Worksheet 1.4 Fractions and Decimals - Macquarie University

1 DecimalsSection1 FractionstodecimalsThemostcommonmethod of convertingfractionsto decimalsis to usea fractionrepresents a divisionso1ais anotherway of writing1 a, andwitha calculatorthisoperationis easyto of :12= 1 2 = 0:5 Example2:78= 7 8 = 0:875 Example3:98= 9 8 = 1:125 Example4:57= 5 7 = 0:7143 Thelastnumber hasbeenroundedto a decimalnumber?Thisis a number which hasa fractionalpartexpressedas a seriesof numbersaftera decimalpoint. It is a shorthandway of rstexaminingcountingnumberswe canthenexpandthisthinkingto 563canbe thought of as 5 hundreds+ 6 tens+ 3 cansay thereare5hundredsin 563;we readthisinformationo tensin563- thereare50 fromthehundredscolumnand6 rstplaceafterthedecimalpoint represents how many110's therearein how many hundredthsandthethirdplacerepresents how manythousandthstherearein : 65:83 canbe writtenas:6 tens+ 5 ones+ 8 tenths+ 3 tensin 65:83 Thereare65 onesin 65:83 Thereare658tenthsin 65:83andthereare6583hundredthsin 65:83 Example6: For thenumber 5:07 we have:Thereare5 onesin 5:07 Thereare50 tenthsin 5:07 Thereare507hundredthsin 5:07 Note:Thisis di erent from5:7.

2 Thezerosin a number we arein a positionto say:0:1=1100:01=11000:001=11000 Andwe canconvertsomefractionsto :310=0:337100=0:37371000=0:0373710=3:7 Page2 Becausethedecimalplacesrepresent tenths,hundreths,etc,whenwe wishto converta fractionto a decimalwe useequivalent fractionswithdenominatorsof 10;100; ndingthedecimalequivalent formany fractionsis to ndanequivalent fractionwiththeright thenusetheinformationthat110=0:11100=0:0 111000=0:001to convertit to a :14=14 2525=25100=20100+5100=210+5100=0:2525=25 22=410=0:418=18 125125=1251000=0:125 Sometimesit is notimmediatelyobviouswhatnumber youneedto multiplyby to gettherightdenominator,butonthewholetheo nesyouareaskedto dowithouta :1. Convertthefollowingfractionsto Decimals (a)310(b)15100(c)81000(d)3671000 (e)8510(f)12(g)34(h)45(i)85100(j)1950 Section2 DecimalstofractionsTo convertdecimalsto fractionsyouneedto recallthat0:1=1100:01=11000:001=11000 Thusthenumber afterthedecimalplacetellsyouhow many tenths,thenumber afterthathow many hundredths, sumof Fractions ,addthemtogetheras fractionsandthensimplifyusingcancellatio nof :0:51=510+1100=50100+1100=51100 Page4 Example2:0:75=710+5100=70100+5100=75100= 34 2525=34 Example3::102=110+0100+21000=1001000+210 00=1021000=51500 Exercises:1.

3 Convertthefollowingdecimalsto Fractions (a)0:7(b)0:32(c)0:104(d)0:008(e )0:0013 Section3 OperationsondecimalsWhenaddingor subtractingdecimalsit is important to remember wherethedecimalpoint donejustlike addingandsubtractinglargenumbersPage5in themissingcolumnswithzerosto givebothnumbersthesamenumber of thatthezeroseithergoat theveryendof numbersafterthedecimalpoint or at : Calculate0:5 0 :46 Lineupthedecimalpoints Insertzerossothatbothnumbershave thesamenumber of digitsafterthedecimalpoint Performthecalculation,keepingthedecimalp oint in placeExample2:Calculate0:07 0 :04 Example3: Calculate1:1 0 :097 Exercises:1. Evaluatewithoutusinga calculator(a)0:72 + 0:193(b)0:604 0:125(c)0:8 0:16(d)32:104+ 41:618(e)54:119 23 (a)How many hundreds,tens,ones,tenths, thefollowing?i. (b)Writethenumber representedbyi. 6 hundreds,4 ones,9 tens,2 ones,2 tenths,3 +110+41000+610000v. 100+ 60 + 2 +1100+ +310+91002.(a)Changethefollowingdecimals into fractionswithouttheuseof a (b)Changethesefractionsto decimalswithouttheuseof a (c)Usinga calculator,convertthefollowingfractionst o Evaluatethefollowingwithouta calculator.

4 (a)0:62 0:37(b)0:08 + 0:2(c)6:72 + 6:1(d)0:675+ 0:21 + 0:008(e)4:70 0:356(f) 6:32 2:8 + 1:01 Page7 Answers (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (a)710(b)825(c)13125(d)1125(e)131000 Section31.(a) (b) (c) (d) (e) (a)i. 6 tens,0 ones,3 tenths,1 hundreds,0 tens,4 ones,2 ten,4 ones,2 tenths,9 hundredths,6 thousandths(b)i. (a) (b)i. (c)i. (a) (b) (c) (d) (e) (f)