Numeracy 1

N4Rounding

Roundingmakesiteasiertodescribe&understandnumbers

Mycounciltaxisalmost900p.a.Thisiseasierthansaying883p.a.

Theactualmileageis392GlasgowCardiffisroughly400miles

Workingwithsimplernumbersmakescalculationseasier

4.753.953.250.95

5+4+3+1=13 Billisapprox13

Youwanttocheckthebillforpizzas:

Roundingtothenearestpoundgives

Itmakesiteasiertoestimateanswerstomathsquestions

Youpay12.62andhandover20

2013=7 Approx7change

Checkcalculationsmentally.Usefulwhenshopping.Checkingchange.

Helpidentifymistakesinyourmathswork

Thisisausefulhabittodevelopinmaths

782 4

Approx800 4=200 Ifnotcheckagain

Learningtomakequickestimatesshowsyou'llhaveasensibleanswer

N4Rounding NearestWholeNumber

44.3

5 65.8

4.3liesbetween4and5

itiscloserto4(tothenearestwholenumber)

5.8

Lookatthe1stdecimalfigure

ifit'sa5,6,7,8,9 roundthewholenumberupby1

ifit'sa0,1,2,3,4 leavethewholenumberasitis

liesbetween5and6

itiscloserto6(tothenearestwholenumber)

N4Rounding NearestWholeNumber

Roundinglargernumbersisdonethesameway

Examples

3.14159265358979...3.141519.....=3(nearestwholenumber)

6.83123544556799...6.831235.....=7(nearestwholenumber)

N4Rounding incontext

N4Rounding

Roundeachnumbertothenearest10

Examples

a)78 b)14 c)95

Nearest10,100,1000

= = =


a)121 b)576 c)1356= = =


a)1325 b)6876 c)12581= = =

80 10 100

100 600 1400

1000 7000 13000

N4Rounding Usingroundingtofindestimates

Helpidentifymistakesinyourmathswork

Thisisausefulhabittodevelopinmaths

782 4

Approx800 4=200 Ifnotcheckagain

Learningtomakequickestimatesshowsyou'llhaveasensibleanswer

58 x 407is approximately

60 x 400 24000

193 x 712is approximately

200 x 700 140000

605 32is approximately

600 30 20

8105 17is approximately

8000 20 400

N4Multiplicationbymultiplesof10,100,1000

To multiply 84 x 4084 x 10 = 840 Now find 840

x 4

Step1

Step2

To multiply 132 x 200132 x 100 = 13200 Now find 13200

x 2

Step1

Step2

Simpleifyouknowyourtimestables!

N4Divisionbymultiplesof10,100,1000

To divide 630 70630 10 = 63

Now find 63

Step1

Step2

To divide 13200 40013200 100 = 132Step1

Step2

Simpleifyouknowyourtimestables!

7 Now find 132 4

N4Whataredecimals

= 110 0.1or

Inthedecimalnumber,0.3,the3refersto3tenthsor310

0 3

WhatisaDecimal?

1100 0.01or

Inthedecimalnumber,0.03,the3refersto3hundredthsor3

100

=

0 30

110

110of

TheSecondDecimalPlace

WhatisaDecimal?

0 10

1Whole

110

1100 1

1000

0

TheThirdDecimalPlaceandbeyond

UTH 1101100

11000

0 4

UTH 1101100

11000

0 70

4 is under the

tenths column

0.4 =

4

10

7 is under the

hundredths column

0.07 =

7

100

Fractions&Decimals

UTH 1101100

11000

0 2

UTH 1101100

11000

0 65

0.27 = 27 100

0.56 = 56 100

7

Use this column

Fractions&Decimals

UTH 1101100

11000

0 2

UTH 1101100

11000

0 91

0.072 = 27

0.193 = 56 100

70

Use this column

3

72

1000

193

1000

Fractions&Decimals

ReadingDecimalScales TheFirstDecimalPlace

4 5 6

21 22 23

7 8 9 10 11

ReadingDecimalScales TheSecondDecimalPlace

4.1

31.2

7.4

4.2 4.3

31.3 31.4

7.5 7.6 7.7 7.8

Roundingto1DecimalPlace

4.14.13

4.2 4.34.28

4.13liesbetween4.1and4.2

itiscloserto4.1(to1decimalplace)

4.28liesbetween4.2and4.3

itiscloserto4.3(to1decimalplace)

Lookatthe2nddecimalfigure

ifit'sa5,6,7,8,9 roundthefirstdecimalfigureupby1

ifit'sa0,1,2,3,4 leavethefirstdecimalfigureasitis

12.4 12.512.47


4.0 4.14.05

8.9 9.08.98

Roundeachnumberto1decimalplace

12.47=12.5(1d.p.)

4.05=4.1(1d.p.)

8.98=9.0(1d.p.)

Examples

HelpfromDiagrams


Roundinglargernumbersisdonethesameway

Examples

3.14159265358979...3.141519.....=3.1(1d.p.)

6.18123544556799...6.181235.....=6.2(1d.p.)


Changingfractionsintodecimalswithacalculator

Examples

means3 7=0.428571....=0.4(1d.p.)37

means7 9=0.777777....=0.8(1d.p.)79

N4

Roundingincontext

Thisplaneholds89passengerswhenfull

Howmanyplanesarerequiredto

transport700peopleatthesametime?

700

89=7.865....

8planesneeded

Arolloftoiletpaperis50metres

Asheetneedstobe0.11cmlong

50

0.11=454.55

Youget454sheets

Howmanysheetswillyougetfromaroll?

Add/SubtractDecimals

Whenyouaddorsubtractdecimalsyoumustlineupthedecimalpoints

7 8 56 1 6+

7 8 56 1 6+or

7 8 56 1 6+

U110

1100T



7 8 53 4 2

5 1 42 6 3

9 0 04 8 1

Remembertolookatthesign.Manymistakesaremadebydoingthewrongcalculation!!



7 8 56 1+

U110

1100T

2 0Whatifthenumbers

arenotthesamesize?

Q1 48.2+7.68 Q2 6.234.6Trythese

Problema)Chrisweighs48.25Kg.Hissisterweighs31.3Kg.Whatdotheyweighaltogether?

Chrisb)ByhowmanyKgisChrisheavier?

Multiplyingdecimalsbyasingledigit

Youmustknowyourtimestables!

7 8 54x

U110

1100T

Q1 46.2x5Trythese

4 7 56x

U110T

6 3 49x

U110

1100TH

1

Q2 345.26x8

Problem

1.28Youhavestartedrunningeverynightoftheweekandwanttostockuponlucozade.

Howmuchdo7bottlescost?

Whyisbuyingamultipackcheaper?

Dividingdecimalsbyasingledigit

Youmustknowyourtimestables!

71 33 4 52 67 4 1

Q1 13.55Trythese

Q2 98.328

Problem

IfIpay84.12for6monthsbroadband,howmuchamIpayingeachmonth?

N4Multiplication/Divisionofdecimalsby10,100&1000

To Multiply by 10move all the numbers1 place to the left

To Divide by 10

move all the numbers1 place to the right

To Multiply by 100move all the numbers2 places to the left

To Divide by 100

move all the numbers2 places to the rightN

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Significant FiguresThis is another method of rounding, often used with larger numbers

Imagine you bought a car for 125,659.99

If you were telling somebody how much it cost your more likely to round the price

I paid 126,000This price has been rounded

to 3 significant figures

125,659.991st sig.fig

2nd sig.fig3rd sig.fig

More Examples

Significant Figures125,659.99 was rounded to 126,000 (3 s.f.)

Round 23,567.89 to 3 s.f.

Round 45,633 to 3 s.f.

Round 359,789.66 to 2 s.f.

Round 654.89 to 2 s.f.

23,600

45,600

360,000

650

Attachments

MultiplyingandDividingbymultiplesof10.notebook

MultiplyingandDividingdecimalsbymultiplesof10.notebook

LongMultiplication.notebook

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Nov 9-09:22 Oban 2011 14 per rocket How much would 100 rockets cost?

page15.svg

Nov 25-09:43 H T U TH x 1 0 6 0 1 10

page16.svg

Nov 9-09:51 42 x 1 0 = 382 x 1 0 = 6 x 1 00 = 543 x 1 00 = 178 x 1 000 = 42 0 382 0 6 00 543 00 178 000

page10.svg

Nov 9-09:22 120 for 10 rockets How much would 1 rockets cost?

page6.svg

Nov 25-09:43 H T U TH 1 0 6 0 0 1 10

page14.svg

Nov 9-09:51 4 0 1 0 = 38 0 1 0 = 6 00 1 00 = 543 00 1 00 = 178 000 1 000 = 4 38 6 543 178

SMART Notebook

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Nov 9-09:22 Oban 2011 14.23 per rocket How much would 100 rockets cost?

page15.svg

Nov 25-09:43 H T U TH 1 10 x 1 0 0 1 100

page16.svg

Nov 9-09:51 4.2 x 1 0 = 3.82 x 1 0 = 6.5 x 1 00 = 54.3 x 1 00 = 17.8 x 1 000 = 42 38.2 65 0 543 0 178 00

page10.svg

Nov 9-09:22 124 for 10 rockets How much would 1 rockets cost?

page6.svg

Nov 25-09:43 H T U TH 1 0 0 1 10

page14.svg

Nov 9-09:51 5.26 1 0 = 0.98 1 0 = 6.75 1 00 = 456.45 1 00 = 1.23 1 000 = 0.526 0.098 0.0675 4.6545 0.00123

SMART Notebook

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assessment.xml

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page0.svg

May 7-09:04 Solve 87 2 3 x Working 87 2 3 x 261 174 0 + 2001 2 1 1 1

page1.svg

May 7-09:04 Solve 53 2 7 x Working 53 2 7 x +

page2.svg


page3.svg


page6.svg

May 7-09:04 705 3 4 x + 64 2 8 x + 512 128 0 1792 2820 2115 0 23970 64 x 8 Step 1 Step 1 705 x 4 Step 2 64 x 2 0 Step 2 705 x 3 0 3 2 1

page4.svg

May 7-09:04 Q1. 65 x 23 Q2. 82 x 35 Q3. 99 x 32 Q4. 76 x 52 Q5. 88 x 25 Q6. 89 x 52 Q7. 65 x 98 Q8. 69 x 82 Q9. 36 x 74 Q10. 88 x 88 Q11. 85 x 63 Q12. 92 x 55 Q13. 79 x 15 Q14. 66 x 75 Q15. 88 x 95 Q16. 25 x 43 Q17. 32 x 75 Q18. 84 x 62 Q19. 56 x 72 Q20. 98 x 95 1495 2870 3168 3952 2200 4628 6370 5658 2664 7744 5355 5060 1185 4950 8360 1075 2400 5208 4032 9310

page7.svg

May 7-09:04 283 3 2 8 x + 2264 566 0 92824 283 x 8 Step 1 Step 2 283 x 2 0 849 00 Step 3 283 x 3 00 157 5 4 9 x + 1413 628 0 86193 785 00 157 x 9 Step 1 Step 2 157 x 4 0 Step 3 157 x 5 00 2 6 1 2 1 1 1 6 5 2 2 3 2 1 1

page5.svg

May 7-09:04 Q1. 381 x 23 Q2. 471 x 35 Q3. 781 x 42 Q4. 980 x 52 Q5. 570 x 65 Q6. 802 x 32 Q7. 741 x 53 Q8. 666 x 24 Q9. 161 x 19 Q10. 570 x 65 Q11. 911 x 329 Q12. 119 x 538 Q13. 717 x 247 Q14. 341 x 296 Q15. 407 x 655 Q16. 111 x 321 Q17. 535 x 632 Q18. 666 x 848 Q19. 258 x 391 Q20. 500 x 600 8763 16485 32802 50960 37050 25664 39273 15984 3059 37050 299719 64022 177099 100936 266585 35631 338120 564768 100878 300000

flash/flash191/simple_calc.swf



SMART Notebook

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Numeracy 1