CONVERTING UNITS. Converting Units PASSPORT
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1 CONVERTING UNITS PASSPORT
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3 This ook shows how to writ th sm vlu using smllr or lrgr units o msurmnt. Mny nint ivilistions msur lngths/istns y rlting thm to rtin oy prts. Invstigt ths trms n writ wht th originl msurmnt rrr to. Rmn (Anint Egyptin) Hn (Anint Egyptin) Cuit (Anint Egyptin) C (Ari) Pollx (Romn) Swung szhn (Russin) Prmnus (Hinu) Spn (English) Kis rsz (Hungrin) Fthom (English) Q Dsri th totl mss o th oxs ing rri low in s mny irnt wys s you n. Work through th ook or grt wy to o this P Lrning H SERIES 7 TOPIC
4 How os it work? Prixs Prixs lt us writ own vry smll or vry lrg numrs quikly n sily. Thy r us or S.I. units ommon intrntionl systm o units vlop so ll ntions n rs o sin/mthmtis oul ommunit rsults th sm wy. Eh prix tlls us wht to multiply th msur vlus y i writing thm in th s units us. Th s units o msurmnt w will using in this ook r mtr (m) kilogrm (kg) son (s) litr (L) yts (B) - Lngth - Mss - Tim - Cpity - Digitl inormtion This hrt shows som ommonly us prixs n th multiplying powr o 0 thy rprsnt H 7 SERIES TOPIC P Lrning
5 How os it work? Prixs Ths xmpls show how prixs n simpliy msurmnt sttmnts. R-writ ths msurmnts using singl igits only (i) litrs L = # litrs = mglitrs = ML Multiplir us on s unit Singl igit prix orm Singl igit symol orm (ii) 7 # grms 0 7 # 7milligrms = 0 = 7 mg Singl igit prix orm Singl igit symol orm (iii) mtrs m = 5 # 000 mtrs = 5 # 000 mtrs Multiplir us on s unit Rmmr: # = ' = 5 millimtrs = 5 mm Singl igit prix orm Singl igit symol orm (iv) yts yts = 8 # yts = 8 # 0 9 yts = 8 gigyts = 8 GB Multiplir us on s unit Singl igit prix orm Singl igit symol orm P Lrning H SERIES 7 TOPIC
6 How os it work? Your Turn Prixs Writ th prix us to rprsnt h o ths multiplitions: #000 # # 00 # # 000 #0 9 Us prixs to sri h o ths msurmnts in singl-igit prix orm. 6 km 9 ms Six kilomtrs 5 G 7 ML g g 00 m h 80 L i 0.0 m j g k L l s m 000 L n 4 0 g o m p s 4 H 7 SERIES TOPIC P Lrning
7 How os it work? Your Turn Prixs Solv th puzzl low to in th two Frnh wors tht th rvition S.I. stns or. O 5000 yts N mirosons R millilitrs È 5 gigyts A yts E 000 litrs S 000 mtrs L # 0 9 m N 4 mirogrms M 0.00 sons T 4 # 0 yts Emtrs 00 ' T nnomtrs E 4 # grms 000 N 0.00 mtrs # Tlitrs Alitrs # 00 4 # 000 Igrms Y 4 igrms I 00 L S # L PREFIXES * PREFIXES * PREFIXES * PREFIXES * μl 4 g km ML 5 GB ms 4 mg.../.../ kg mm 5 TB m ml 4 μg 5 MB nm hl 5 kb μs L Gm kl P Lrning H SERIES 7 TOPIC 5
8 Whr os it work? Chnging twn units o mss Th mss o n ojt tlls us how hvy it is. Th s msurmnt or mss is kilogrms (kg). Follow th rrows on this hrt to hng (onvrt) twn ommonly us units o mss. Lrgr units ' 000 ' 000 ' 000 ' milligrms mg grms g kilogrms kg tonns t # Smllr units # 000 # 000 # 000 Rmmr lik this: For smllr units, you Multiply n or Iggr units, you Ivi. tonn = 000 kg Us th onvrsion hrt to onvrt ths mss msurmnts (i) kg into tonns '000 kg ' 000 =.0kg ' 000 kg t =.. 0tonns Mov th iml point sps lt = t Sm mss in lrgr units (ii) 5.4 g into milligrms t kg 54. kg # 000 = # 000 milligrms Mov th iml point sps right #000 = 540 mg Sm mss in smllr units Somtims you n to tk two or mor stps with th onvrsion (iii) 890 g into tonns 890 g' 000 ' 000 = 890.0' t ' 000 ' 000 = t Mov th iml point 6 sps lt g kg t = tonns Sm mss in lrgr units 6 H 7 SERIES TOPIC P Lrning
9 Whr os it work? Your Turn Chnging twn units o mss Convrt th mss msurmnts low into th rkt units. 000 g [kilogrms] mg [grms].5 kg [grms] 50 kg [tonns] 0. g [milligrms] 70 t [kilogrms] Convrt th mss msurmnts low into units givn in squr rkts. 0. g [kilogrms] 000 mg [kilogrms] 6 t [grms] g [tonns] kg [milligrms] t [grms] Como tim! Drw lins onnting th mthing mss msurmnts low g 4 g 40 kg A 400 kilogrms t 4 kg 400 g V kg 0.40 mg S M 40 mg 4000 t Mg kg E S 4' 0 7 kg mg I grms 0.04 g # grms P Lrning H SERIES 7 TOPIC 7
10 Whr os it work? Chnging twn units o lngth Th originl mtr lngths wr trmin using two mthos: Th lngth o string on pnulum tht h prio o xtly son. # th lngth o th mriin roun th Erth s qutor Ths ys, spil typ o light is us to trmin mtr vry prisly. It is th s msurmnt or istn. ' 0 '00 '000 ' Smllr units millimtrs mm ntimtrs m mtrs m kilomtrs km Lrgr units # #0 #00 #000 Us th onvrsion hrt to onvrt ths lngth msurmnts (i).5 mtrs into ntimtrs m m.5m m # = = 50 m Choos th orrt multiplir Sm istn in smllr units #00 (ii) 8 mm into m '0 8mm ' 0 = 8.0 ' 0 m =. 8. 0m Writ whol numr in iml orm mm m = 08. m Put zro in ront o iml point B rul to us th orrt multiplirs or onvrsions ning two or mor stps. (iii) 0.8 kilomtrs into ntimtrs 0. 8km # 000 # 00 = 0. 8 # m m m km = m #00 #000 = m Mov th iml point 5 sps right Sm istn in smllr units 8 H 7 SERIES TOPIC P Lrning
11 Whr os it work? Your Turn Chnging twn units o lngth Convrt th lngth msurmnts low into th units givn in squr rkts. CHANGING BETWEEN UNITS OF LENGTH *.../.../ m [millimtrs] 9 m [ntimtrs] 600 m [mtrs] 4 km [mtrs] 7000 m [kilomtrs] 50 mm [ntimtrs] Convrt th lngth msurmnts low into th rkt units. 0.0 m [ntimtrs] 50 m [mtrs] 8 mm [ntimtrs] 90 m [kilomtrs] km [mtrs] hm [millimtrs] Chng th lngth msurmnts into th units in squr rkts mm [mtrs] 400 m [kilomtrs] 7. km [millimtrs] 0.75 m [ntimtrs] 0.9 m [millimtrs] 870 mm [ntimtrs] 4 Convrt ths trikir lngth msurmnts into th units shown in squr rkts km [m] 0.09 m [mm] km [mm] 4 mm [km] ^78. ' 0 5 hkm [mm] ^# 0 6 hm [km] P Lrning H SERIES 7 TOPIC 9
12 Whr os it work? Ar, volum n pity onvrsions Ar '00 '0 000 ' squr millimtrs mm squr ntimtrs m squr mtrs m squr kilomtrs km h = m #00 #0 000 # You n lso o r onvrsions lik this: m = 000 mm Volum ^mh = ^000 mmh m = mm '000 ' ' ui millimtrs mm ui ntimtrs m ui mtrs m # #000 # m hols litr o liqui Cpity (Volum or liqui) ' 000 ' 000 ' 000 ' mirolitr μl millilitrs ml litrs L kilolitrs kl mglitrs ML #000 # # 000 # 000 # H 7 SERIES TOPIC P Lrning
13 Whr os it work? Ar, volum n pity onvrsions Us th r, volum n pity hrts to onvrt ths msurmnts For r n volum onvrsions, rul with hnging multiplirs. (i) squr mtrs into htrs ' m ' = 9.5 htrs Sm r in lrgr units m h (ii) mtrs u into millimtrs u mm m m #000 # m # # 000 = # mm = mm Sm volum in smllr units (iii) 5 kilolitrs into millilitrs ml L # 000 # 000 kl 5kL # 000 # 000 = 5 # ml = ml Comin th multiplirs Sm pity in smllr units To in how muh liqui ontinr n hol, volum msurmnts n onvrt to pity units. Rmmr: Volum to Cpity mm = μl m = ml 000 m = L m = kl (iv) Th volum o ror milk ontinr is 500 m. How mny litrs o milk os th rton hol? 000 m = litr ` 500 m ' 000 m = 5. ` 500 m milk rton n hol.5 litrs o milk P Lrning H SERIES 7 TOPIC
14 AREA,VOLUME AND CAPACITY CONVERSIONS * Whr os it work? Your Turn Ar, volum n pity onvrsions.../.../0... Convrt th r msurmnts low into th units shown in squr rkts m 6 5 km 6 h m 6 m 6 50 km 6 h@ g 9.mm h m m 4 m Convrt th volum msurmnts low into units shown in squr rkts mm 6 5 m m m 6 Convrt th pity msurmnts low into th units writtn in squr rkts kl 6 ML@ 500 ml 6 90 ml 6 μl@ 0.0 kl L 6 kl@ 67 ML 6 kl@ 4 Chng ths msurmnts into th units writtn in squr rkts. 7 L L 6 00 m 6 5 mm 6 μl@ 56.8 m 6 4 m 6 kl@ H 7 SERIES TOPIC P Lrning
15 Whr os it work? Your Turn Ar, volum n pity onvrsions 5 Us two stps to onvrt ths mix msurmnts into th rkt units ml 6 kl@ 7.49 m mm 6 0 L m 6 ml@ h 6 6 Us thr stps to onvrt ths mix msurmnts into th units givn in squr rkts km ml 6 ML@ 0.00 t 6 mg@ mm 6 h@ 7 During long wlk, prson rnk 5 ull 600 ml ottls o wtr. How mny m o wtr is this qul to? 8 Th sls rohur or nw rrigrtor si tht it hs pity o 560 L. Wht volum o wtr is this qul to in m? Th volum o rtngulr rrigrtor is oun y lulting with # pth # hight. I th rrigrtor on sl is 80 m wi,.5 m high n 500 mm p, is th sls rohur urt? Explin your nswr. (hint: hng ll rrigrtor imnsions to m irst) P Lrning H SERIES 7 TOPIC
16 Whr os it work? Your Turn Ar, volum n pity onvrsions 9 To rn this wsom stmp, omplt th puzzl low to rvl somthing tht onvrts rom on orm to nothr in ntur. Sh ll th rs ontining vlus qul to m yllow Sh ll th rs ontining vlus qul to m lk Sh ll th rs ontining vlus qul to m lu mm km 0 ml 00 mm L ML ML m m # kL 0.0 h 0.0 km ml 00 mm 0.000L m km ' 000 L 000 mm μm h 000μL 000 mm 0.m mm m 0.00L 00. m 0 # 0 mm 000 mm m 0 # 00 mm m m.../.../ H 7 SERIES TOPIC P Lrning
17 Whr os it work? Chnging twn units o tim Lrgr units ' 60 '60 ' 4 ' 7 wks millisons ms Sons s Minuts min Hours h Dys 4 # 000 # 60 # 60 # 4 Smllr units Othr tim onvrsions inlu: '7 ' ' ys wks ortnight months yr #7 # # '5 ' 0 ' 0 wks yrs s nturis #5 # 0 # 0 Us th onvrsion hrt to onvrt ths tim msurmnts. (i) s into yrs '0 s = # 0 yrs Choos th orrt multiplir yrs s = 0 yrs Sm tim in smllr units #0 B rul with hnging multiplirs or tim onvrsions ning two or mor stps (ii) millisons into minuts ' 000 ' 60 ms s min ' 000 ' 60 = 7 ' 60 min =. min Work lt to right Sm tim in minuts P Lrning H SERIES 7 TOPIC 5
18 CHANGING BETWEEN UNITS OF TIME * Whr os it work? Your Turn Chnging twn units o tim.../.../0... Convrt ths tim msurmnts into th units givn in squr rkts. 40 min 6 sons@ ys 6 hours@ 600 s 6 minuts@ 7000 ms 6 sons@ 54 hours 6 minuts@ 00 hours 6 ys@ g yrs 6 wks@ h s 6 nturis@ Convrt ths tim msurmnts into th units givn in squr rkts. 0. s 6 millisons@ 0.4 h 6 minuts@ 400 ms 6 sons@ 8 hours 6 ys@ 0.0 hours 6 minuts@ 4 s 6 minuts@ g.5 ortnights 6 wks@ h 0.74 yrs 6 months@ Chng ths tim msurmnts into th rkt units. 0.0 hours 6 sons@ 4. min 6 millisons@ ys 6 minuts@ 40 ms 6 minuts@ min 6 ys@ 9 hours 6 wks@ 4 Convrt ths prix tim msurmnts into th units shown in squr rkts. 500 ms 8 ms minuts 6 sons@ 4 mins 6 millisons@ ms 6 hours@ s 6 millisons@ ^54 # 0 4 h min 6 hours@ 6 H 7 SERIES TOPIC P Lrning
19 Wht ls n you o? Mix units prolms Chnging ll msurmnts to th sm units llows lultions to muh simplr. Eg: Wht is th totl mss o th mrk oxs low? First, hng ll th msurmnts into th sm units. Lt s us kg! Box : 00 g = 00' 000 kg = 0. kg 0. kg Box :.0 kg.0 kg Box : 0.7 kg 0.7 kg Box 4: 50g = 50 ' 000 kg = 0.5 kg 0.5 kg Thn togthr th vlus in th sm units, so totl mss is: 4.5 kg W oul hv hng thm ll into grms or ny othr unit o mss inst i n. Hr is nothr xmpl whih uss lngth onvrsions. Four silors msur how r thir ot ws rom th ost whn th nhor ws st km, 75 m, 750 m, mm I only on o th msurmnts ws inorrt, whih on ws it? : 0.75km m # = : 75 m : 750 m ' 00 = 7.5 m hng to sm units to ompr : mm ' 000 = 75 m ` th msurmnt o 750 m ws th inorrt on P Lrning H SERIES 7 TOPIC 7
20 Wht ls n you o? Your Turn Mix units prolms MIXED UNIT PROBLEMS * MIXED UNIT PROBLEMS * Th istn twn two itis on Erth r on million, on hunr n twlv thousn, iv hunr mtrs prt. How r prt r th two points in km?.../.../0... Dsri th totl mss o th oxs ing rri low in s mny irnt wys s you n. To rn ronz rtiit in th Fthom Frins Diving Clu, ivr must hv omplt totl o 5 hours iving. Our ivr low hs so r omplt ivs o 45 minuts, 600 sons n 8 th o y. How muh longr os th ivr hv to iv or to rn ronz rtiit? 8 H 7 SERIES TOPIC P Lrning
21 Wht ls n you o? Your Turn Mix units prolms 4 To win holiy, milis rom on ity took prt in wtr ryling omptition. Whih o th ollowing top prorming milis won th holiy y ryling th most wtr? Th Hkim mily: 500 L Th Okk mily: ML Th Evns Fmily: m Th Akhtr mily: ml 5 Ern yoursl n wsom pssport stmp with this on! Plnts r importnt or hlping kp grnhous gss in th tmosphr in hk. In h yr pproximtly: 0 splings sor 0 kg, 0 htrs o pin orst sor 00 tonns, n 0 htrs o prsrv orst sor 000 tonns o hrmul gss, How mny totl kilotonns o grnhous gsss r sor in on yr y splings, 00 htrs o pin orst n 000 htrs o prsrv orst?.../.../0... P Lrning H SERIES 7 TOPIC 9
22 Wht ls n you o? Convrsion pplitions: Rsistor vlus Chrts r otn us to hlp popl quikly lult vlus or onvrsions. Rsistor hrts hlp thniins r th vlu o rsistor, whih is importnt to nsur tht th ltronis oprts proprly. Dirnt olour ns show th vlus n multiplir us to tll th rsistn o h omponnt. Th unit or rsistn is Ohm s (Ω) Rsistor n olour hrt st Digit n Digit Multiplir Blk 0 0 Brown 0 R 00 Orng 000 Rsistor olour os: Yllow Grn Blu Violt 7 7 Gry 8 8 Whit # 000 Th vlu o this rsistor is ohms, or using prixs is 5 kω (or kilo-ohms) Us th rsistor hrt to writ th vlu o this rsistor in mg-ohms. Th vlu o this rsistor is 8 4 # ohms ohms # = = 84 MΩ Mg-ohms 0 H 7 SERIES TOPIC P Lrning
23 Wht ls n you o? Your Turn Convrsion pplitions: Rsistor vlus CONVERSION APPLICATION: RESISTOR VALUES * Us th rsistor hrt to writ th vlu o ths rsistors..../.../0... Rsistor vlu = Ohms Rsistor vlu = Ohms Rsistor vlu = Ohms Rsistor vlu = Ohms Us th rsistor hrt to writ th vlu o ths rsistors using th rkt prixs. [kilo-ohms] [mg-ohms] Rsistor vlu = Ω Rsistor vlu = Ω = kω = MΩ [mg-ohms] [kilo-ohms] Rsistor vlu = Ω Rsistor vlu = Ω = MΩ = kω P Lrning H SERIES 7 TOPIC
24 Wht ls n you o? Your Turn Rltion Tim Rlting on th work ovr within this ooklt: Wht usul skills hv you gin y lrning how to onvrt twn irnt units? Writ out on or two wys you think you oul pply onvrting units to rl li sitution. I you isovr or lrnt out ny shortuts to hlp with onvrting units or som othr ool ts/onvrsions, jot thm own hr: H 7 SERIES TOPIC P Lrning
25 Cht Sht Hr is wht you n to rmmr rom this topi on Multiplying n iviing y powrs o tn Mov th iml point pning on th numr o zros # = mov iml point to th right, ' = mov iml point to th lt Prixs Prixs lt us writ own vry smll or vry lrg numrs quikly n sily. Eh prix tlls us wht to multiply th msur vlu y i w wnt to writ it in th s units us. Chnging twn units o mss ' 000 milligrms mg # ' 000 kilogrms kg grms g # 000 ' 000 # 000 ' tonns t # 000 P Lrning H 7 SERIES TOPIC
26 Cht Sht Chnging twn units o lngth '0 '00 ' 000 ' Smllr units millimtrs mm ntimtrs m mtrs m kilomtrs km Lrgr units # # 0 # 00 # 000 Ar, volum n pity onvrsions '00 '0000 ' Ar squr millimtrs mm squr ntimtrs m squr mtrs m squr kilomtrs km # 00 # # ' 000 ' ' Volum ui millimtrs mm ui ntimtrs m ui mtrs m # #000 # ' 000 ' 000 ' 000 ' Cpity mirolitr μl millilitrs ml litrs L kilolitrs kl mglitrs ML # #000 # 000 # 000 Chnging twn units o tim ' 60 ' 60 ' 4 ' 7 wks millisons ms Sons s Minuts min Hours h Dys 4 # 000 # 60 # 60 # 4 4 H 7 SERIES TOPIC P Lrning
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28 AREA,VOLUME AND CAPACITY CONVERSIONS * CHANGING BETWEEN UNITS OF LENGTH *.../.../0... CONVERSION APPLICATION: RESISTOR VALUES *.../.../0... CHANGING BETWEEN UNITS OF TIME *.../.../ /.../0... MIXED UNIT PROBLEMS * MIXED UNIT PROBLEMS *.../.../0...
# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.
How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 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
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