using decimals for large whole numbers 1 - · pdf fileguided you will need • place value...

OPEN-ENDEDPathway 1

You will need•Internetaccess,or

MillionsandBillions(BLM1)

•PlaceValueCharts(toBillions)(BLM2)

ApopularTVshowhadabout12.3millionviewersinonenight.

12.3millionisbetween12millionand13million.

LEAP 7/8 SR

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Approved

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D. Loates

1st pass

13 million12 million 12.3 million

Theplacevaluechartbelowshowsthat12.3million,writteninstandard form,isthewholenumber12300000.

Toexplainwhyyoucanwriteawholenumberusingadecimal,youcanthinkof1millionas1unit.– The12in12300000is12million,soitis12units.– The3in12300000is3tenthsof1million,or0.3units.

Billions Millions Thousands Ones

H T O H T O H T O H T O

1 2 3 0 0 0 0 0

Part A

• Find3numbersthatarewrittenasadecimalnumberofmillions.– Tellwhateachnumberdescribes.– Writeeachnumberinstandardform.– Explainhowyouknowyouareright.

Decimal number of millions and what it describes

Standard form

How you know

LB56SR

ISBN: 0-17-635153-1FNCO Dave McKay Illustration

T01-F01-LB78SR

dhmPass 4th passApprovedNot Approved

Using Decimals for Large Whole Numbers

standard formtheusualwayweseeandwriteanumber

Copyright © 2012 by Nelson Education Ltd.1

Leaps and Bounds UsingDecimalsforLargeWholeNumbers,Pathway1

Leap SR 7-8_Topic 1.indd 1 2/25/12 2:46 PM

• Find2numbersgreaterthan1millionthatarewritteninstandardform.– Tellwhateachnumberdescribes.– Estimatethedecimalformofeachusingunitsof1million.

Standard form

What it describes

Estimate in decimal number of millions

Part B

• RepeatPartAfor3numberswrittenasadecimalnumberofbillions.

Decimal number of billions and what it describes

Standard form

How you know

• Repeatfor2numbersgreaterthan1billionwritteninstandardform.

Standard form

What it describes

Estimate in decimal number of billions

Part C

• Writeall10numbersfromPartsAandBinorderfromleasttogreatest.Explainyourthinking.

LB56SR

ISBN: 0-17-635153-1FNCO Dave McKay Illustration

T01-F03-LB78SR

dhmPass Third Pass 111103ApprovedNot Approved

Copyright © 2012 by Nelson Education Ltd.2

Leaps and BoundsUsingDecimalsforLargeWholeNumbers,Pathway1

Leap SR 7-8_Topic 1.indd 2 2/25/12 2:46 PM

GuiDED

You will need•PlaceValueCharts

(toBillions)(BLM2)•Internetaccessor

MillionsandBillions(BLM1)

Pathway 1

Recently,agoldanddiamondsmartphonecasehadapriceof$3.2million.

3.2millionisanumberbetween3millionand4million.

LEAP 7/8 SR

0-176351531

FN

CO

Pass

Approved

Not Approved

T01-F05-LB78SR.ai

VISUTronX

D. Loates

1st pass

4 million3 million 3.2 million

• Youcanseefromtheplacevaluechartbelowthat3.2millionwritteninstandard formisthewholenumber3200000.

Toexplainwhyyoucanwriteawholenumberusingadecimal,youcanthinkofonemillionasoneunit.– The3in3200000is3million,soitis3units.– The2in3200000is2tenthsof1million,or0.2units.

Billions Millions Thousands Ones

H T O H T O H T O H T O

3 2 0 0 0 0 0

• Youcanwritesomeverylargenumbersusingabillionsunitinsteadofamillionsunit.

Forexample,4650000000is4.65billion.The6in4650000000is0.6,or 6

10ofthebillionsunit.

The5in4650000000is0.05,or 5100ofthebillionsunit.

So,the65in4650000000is0.65units.

Billions Millions Thousands Ones

H T O H T O H T O H T O

4 6 5 0 0 0 0 0 0 0

• Whatis3.28millionwritteninstandardform?Howdoyouknow?

LB56SR

ISBN: 0-17-635153-1FNCO Dave McKay Illustration

T01-F04-LB78SR

dhmPass Third Pass 111103ApprovedNot Approved

110

Using Decimals for Large Whole Numbers

standard formtheusualwayweseeandwriteanumber

• Youcanwritelargewholenumbersindecimalformtofocusonthedigitsthatmattermost.Readingthisformisusuallyquickerthancountingallthezeros.

Remember1

1001

10

Copyright © 2012 by Nelson Education Ltd.3

Leaps and Bounds UsingDecimalsforLargeWholeNumbers,Pathway1

Leap SR 7-8_Topic 1.indd 3 2/25/12 2:46 PM

Try These 1. Showeachnumberinstandardformontheplacevaluechart.

a) 4.5million Billions Millions Thousands Ones

H T O H T O H T O H T O

b) 12.0million Billions Millions Thousands Ones

H T O H T O H T O H T O

c) 4.13billion Billions Millions Thousands Ones

H T O H T O H T O H T O

d) 0.5billion Billions Millions Thousands Ones

H T O H T O H T O H T O

2. Writeeachnumberinstandardform.

a) 7.12billion

b) 7.8million

c) 13.24million

d) 12.23billion

3. Writeeachnumberusingadecimalnumberofmillionsorbillions,whichevermakesmoresensetoyou.

a) 12345000

b) 500000

c) 1200000000

d) 314120000000

Copyright © 2012 by Nelson Education Ltd.4

Leaps and BoundsUsingDecimalsforLargeWholeNumbers,Pathway1

Leap SR 7-8_Topic 1.indd 4 2/25/12 2:46 PM

4. Use.or,tomakeeachstatementtrue.

a) 4.1million 3.24million

b) 5.3million 0.9billion

c) 1.23billion 9.0billion

d) 0.01billion 12.4million

5. Inwhichnumberisthedigit5worththemost?Howdoyouknow?

4.5billion 5.1million 5.4billion

6. Fillintheblanks.Usetheplacevaluecharttohelpyou.

a) 4.2million5________thousand

b) 0.6million5________thousand

c) 2.13billion52130________________

Billions Millions Thousands Ones

H T O H T O H T O H T O

7. Ofthe7.0billionpeoplewholiveintheworld,about1.3billionliveinChina.Findatleast3morereal-worldnumbersthatareexpressedasdecimalmillionsorbillions.Tellwhateachnumberdescribes.

8. Whyarepeoplemorelikelytowrite3100000as3.1millionthantowrite3100as3.1thousand?

Inthemedia,largewholenumbersareoftenwrittenusingdecimals.

FYI

Copyright © 2012 by Nelson Education Ltd.5

Leaps and Bounds UsingDecimalsforLargeWholeNumbers,Pathway1

Leap SR 7-8_Topic 1.indd 5 2/25/12 2:46 PM

OPEN-ENDEDPathway 2

You will need•PlaceValueCharts

(toBillions)(BLM2)

About111millionpeoplewatchedtheSuperBowlonTV.

111millioncanbewritteninstandard formas111000000.

Billions Millions Thousands Ones

H T O H T O H T O H T O

1 1 1 0 0 0 0 0 0

• Whydoesitmakesensethatthenumberofviewerswasabout111millionandnotabout111billion?

Part A

• Write5numbersthatarecloseto111million.– Writeeachnumberinstandardform.– Includethedigits3,5,7,and9onceineachnumber.

Youcanuseotherdigitsaswell.– Includenumbersthataregreaterthan111millionand

numbersthatarelessthan111million.

• Tellhowyouwouldreadeachnumber.

Representing Millions and Billions

standard formtheusualwayweseeandwriteanumber

Copyright © 2012 by Nelson Education Ltd.6

Leaps and BoundsRepresentingMillionsandBillions,Pathway2

Leap SR 7-8_Topic 1.indd 6 2/25/12 2:46 PM

• Explainhowyouknoweachnumberiscloseto111million.

Part B

• Write5numbersthatarecloseto278billion.Includenumbersthatarelessthanandgreaterthan278billion.

• Tellhowyouwouldreadeachnumber.

Part C

• Writeall10numbersfromPartsAandBinorderfromleasttogreatest.Explainyourthinking.

LB56SR

ISBN: 0-17-635153-1FNCO Dave McKay Illustration

T01-F08-LB78SR

dhmPass Third Pass 111103ApprovedNot Approved

Copyright © 2012 by Nelson Education Ltd.7

Leaps and Bounds RepresentingMillionsandBillions,Pathway2

Leap SR 7-8_Topic 1.indd 7 2/25/12 2:47 PM

GuiDEDPathway 2

You will need•PlaceValueCharts

(toBillions)(BLM2)•MillionsandBillions

(BLM1)

WhenKaiwasborn,thepopulationofTorontowas2503281.

Thenumber2503281isinstandard form.

Thespacesinthestandardformofthenumberseparatethebillions,millions,thousands,andonesperiods.

Billions Millions Thousands Ones

H T O H T O H T O H T O

2 5 0 3 2 8 1

Youcanusetheperiodsandtheplacevaluecharttoread,interpret,andrenamelargenumbers.

• Youcanread2503281as2 million 503 thousand 281.

• Youcanestimatethat2503281isabouthalfwaybetween2millionand3million.

• Youcanrename2503281as2million1503thousand1281.

• Youcanalsorename2503281inotherways.1million51000thousandSo,250328152000thousand1503thousand1281

52503thousand1281

• Useaplacevaluecharttohelpyouread250000003281.

Try These 1. Whatisthesameandwhatisdifferentinhowyouwouldread

2500030and2005300?

same:

different:

Representing Millions and Billions

standard formtheusualwayweseeandwriteanumber

periodagroupof3placevaluecolumnsbasedonhundreds,tens,andonesofthesameunit

Copyright © 2012 by Nelson Education Ltd.8

Leaps and BoundsRepresentingMillionsandBillions,Pathway2

Leap SR 7-8_Topic 1.indd 8 2/25/12 2:47 PM

2. Writeeachnumberinstandardformonaplacevaluechart.

a) 22million312thousand21

Billions Millions Thousands Ones

H T O H T O H T O H T O

b) 3million8thousand12

Billions Millions Thousands Ones

H T O H T O H T O H T O

c) 17billion12million34thousand

Billions Millions Thousands Ones

H T O H T O H T O H T O

d) 100billion32thousand

Billions Millions Thousands Ones

H T O H T O H T O H T O

3. Circlethegreaternumberineachpair.

a) 89hundredthousand121 2billion

b) 153million132thousand 1billion

c) 110million 312thousand

d) 42million 42hundredthousand

4. Estimate.Useaplacevaluecharttohelpyou.

a) 4128756isabout________________million.

b) 4128756isabout________________thousand.

c) 1834567109isabout________________billion.

d) 1834567109isabout________________million.

Copyright © 2012 by Nelson Education Ltd.9

Leaps and Bounds RepresentingMillionsandBillions,Pathway2

Leap SR 7-8_Topic 1.indd 9 2/25/12 2:47 PM

5. Writeanumberinstandardformforeachdescription.

a) 1hundredthousandmorethan2348172

b) 3millionmorethan152417

c) 1billionmorethan3425617

d) 2millionmorethan8413465

6. Howmanydigitsareinanumberthatbeginswitheachphrase?

a) 42million… ________

b) 250million… ________

c) 20billion… ________

d) 300thousand… ________

7. Inwhichnumberisthedigit5worththemost?Howdoyouknow?

53143200 153787 5203412111

8. Use.or,tomakeeachstatementtrue.

a) 4000003 1000000003

b) 3045020 3450200

c) 2781235 2781532

d) 4528134 528478

Explainyouranswertopartd):

9. Fillintheblanks.

a) 4million5____________thousand

4million5____________hundredthousand

b) 2billion5____________million

2billion5____________hundredmillion

Beingabletowritenumbersindifferentwayscanbehelpfulwhenyouperformcalculations.

FYI

Copyright © 2012 by Nelson Education Ltd.10

Leaps and BoundsRepresentingMillionsandBillions,Pathway2

Leap SR 7-8_Topic 1.indd 10 2/25/12 2:47 PM

10. Use,or.tomakeeachstatementtrue.

a) 30million 40hundredthousand

b) 25million 260hundredthousand

c) 8billion 9000million

d) 2billion 200million

Explainyouranswertopartd):

11. TheworldpopulationonFebruary28,2011,was7090669275.Onthesameday,thepopulationofChinawas1319175336.Describe2otherreal-worldvaluesthatwouldlikelybeexpressedinbillionsormillions.

12. Decidewhetheryouagreeordisagree.Explainyourthinking.

a) Anynumbergreaterthan1billionismorethan900million.

b) Anynumbergreaterthan1millionislessthan1billion.

c) Anynumberofbillionsisalwaysgreaterthananynumberofmillions.

LEAP 7/8 SR

0-176351531

FN

CO

Pass

Approved

Not Approved

T01-F10-LB78SR.ai

VISUTronX

D. Loates

1st pass

Sun. Mon. Tues. Wed.February 2011

Thurs. Fri. Sat.1 2 3 4 5

7 8 9 10 11 12

14 15 16 17 18 19

21 22 23 24 25 26

6

13

20

27 28

Copyright © 2012 by Nelson Education Ltd.11

Leaps and Bounds RepresentingMillionsandBillions,Pathway2

Leap SR 7-8_Topic 1.indd 11 2/25/12 2:47 PM

OPEN-ENDED

You will need•PlaceValueCharts

(toHundredThousands)(BLM3)

Pathway 3Representing Six-Digit Numbers

Acarcompanyhadtorecallabout750thousandcarstohavethetransmissionschecked.

750thousandwritteninstandard formis750000.

Hundredthousands

Tenthousands

Thousands

Hundreds

Tens

Ones

7 5 0 0 0 0

• Write5numbersthatarecloseto750thousand.– Writeeachnumberinstandardform.– Usethedigits3,5,7,and9atleastonceineachnumber.– Includenumbersgreaterthan750000andlessthan750000.

• Suppose100fewercarsthan750000wererecalled.List5numbersthatareclosetothatnumber.Useanydigits.

• Writeall10numbersaboveinorderfromleasttogreatest.Explainyourthinking.

standard formtheusualwayweseeandwriteanumber

Copyright © 2012 by Nelson Education Ltd.12

Leaps and BoundsRepresentingSix-DigitNumbers,Pathway3

Leap SR 7-8_Topic 1.indd 12 2/25/12 2:47 PM

GuiDED

You will need•PlaceValueCharts

(toHundredThousands)(BLM3)

In2006,thepopulationofEdmontonwas730372.

Thenumber730372isinstandard form.

Thespaceinthestandardformofthenumberseparatesthethousandspartofthenumberfromthepartthatincludesthehundreds,tens,andones.

Hundredthousands

Tenthousands

Thousands

Hundreds

Tens

Ones

7 3 0 3 7 2

Youcanusethe2partsofthenumbertoread,interpret,andrenamelargenumbers.

• Youcanread730372as730 thousand 372.

• Youcanestimate730372asabout730thousand.

• Youcanrename730372as730thousand1372.

• Usetheplacevaluecharttohelpyoureadthenumber503020.

Try These 1. Whatisthesameandwhatisdifferentinhowyouwouldread

402030and420030?

same:

different:

Representing Six-Digit Numbers Pathway 3

standard formtheusualwayweseeandwriteanumber

Copyright © 2012 by Nelson Education Ltd.13

Leaps and Bounds RepresentingSix-DigitNumbers,Pathway3

Leap SR 7-8_Topic 1.indd 13 2/25/12 2:47 PM

2. Writeeachnumberinstandardformonaplacevaluechart.

a) 300thousand78

Hundredthousands

Tenthousands

Thousands

Hundreds

Tens

Ones

b) 420thousand10

Hundredthousands

Tenthousands

Thousands

Hundreds

Tens

Ones

c) 10thousand312

Hundredthousands

Tenthousands

Thousands

Hundreds

Tens

Ones

3. Circlethenumberineachpairthathasmoredigitswhenwritteninstandardform.

a) 58hundred 22thousand

b) 20tenthousand 80thousand

c) 6hundredthousand 50hundred

4. Estimate.Useaplacevaluecharttohelpyou.

a) 562103isabout________hundredthousand.

b) 493127isabout________hundredthousand.

c) 213856isabout________thousand.

d) 478100isabout________thousand.

5. Writeanumberinstandardformforeachdescription.

a) 100000morethan203652

b) 10000lessthan243652

c) 8000morethan483622

d) 5000lessthan453000

Copyright © 2012 by Nelson Education Ltd.14

Leaps and BoundsRepresentingSix-DigitNumbers,Pathway3

Leap SR 7-8_Topic 1.indd 14 2/25/12 2:47 PM

6. Inwhichnumberisthedigit5worthmost?Howdoyouknow?

503207 953218

7. Use.or,tomakeeachstatementtrue.

a) 202020 92999 c) 882135 885134

b) 410014 140410 d) 711234 79929

8. Supposethenameforawholenumberincludesthesewords:

twenty thirty thousand hundred four two

Howmanydigitsmightthenumberhave?Explainyourthinking.

9. Howmany$100billsiseachamount?

a) $20000is____________$100bills.

b) $530400is____________$100bills.

c) $300000is____________$100bills.

d) $904900is____________$100bills.

10. Describe2ormorereal-worldsituationsthatmightinvolvenumbersinthehundredthousands.Considerpopulationsormoneysituations.

LB56SR

ISBN: 0-17-635153-1FNCO Dave McKay Illustration

T01-F01-LB78SR

dhmPass First Pass 110801ApprovedNot Approved

Beingabletounderstandlargenumbersisuseful,sincelargenumbersappearfrequentlyinthemedia.

FYI

Copyright © 2012 by Nelson Education Ltd.15

Leaps and Bounds RepresentingSix-DigitNumbers,Pathway3

Leap SR 7-8_Topic 1.indd 15 2/25/12 2:47 PM