnths hunr thousnths 8 millionths Writ th rtion tht rprsnts ths: tnths 7 thousnths hunrth 9 tn thousnths hunrths tn thousnths Writ th pl vlu o th iit writtn in squr rkts or h o Cirl th iit oun in th pl vlu ivn in squr rkts: [tnths] [thousnths] [hunr thousnths] [hunrths] [tn thousnths] [millionths] Mthltis Dimls P Lrnin Lt H SERIES TOPIC

6 How os it work? Your Turn Dimls Pl vlu o imls Eh iit is multipli y th pl vlu n thn tothr whn writin numr in xpn orm. Writ th iml.0 in xpn orm # + # + # + # + # # + # + # + # Multiply h iit y its pl vlu Zro iits n rmov to simpliy Writ ths imls in xpn orm: Simpliy ths numrs writtn in xpn orm: # + # + # # + # + # + # /.../0... LACE VALUE OF DECIMALS PPLACE VALUE OF DECIMALS # + # + # + # + # + # # + # + # + # + # + 9 # Psst: Rmmr to inlu lin zro or ths ons # # # 7 0 # + # + # + # # # # # # H Dimls SERIES TOPIC Mthltis P Lrnin Lt

7 How os it work? Dimls Approximtions throuh rounin numrs Look t ths two sttmnts m out tm o snoworrs: Thy hv ttmpt 97 triks sin strtin Aurt sttmnt Thy hv ttmpt nrly 000 triks sin strtin Roun o pproximtion Rounin o vlus is us whn rt l o ury is not n. Th nxt iit ollowin th pl vlu whr numr is in roun o to is th importnt prt. Nxt iit Closr to lowr vlu, so roun own Lv th pl vlu unhn Closr to hihr vlu, so roun up A to th pl vlu Hr r som xmpls to s how w roun o numrs. Roun ths numrs to th nrst hunr 0 0 Th iit is in th hunrs position Th nxt iit is, so roun up y in to Chn th othr smllr pl vlu iits to 0 s `. 00 roun to th nrst hunr 0. to on iml pl (or to th nrst tnth) Th iit is in th irst iml pl Th nxt iit is, so roun own Writ iml with on iml pl only ` roun to on iml pl (iii).89 to our iml pls (or to th nrst tn thousnth) Th iit is in th ourth iml pl Th nxt iit is 9, so roun up y in to Writ iml with our iml pls only ` roun to our iml pls Mthltis Dimls P Lrnin Lt H SERIES TOPIC

8 How os it work? Your Turn Dimls APPROXIMATION THROUGH ROUNDING NUMBERS. Approximtions throuh rounin numrs Roun ths whol numrs to th pl vlu ivn in squr rkts..../.../0... [nrst tn] [nrst hunr] [nrst thousn] (iii) 90. (iii) (iii) 00. Roun ths imls to th iml pls ivn in th squr rkts. [nrst tnth] [nrst hunrth] [nrst thousnth] (iii). 8. (iii). 00. (iii) Approximt th ollowin istn msurmnts: A roup o popl orm n 8.8 m lon lin whn thy stn tothr. How lon is this lin to th nrst 0 m (i.. iml pl)?. Wht is th pproximt lnth o this lin to th nrst 0 mtrs?. Unr mirosop th lnth o ust mit ws m Approximt th lnth o this ust mit to th nrst tn thousnth o mtr.. Approximt th lnth o this ust mit to th nrst hunrth o mtr.. I Lihn City is 8 m wy rom Moss City: Wht is this istn pproximt to th nrst km? (i.. nrst thousn). Wht is th pproximt istn twn th itis to th nrst 00 km?. (iii) Ar th iits, or vn importnt to inlu whn sriin th totl istn twn th two itis? Brily xplin hr why/why not. H Dimls SERIES TOPIC Mthltis P Lrnin Lt

9 How os it work? Your Turn Dimls Approximtions throuh rounin numrs Rounin up n t mor thn on iit whn th numr 9 is involv. Roun 0.9 to on iml pl 0. 9 Th iit 9 is in th tnths position 9 rouns up to 0, so th 9 oms 0 n is to th iit in ront Th nxt iit is, so roun up y in to 9 Chn th othr smllr pl vlu iits to 0s ` roun to on iml pl Roun o ths numrs orin to th squr rkts. [on iml pl] 98.. [nrst ons] [nrst thousn] [nrst tn] 98. [thr iml pls] h [nrst ons] [two iml pls] [thr iml pls] 99.. i [our iml pls] Approximt ths vlus: A ll ntr rivs n vr o 9.9 lls h y urin on month. Approximt th numr o lls riv to th nrst hunrs. Approximtly how mny thousns o lls i thy riv? (iii) Estimt th numr o lls riv ily throuhout th month.... A swimmin pool h slow lk, usin it to mpty L in on wk. How muh wtr ws lost to th nrst 0 litrs? How muh wtr ws lost to th nrst ml i ml 000 L?.. (iii) Is th iit importnt whn pproximtin to th nrst whol litr? Brily xplin hr why/why not. Mthltis Dimls P Lrnin Lt H SERIES TOPIC 7

10 How os it work? Dimls Dimls on th numr lin Th smllst pl vlu in iml is us to position points urtly on numr lin. Dimls r s on th numr 0, so thr r lwys tn ivisions twn vlus E: Hr is th vlu. on numr lin:.0..0 Six tnths o th wy rom.0 to.0 Th mjor intrvls on th numr lin r mrk orin to th son lst iml pl vlu 8 So its iht thousnths o th wy rom.0 to Hr r som mor xmpls involvin numr lins: Wht vlu o th plott points rprsnt on th numr lins low? ) Point is our stps rom 0. towrs 0., so th plott point is: 0. ) Point is nin stps rom 0.0 towrs 0.07, so th plott point is: 0.09 Roun th vlu o th plott points low to th nrst hunrth. ).. Point is thr stps rom. towrs., so th plott point is. ` th vlu o th plott point to th nrst hunrth is:. ) Point is iv stps rom 8.79 towrs 8.80, so th plott point is 8.79 ` th vlu o th plott point to th nrst hunrth is: H Dimls SERIES TOPIC Mthltis P Lrnin Lt

11 How os it work? Your Turn Dimls Dimls on th numr lin Disply ths imls on th numr lins low: 0.7. ECIMALS ON THE NUMBER LINE.../.../0... DDECIMALS ON THE NUMBER LINE Ll ths numr lins n thn isply th ivn iml on thm: Roun th vlu o th plott points low to th nrst pl vlu ivn in squr rkts. [tnth] [hunrth] ` th vlu. ` th vlu. [tnth] [hunrth] ` th vlu. ` th vlu. [thousnth] [thousnth] ` th vlu. ` th vlu. [thousnth] h [thousnth] ` th vlu. ` th vlu. Mthltis Dimls P Lrnin Lt H SERIES TOPIC 9

12 How os it work? Dimls Multiplyin n iviin y powrs o tn Mov th iml point pnin on th numr o zros iml point movs riht, iml point movs lt Clult ths multiplition n ivision qustions involvin powrs o 0: # 000 W n simply th sm numr o zros to th n o th whol numr # # Th whol numr in iml orm Fill th mpty ouns with 0s I th iml point is on th lt tr iviin, n xtr 0 is pl in ront ' 8' ' 00 Th whol numr in iml orm Rmmr to inlu th lin zro. 80. '00 hs zros, so mov iml point sps lt 0.08 Fill th mpty ouns with 0s n put zro in ront (iii) 89. # # Mov iml point sps riht 89. No mpty ouns to ill, so this is th nswr (iv). 90' ' Mov iml point sps lt Fill mpty ouns with 0s n put zro in ront (v) 0. # # ' # is th sm s ' Mov iml point sps lt 0.0 Pl lin zro in ront o th iml point 0 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

13 How os it work? Your Turn Dimls Multiplyin n iviin y powrs o tn Clult ths multiplitions. Rmmr, multiply mns mov iml point to th riht: 8 00 #. # 0 9 # # 0. # # Clult ths ivisions. Rmmr, ivi mns mov iml point to th lt: ' ' ' ' ' 900 ' Hr r som o th powrs o 0 in inx orm. Th powr th numr o zros Clult ths mix prolms writtn in inx orm: 0 # 00 ' # #. 0 ' 9 9 ' 0 7 Mthltis Dimls P Lrnin Lt H SERIES TOPIC

14 MULTIPLYING AND DIVIDING BY POWERS OF TEN How os it work? Your Turn Dimls Multiplyin n iviin y powrs o tn For ths lultions: Show whr our hrtr ns to spry pint nw iml point, n writ own th two numrs th nw iml point is twn to solv th puzzl.../.../ # I 9 n 87 ' N # A ' 8 9 O # X 8.970# T # R h ' I i # D j # P This is nothr mthmtil nm or iml point: I 0 n 9 8 n 9 8 n 7 9 n 0 n 7 n 9 8 n 0 n 8 n 8 n 7 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

15 How os it work? Dimls Trmintin imls to rtions Ths hv iml prts whih stop (or trmint) t prtiulr pl vlu. Th pl vlu o th lst iit on th riht hlps us to writ it s rtion. Writ 0. s rtion: Diml 0. Frtion 0 Diml iits in th numrtor Lst iit is in tnths position Intrs in ront o th iml vlus r simply writtn in ront o th rtion. Writ.07 s rtion: Diml iits in th numrtor Lst iit is in hunrths position 07 is just 7 Alwys simpliy th rtion prts i possil. Ths two xmpls show you how. Writ h o ths imls s n quivlnt (qul) rtion in simplst orm Equivlnt, un-simplii rtion 00 Lst iit is in hunrths position ' 00 ' Divi numrtor n nomintor y HCF Equivlnt rtion in simplst orm Equivlnt, un-simplii mix numrl Lst iit is in thousnths position 0 ' 000 ' Divi numrtor n nomintor y HCF 00 Equivlnt mix numrl in simplst orm Mthltis Dimls P Lrnin Lt H SERIES TOPIC

16 How os it work? Your Turn Dimls Trmintin imls to rtions Writ h o ths imls s quivlnt rtions: h i 0.9 j. k l Writ h o ths imls s quivlnt rtions n thn simpliy: Simplst orm Simplst orm Simplst orm Simplst orm Simplst orm Simplst orm 0. h 0. i 0.0 Simplst orm Simplst orm Simplst orm j 0.0 k l 0.00 Simplst orm Simplst orm Simplst orm H Dimls SERIES TOPIC Mthltis P Lrnin Lt

17 TERMINATING DECIMALS TO FRACTIONS * Whr os it work? Your Turn Dimls Trmintin imls to rtions Writ h o ths imls s quivlnt mix numrls: 0..../.../ Writ h o ths imls s quivlnt mix numrls n thn simpliy:.8..0 Simplst orm Simplst orm Simplst orm Simplst orm Simplst orm Simplst orm. 00 h.0 i. Simplst orm Simplst orm Simplst orm Mthltis Dimls P Lrnin Lt H SERIES TOPIC

18 How os it work? Dimls Frtions to trmintin imls Whr possil, just writ s n quivlnt rtion with powr o 0 in th nomintor irst. numrtor nomintor ` # # 0 0. Multiply numrtor n nomintor y th sm vlu Equivlnt rtion with powr o 0 in th nomintor Thr iths six tnths zro point six Somtims it is sir to irst simpliy th rtion or hnin to iml. Writ ths s n quivlnt iml ' ' Simpliy rtion # # 00 Equivlnt rtion with powr o 0 in th nomintor ` 0. Thr twlths on qurtr twnty iv hunrths zro point two iv ' ' Simpliy rtion prt # # 0. Equivlnt rtion with powr o 0 in th nomintor Two n thr itnths two n on ith two n two tnths two point two H Dimls SERIES TOPIC Mthltis P Lrnin Lt

19 How os it work? Your Turn Dimls Frtions to trmintin imls inlu lin zro Writ h o ths rtions s quivlnt imls Writ h o ths s quivlnt rtions with powr o 0 in th nomintor h 0 00 i j k 7 0 Writ h o ths s quivlnt rtions with powr o 0 in th nomintor. Chn to quivlnt imls h 00 i Mthltis Dimls P Lrnin Lt H SERIES TOPIC 7

20 How os it work? Your Turn Dimls Frtions to trmintin imls Chn h o ths rtions to quivlnt imls tr irst simpliyin. Show ll your workin FRACTIONS TO TERMINATING DECIMALS 0..../.../ h 0 8 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

21 How os it work? Your Turn Dimls Frtions to trmintin imls Whn hnin th nomintor to powr o 0 is not sy, you n writ th numrtor s iml n thn ivi it y th nomintor. Writ this rtion s n quivlnt iml ' 8 Writ numrtor s iml n ivi y th nomintor I you n mor iml pl 0s, you n thm in ltr! Complt ivision, kpin th iml point in th sm pl ` 0. Fiv ihths zro point six two iv Complt ths ivisions to in th quivlnt iml:. 000 '.000 '.000 ' '.000 ' ' Mthltis Dimls P Lrnin Lt H SERIES TOPIC 9

22 How os it work? Your Turn Dimls Frtions to trmintin imls Simpliy ths rtions n thn writ s n quivlnt iml usin th ivision mtho. Show ll your workin H Dimls SERIES TOPIC Mthltis P Lrnin Lt

23 Whr os it work? Dimls Ain n sutrtin imls Just or sutrt th iits in th sm pl vlu. To o this, lin up th iml points n mthin pl vlus vrtilly irst. A. to. (i... +.) Diml points lin up vrtilly A mthin pl vlus tothr Sutrt.8 rom.89 (i ) Diml points lin up vrtilly Sutrt mthin pl vlus Clult h o ths urthr itions n sutrtions Diml points lin up vrtilly Any pl vlu sps. 7 A mthin pl vlus tothr r trt s 0s ` Rounin iml vlus or in is somtims us to quikly pproximt th siz o th nswr. Roun h vlu in qustion to th nrst whol numr or in. ` Vlus roun to nrst ons Approximt vlu or ition Not: Rounin vlus or in/sutrtin is not s urt s rounin tr in/sutrtin. (iii) Fill pl vlu sps in th top numr with 0 whn sutrtin ` Diml points lin up vrtilly Sutrt mthin pl vlus Mthltis Dimls P Lrnin Lt H SERIES TOPIC

24 ADDING AND SUBTRACTING DECIMALS Whr os it work? Your Turn Dimls Ain n sutrtin imls Complt ths itions n sutrtions: h Clult ths itions n sutrtions, showin ll workin: A 8.7 to. Sutrt. rom.79.../.../0... A 0.9 to 0.8 A.9,. n 0. Sutrt 0.9 rom 8.0 A 0.0,. n 8.09 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

25 Whr os it work? Your Turn Dimls Ain n sutrtin imls Approximt ths lultions y rounin h vlu to th nrst whol numr irst (iii) (iv) (v) (vi) Clult prts (v) n (vi) in, this tim rounin tr in th numrs to t mor urt pproximt vlu Clult ths sutrtions, showin ll your workin: Mthltis Dimls P Lrnin Lt H SERIES TOPIC

26 Whr os it work? Dimls Multiplyin with imls Just writ th trms s whol numrs n multiply. Put th iml point k in whn inish. Th numr o iml pls in th nswr th numr o iml pls in th qustion! Clult #. 8 # Multiply oth trms s whol numrs 8 iml pl in qustion iml pl in nswr ` #. 8. Clult 0.0 #. 90 # Multiply oth trms s whol numrs 90 ` 0.0 # iml pls in qustion iml pls in nswr How os this work whn multiplyin with imls? Exllnt qustion! Vry l you sk! Lt s o th son on in ut this tim hn th imls to quivlnt rtions irst 00. #. # Chnin th imls to rtions # 00# Multiply numrtors n nomintors tothr Numr o zros in nomintor totl o iml pls in qustion 90' Diviin y movs iml point our pls to th lt ` iml pls in qustion iml pls in nswr Try this mtho or yoursl on th irst xmpl ov, rmmrin tht s rtion. H Dimls SERIES TOPIC Mthltis P Lrnin Lt

27 Whr os it work? Your Turn Dimls Multiplyin with imls Clult ths whol numr n iml multiplitions, showin ll you workin: #. 0.8 # 0. # 0. # # # Clult ths iml multiplitions, showin ll your workin:.8 # # #. ULTIPLYING WITH DECIMALS.../.../0... MMULTIPLYING WITH DECIMALS 7. #.. #. 7. # 9. Mthltis Dimls P Lrnin Lt H SERIES TOPIC

28 Whr os it work? Dimls Diviin with imls Opposit to multiplyin, w mov th iml point or iviin i n. To in th quotint involvin imls, th qustion must hn so th ivisor is whol numr. ivin ' ivisor quotint Clult 8. ' Divisor lry whol numr so no hn n `.8 '.07 Clult 00. ' ' ' 000. Mov oth iml points riht until ivisor is whol numr. ' Quotint Divin i ivisor ` 0.0 ' Drop o ny 0s t th ront o th nswr Hr s nothr xmpl showin how to trt rminrs Clult. ' 08.. ' 0.8. ' 0.8 Mov oth iml points riht until ivisor is whol numr. ' A 0s on th n o th ivin or h nw rminr `. ' Drop o ny 0s t th ront H Dimls SERIES TOPIC Mthltis P Lrnin Lt

29 Whr os it work? Your Turn Dimls Diviin with imls Clult ths iml n whol numr ivisions:.' 7. '. ' 9.../.../0... IVIDING WITH DECIMALS DDIVIDING WITH DECIMALS `.' ` 7. ' `. ' 9 0. ' 089. ' 0. 97' 7 ` 0. ' ` 0.89' ` 0.97 ' 7 Clult ths iml ivisions, showin ll your workin:. ' ' ' 08. `.' 0. ` 9.' 0. ` 0. ' ' ' ' `.8 ' 0. ` 0.8 ' 0.0 `.8 ' 0.00 Mthltis Dimls P Lrnin Lt H SERIES TOPIC 7

30 Whr os it work? Dimls Rurrin imls Non-trmintin imls hv iml prts tht o not stop. Thy kp oin on n on Thr ots mns it kps oin I th iml prts hv rptin numr pttrn, thy r ll rurrin imls..... Hr r som xmpls involvin rurrin imls A ot ov th strt n n iit o th rptin pttrn is us to show it is rurrin iml. Writ ths rurrin imls usin th ot nottion Th pttrn kps rptin in th iml prts ) ) ) o o 00. A r ovr th whol pttrn n lso us inst o ots Strt En 0. 8 o o Strt En 00. o o Strt n En 07. o or.07r Intiy th strt n n o th rptin pttrn Dot ov strt n n o th rptin pttrn Intiy th strt n n o th rptin pttrn Dot ov strt n n o th rptin pttrn Intiy th strt n n o th rptin pttrn Dot ov strt n n o th rptin pttrn Clult ' 0. ' 0. ' ' Writ s iml with w 0s ` ' o Rpts th sm rminr whn iviin Rurrin iml in simplst nottion 8 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

31 Whr os it work? Your Turn Dimls Rurrin imls Wht is th nm o th horizontl lin ov th rpt numrs in rurrin iml? Hihliht th oxs tht mth th rurrin imls in h row with th orrt simplii nottion in h olumn to in th nswr. Not ll o th mths orm prt o th nswr! 0. 0r.. o o o o o C z F h N W D A U n P t L O m Y n A m R T t K z E h R I U S L D A m I h M t B S A U z Q n R h Z A n E z A N t 0 M A h G.... A T z P H T Y n A t A h C m A 0... I Y t A U n H m I z E S m I t T A L D t E A N L m E z O N h.... W J B A X h M m A U n A A z P m V E F A n B T Y E I t H t A n A m A m U A A h A D R z h m n Clult ths ivisions whih hv rurrin imls s rsult. Writ nswrs usin ot nottion. ' ' 9 ' ` ' ` ' 9 ` '.'. ' 9 0. ' `. ' `. ' 9 ` 0. ' Mthltis Dimls P Lrnin Lt H SERIES TOPIC 9

32 ...RECURRING DECIMALS...RECURRING DECIMALS...RECURRING DECIMALS Whr os it work? Your Turn Dimls Rurrin imls Complt th ollowin ivisions to iv iml pls. Dtrmin whthr th nswr is rurrin iml or not. ' ' ' 7.../.../0... ` ' ` ' ` ' 7 Rurrin iml? Rurrin iml? Rurrin iml? Ys No Ys No Ys No. ' 7 9. ' 0. ' 08. `. ' 7 ` 9. ' ` 0. ' 0.8 Rurrin iml? Rurrin iml? Rurrin iml? Ys No Ys No Ys No 0.8' ' ' h i ` 0.8 ' 0. ` 0.09' 0.0 ` 0.00 ' 0.00 Rurrin iml? Rurrin iml? Rurrin iml? Ys No Ys No Ys No 0 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

33 Wht ls n you o? Dimls Simpl rurrin imls into sinl rtions Only rurrin, non-trmintin imls n writtn in rtion orm. Hr is quik wy or simpl imls with th pttrn strtin riht tr th iml point o 9 On iit in rptin pttrn, so tht iit ovr o o 99 ' 99 ' Two iits in rptin pttrn, so thos two iits ovr 99 Alwys simpliy rtions o o Thr iits in rptin pttrn, so thos thr iits ovr 999 Hr r som othr xmpls inluin mix numrls. Writ h o ths rurrin imls s mix numrls in simplst orm o On iit in rptin iml pttrn, so tht iit ovr Diits in ront o iml point orm th whol numr prt o o Thr iits in rptin iml pttrn, so thos iits ovr Diits in ront o iml point orm th whol numr ' 999 ' Simpliy th rtion prt Mthltis Dimls P Lrnin Lt H SERIES TOPIC

34 Wht ls n you o? Your Turn Dimls Simpl rurrin imls into sinl rtions Us th shortut mtho to writ h o ths rurrin imls s rtion in simplst orm: 0. o 08r. 0. o 0. oo 07. o o 07. o o Us th shortut mtho to writ h o ths rurrin imls s mix numrls in simplst orm.. o 7r. r. r. 0.7 o o o o h i Writ 09. o s rtion in simplst orm. (Ii) Dos nythin unusul sm to hppnin with your nswr? Explin. SIMPLE RECURRING DECIMALS INTO SINGLE FRACTIONS /.../0... H Dimls SERIES TOPIC Mthltis P Lrnin Lt

35 Wht ls n you o? Dimls Cominin iml thniqus to solv prolms All th thniqus in this ooklt n us to solv prolms. Ths xmpls show irnt wys imls pop up in vry-y li Ths rinll msurmnts wr tkn urin thr ys o rin rom smll wthr u:.8 mm. mm 7. mm Wht ws th totl rinll or th thr ys, to th nrst whol mm? mm ` Th totl rinll ovr th thr ys ws pproximtly 78 mm A th iml vlus tothr Roun to nrst whol mm Answr with sttmnt Th rsults or iv runnrs in 00 m r wr plott on th numr lin low. sons.. ) Wht ws th stst tim run (to th nrst thousnth o son)? Fstst tim lt-most plott point. sons ) Wht tim i two runnrs inish th r tothr on? Two runnrs with th sm tim two ots t th sm point. sons ) Wht ws th vr tim rn y ll runnrs in this r? Avr tim Th sum o ll th tims rn ivi y th numr o runnrs ( ) '. '.. 0 Th vr tim rn y ll th runnrs in th r. sons R o ll th tims A, thn ivi y Answr with sttmnt Mthltis Dimls P Lrnin Lt H SERIES TOPIC

36 Wht ls n you o? Your Turn Dimls Cominin iml thniqus to solv prolms To mk rk-rn olour pint, you n mix yllow n lu tothr, usin xtly 0. (hl) s muh yllow s you o lu. Us multiplition to show how muh yllow pint you will n i you us ll o th. ml o lu pint you hv. Rmmr m? How mny millilitrs o rk-rn pint n you mk with 8. ml o yllow pint in th mix? Roun your nswr to th nrst tnth o ml. Drk typs his ssys t n vr sp o 9. wors vry minut. How mny wors os h typ in iv minuts (to th nrst whol wor)? COMBINING DECIMAL TECHNIQUES TO SOLVE PROBLEMS Nin popl wr tryin out or sp rollr sktin tm roun n ovl lt trk. Th shortst tim to omplt six ull lps o th trk or h prson wr ror on th numr lin low:.../.../ sons Wht ws th slowst tim ror to iml pls? To mk th tm, sktr h to omplt th six lps in lss thn. sons. How mny sktrs m it into th tm? How mny sktrs miss out mkin th tm y lss thn 0.0 sons? H Dimls SERIES TOPIC Mthltis P Lrnin Lt

37 Wht ls n you o? Your Turn Dimls Cominin iml thniqus to solv prolms Th wirlss trnsmittr in Lur s hous rus in sinl strnth y 0.0 or vry mtr o istn sh movs hr omputr wy rom th trnsmittrs ntnn. Hr omputr isplys sinl strnth usin rs s shown low: rs 08. to.0 sinl strnth rs 0. to 0.8 sinl strnth rs 0. to 0. sinl strnth r 0. to 0. sinl strnth 0 rs 0. or low sinl strnth How mny rs o sinl strnth woul Lur hv i usin hr omputr.m wy rom th ntnn? Ruon is puttin tothr vio o rnt krok prty with hr rins. Sh will usin iv o hr vourit musi trks or th vio. Th lnth o tim h o th trks ply or is:. min,. min,.7 min,.8 min n.8 min I sh uss th ntir lnth o th trks with 0. min rk in h o th our ps twn sons, how lon will hr vio run or (to th nrst whol minut)? Show ll your workin. Mthltis Dimls P Lrnin Lt H SERIES TOPIC

38 Wht ls n you o? Your Turn Dimls Cominin iml thniqus to solv prolms Atr rnt stuy y ity ounil, th vr numr o popl in h houshol ws trmin.to.. Explin how this is possil i houshol nnot tully hv 0. o prson? psst: Chk xmpl on p to s how vr lultions r m. 7 A Mxin h hs split up mystry inrint Sl-X into our xtly intil quntitis in sprt jrs. H thn istriuts 8. o ml o th srt inrint S-Y monst th our jrs, prouin in totl 89. o ml o th spil su SlS-XY. How muh o th mystry inrint Sl-X is thr in h jr (to th nrst ml)? Show ll your workin. 8 Atr ompltly lt wtr onitions (wvs with hiht o 0.0m), th hiht o th wvs t lol h strt inrsin y 0. m vry 0. o hours. I th wvs n to t lst. mtrs hih or surrs will ri thm t this h, how lon will it until popl strt surin thr to th nrst minut? Show ll your workin. psst:.0 hours 0 minuts H Dimls SERIES TOPIC Mthltis P Lrnin Lt

39 Wht ls n you o? Your Turn Dimls Rltion Tim Rltin on th work ovr within this ooklt: Wht usul skills hv you in y lrnin out imls? Writ out on or two wys you think you oul pply imls to rl li sitution. I you isovr or lrnt out ny shortuts to hlp with imls or som othr ool ts, jot thm own hr: Mthltis Dimls P Lrnin Lt H SERIES TOPIC 7

40 Cht Sht Dimls Hr is summry o th thins you n to rmmr or imls Pl vlu o imls # # 000 # 00 Tns o thousns Thousns Hunrs Tns Ons W H O L E # 0 # ' 0 Tnths ' 00 ' 000 Hunrths Thousnths Tn thousnths D E C I M A ' ' ' Hunr thousnths Millionths Tn Millionths L ' Approximtions throuh rounin numrs Th nxt iit ollowin th pl vlu whr numr is in roun o to is th importnt prt. Nxt iit Closr to lowr vlu, so roun own Lv th pl vlu unhn Closr to hihr vlu, so roun up A to th pl vlu Dimls on th numr lin Th smllst pl vlu in iml is us to position points urtly on numr lin Six tnths o th wy rom.0 to.0 Eiht thousnths o th wy rom.0 to.0 Multiplyin n iviin y powrs o tn Mov th iml point pnin on th numr o zros iml point movs riht, iml point movs lt # # 000 8' ' H Dimls SERIES TOPIC Mthltis P Lrnin Lt

41 Cht Sht Dimls Trmintin imls to rtions Th pl vlu o th lst iit on th riht hlps us to writ it s rtion. Writ 0. s rtion: Lst iit is in tnths position Diml 0. E: Frtion 0 # # 0 ` 0. Diml Frtion Writ.07 s rtion: Lst iit is in hunrths position Frtions to trmintin imls Whr possil, just writ s n quivlnt rtion with powr o 0 in th nomintor irst. Multiply numrtor n nomintor y th sm vlu Equivlnt rtion with powr o 0 in th nomintor Thr iths six tnths zro point six Whn this mtho is not sy, writ th numrtor s iml n thn ivi it y th nomintor. Ain n sutrtin imls Lin up th iml points n mthin pl vlus vrtilly or in or sutrtin. Multiplyin n iviin imls Writ th trms s whol numrs n multiply. Put th iml point k in whn inish. Th numr o iml pls in th nswr th numr o iml pls in th qustion! E: : #..8 : 0.0 # Diviin with imls Th qustion must hn so th ivisor is whol numr irst. E: :. ' 0. ' : 89. ' ' ivin ' ivisor quotint Rurrin imls Ths hv iml prts with rptin numr pttrn. E: :.... o o. : o o 0.98 Strt En Simpl rurrin imls into sinl rtions Only rurrin, non-trmintin imls n writtn in rtion orm. This is th mtho or simpl imls with th pttrn strtin riht tr th iml point. Strt En Alwys simpliy rtions : o : o o 9 99 On iit in rptin Two iits in rptin pttrn, pttrn, so tht iit ovr 9 so thos two iits ovr 99 : o o Thr iits in rptin pttrn, so thos thr iits ovr 999, Kp whol numr out th ront. Mthltis Dimls P Lrnin Lt H SERIES TOPIC 9

42 Answrs Dimls Pl vlu o imls Pl vlu o imls tnths or hunrths or 00 hunrths or 00 0 tn thousnths or tn thousnths or thousnths or 000 # + # 0 + # # + # + # # # # # # # + 8 # # + # + # + # # + # # # # # + # + # # # + # + # + # # Approximtions throuh rounin numrs # # # # # # # # # # # # # # + # + # + # # + # (iii) (iii) (iii) (iii) (iii) (iii) # # # # # m 0 m 9 km 00 km m 0.00 m 0 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

43 Answrs Dimls Approximtions throuh rounin numrs Dimls on th numr lin. (iii) Ths iits omin to rprsnt m. This is rlly smll prt o th totl istn o pproximtly 00 km (0.% o th totl istn). So thy r not rlly importnt s thy o not hv ny t on th pproximt istn twn th itis. Only importnt i rt l o ury ws n [tnth] ` th vlu [hunrth] h ` th vlu..0 i [tnth].. Dimls on th numr lin 00 (iii) L L (iii) No. Bus ny iit in this pl vlu (tn thousnths) will not hv ny t on th pproximt numr o litrs lk rom th pool ` th vlu. 0.8 [hunrth] ` th vlu [thousnth] ` th vlu..99 [thousnth] ` th vlu. 8.0 [thousnth] ` th vlu h [thousnth] ` th vlu Mthltis Dimls P Lrnin Lt H SERIES TOPIC

44 Answrs Dimls Multiplyin n iviin y powrs o tn Trmintin imls to rtions i k h j l n n 8 8 n 9 8 n 0 n 7 n 7 0 n h i j RADIX POINT 0 n 8 8 n 7 n 9 i h Trmintin imls to rtions Frtions to trmintin imls i k h j l h j i k H Dimls SERIES TOPIC Mthltis P Lrnin Lt

45 Answrs Dimls Frtions to trmintin imls Frtions to trmintin imls.. h ' ' 0 ` i h ' ' # ` 0 8 # ' ' 0 ' ' 0 # 7 # 00 0 # # 00 ` 07. ` ' ' # # 00 ` 0. ' 00 ' 00 ` 0. ' 0 ' 0 `. ' 0 ' 0 # 0 8 # 00 ` ' ' '. 000 ' ' ' ' ' ' ' ' ' '. 000 ' ' ' ' ' ' ' ' ' Ain n sutrtin imls ' ' Mthltis Dimls P Lrnin Lt H SERIES TOPIC

46 Answrs Dimls Ain n sutrtin imls Ain n sutrtin imls h ` ` Multiplyin with imls 08. # 8 # #. 7 # p. in qustion `.p. in nswr.p. in qustion `.p. in nswr ` 0.8 #. ` #. 7.. (iii) (iv) # 8 #.p. in qustion `.p. in nswr ` 0. # 08. # # 8 #.p. in qustion `.p. in nswr ` 0. # 8.. # (v) (vi) #.p. in qustion `.p. in nswr ` # #.p. in qustion `.p. in nswr `. # # #.p. in qustion `.p. in nswr ` # # # p. in qustion `.p. in nswr ` # ` H Dimls SERIES TOPIC Mthltis P Lrnin Lt

47 Answrs Dimls Multiplyin with imls Diviin with imls..7 #. 7. # '. '. 7 # # ' `. ' ' ` 9. ' 0..p. in qustion `.p. in nswr ` # p. in qustion `.p. in nswr ` # '. '.. ' ' # 7.. # 9 ` 0. ' ` 8. ' # 0 7.p. in qustion `.p. in nswr 7 # p. in qustion `.p. in nswr '. 8. '. '. ` 08. ' ' ` 8. ' ` # ` # 99. Rurrin imls. Diviin with imls. ' 7. ' `.' 09. ` 7. '.. 9 ' 0. ' `. ' 9 8. ` 0. ' ' ' o 0r.. o o o 0. o. 00. o o. o 0. o o.... C z F h N W D A U n P t L O m Y n A m R T t K z E h R I U S L D A m I h M t B S A U z Q n R h Z A n E z A N t 0 M A h G.... A T z P H T Y n A t A h C m A 0... I Y t A U n H m I z E S m I t T A L D t E A N L m E z O N h.... W J B A X h M m A U n A A z P m V E F A n B T Y E I t H t A n A m A m U A A h A D R. V I N C U L U M z h m n ' ' ` ' 0. o ` ' 9 0. o ` 0.89' ` 0.97 ' 7. 8 Mthltis Dimls P Lrnin Lt H SERIES TOPIC

48 Answrs Dimls Rurrin imls Rurrin imls. '.'. 0.8' 0. Ys ` ' o `. ' 0. o. ' 9 0. ' `. ' o ` 0. ' 0. o ' Ys h.8 ' ` 08. ' 0.. o 0. 09' ' ` 009. ' o Ys ` ' 0. o i ' ' No ' ` ' 0. o ' 7 Ys No.. ` ' Simpl rurrin imls into sinl rtion ` ' ' `. ' No ' ` 9. ' 09. o 0. ' 08.. ' ` 0. ' Ys No. i h o o Evn thouh th vlu pprs s 0.9 rptr, it tully quls whol numr H Dimls SERIES TOPIC Mthltis P Lrnin Lt

49 Answrs Dimls Cominin imls thniqus to solv prolms Cominin imls thniqus to solv prolms. Amount o yllow pint 0. #. ml. # 0 Thtotl lnth o thvio min 9. min. 0 minutstoth nrstminut.p. in qustion `.p. in nswr ` 0. #.. ml o yllow pint Amount o yllow pint 0. # 8. ml 8 # 9.p. in qustion `.p. in nswr ` 0. # ml o yllow pint. 7. Th totl numr o popl ws not prt multipl o th numr o houss survy, whih will iv iml nswr...so, on vr thr r. popl in h hous, ut h hous will hv irnt numrs, lin to this rsult. Th totl mount o "Sl-X" Th mount o "Sl-X" in h jr ' ` Amount o rk-rn pint ml 7. 7 ml (nrst tnth) Th mount o "Sl-X" in h jr 8. o ml. 8mL to thnrst wholml...p. in qustion `.p. in nswr 9 # 7 ` Numr o wors typ in minuts wors Slowst tim ror.8 sons sktrs h tims lss thn. sons... so sktrs m it into th tm So sktrs miss out y lss thn 0.0 sons 8. Evry 0. o hours vry o n hour tims n hour! # ` Th wvs inrs in hiht y 0. m vry hour. ` Th tim tkn to t to sur-l hiht ' 0. ' o hours.0hours 0 minuts ` 0.o hours 0 minuts ` popl strt surin tr hours, 0 minuts.. Lur will hv rs o sinl strnth. Mthltis Dimls P Lrnin Lt H SERIES TOPIC 7

50 Dimls Nots 8 H Dimls SERIES TOPIC Mthltis P Lrnin Lt

51

52 Dimls H SERIES