Decimals

Click to edit Master title style<= /div>

Clic= k to edit Master text styles

Se= cond level

Th= ird level

Fo= urth level

Fi= fth level

‹date/time› =

‹fo= oter› =

‹#&= #8250; =

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Click to edit Master title style=

Click to edit Master subtitle style

‹date/time› =

‹fo= oter› =

‹#&= #8250; =

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Decimals

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Decimal Notation, Order

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Definitions

pDecimal Notation: Represents parts of whole numbers with place values to the right of the decimal <= /span>point =

pDecimal Point: Separates whole numbers from parts of whole numbers.=

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Place-Value Chart

<= /span>

Hundreds

Tens

Ones

Tenths

Hundredths

Thousandths

Ten-thousands<= span style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro= man"; mso-hansi-font-family:"Times New Roman";mso-special-format:lastCR;display: none'>

Hundred-thousands

<= ![endif]>

Decimal
Po= int

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Converting from Decimals to <= /span>Fract= ions

1)The decimal portion is the numerator of the fraction= 3;

2)The place value of the farthest right digit is the denominator <= /span>

3)Reduce as necessary

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Examples

p.8

<= span style=3D'visibility:hidden'>p

p15.25

<= span style=3D'visibility:hidden'>p

p.6252.02

<= span style=3D'visibility:hidden'>p

p1.005

p1.36

<= span style=3D'visibility:hidden'>p

p.75

<= span style=3D'visibility:hidden'>p

p2.02

<= span style=3D'visibility:hidden'>p

p.0001

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Converting from Fractions to = Decim= als

<= span class=3DBB style=3D'position:absolute;left:-4.08%;top:.3em'>pMove the decimal in the numerator to the left the number of zeros in the denominator

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Examples

p16/10= 0

<= span style=3D'visibility:hidden'>p

p18/10=

<= span style=3D'visibility:hidden'>p

p586/10= 0

p328/10= 000

<= span style=3D'visibility:hidden'>p

p19/10= 00

<= span style=3D'visibility:hidden'>p

p3/10= 000

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Order

= <= span class=3DBB style=3D'position:absolute;left:-4.43%;top:.3em'>pCompare the first different<= span style=3D'mso-hansi-font-family:"Times New Roman"'> digit

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Examples

p1.6 □ 1.8

<= span style=3D'visibility:hidden'>p

p12.3952 □ 12.3948

<= span style=3D'visibility:hidden'>p

p23.6941 □ 23.695

<= span style=3D'visibility:hidden'>p

p3.65 □ 3.62

<= span style=3D'visibility:hidden'>p

p82.346 □ 82.351

<= span style=3D'visibility:hidden'>p

p14.3875 □ 13.3885

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Rounding Decimals

1)Locate (circle) the digit in the appropriate place =

2)Consider the digit to the right: If 5 or higher, round circled digit up. If 4 or lower, leave circled digi= t unchanged.

3)Delete all digits to right of circled digit

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Examples

<= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>pRound 4.972 to the neare= st hundredth

<= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-4.43%;font-family:Wingdings;font-size:75%'>p<= span style=3D'mso-hansi-font-family:"Times New Roman";display:none'>

<= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>pRound 6.4951 to the near= est tenth

p<= span style=3D'mso-hansi-font-family:"Times New Roman";display:none'>

<= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>pRound 18.345 to the near= est hundredth

= <= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>pRound.000316 to the near= est ten-thousandth

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Solving Equations
Addition and Subtraction

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Solving Equations Examples

px + 23.29 =3D 48.75

<= span style=3D'visibility:hidden'>p

p10.1 + x =3D 100. 01

<= span style=3D'visibility:hidden'>p

p5.823 =3D x – .03962

px – 1.436 =3D 5.2

<= span style=3D'visibility:hidden'>p

p.9999 + x =3D 1

<= span style=3D'visibility:hidden'>p

px + .0123 =3D .09

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Multiplication
Powers of Ten

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Multiplying by .1, .01, .001, etc.

Consider

p 368.54 15.039

p x .001 x .0001

1) Count the decimal places

2) Move the decimal point that many places to the left

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Examples

p.013 · .01

<= span style=3D'visibility:hidden'>p

p2.079 · .00001

p58.12 · .0001

<= span style=3D'visibility:hidden'>p

p.962 · .1

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Multiplying by 10, 100, 1000, etc.

Consider

p 368.54 15.039

p x 10 x 10000

1) Count the number of zeros

2) Move the decimal point that many places to the = right

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Examples

p12.62 · 10000

<= span style=3D'visibility:hidden'>p

p.0037 · 100

p1.0025 · 1000

<= span style=3D'visibility:hidden'>p

p12.461 · 1000000

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Powers of Ten

pLarge numbers are often written as powers of ten (a ten with an exponent)

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Write as a Power of Ten

p100

<= span style=3D'visibility:hidden'>p

p10,000

<= span style=3D'visibility:hidden'>p

p1,000,000

p1000

<= span style=3D'visibility:hidden'>p

p100,000

<= span style=3D'visibility:hidden'>p

p1,000,000,000

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Write as a Number

p105

<= span style=3D'visibility:hidden'>p

p107

p1012

<= span style=3D'visibility:hidden'>p

p104

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Dividing by 10, 100, 1000 etc.

pConsider

p5234 ¸ 100

<= span style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio= n: absolute;left:-8.27%;font-family:Wingdings;font-size:75%'>p<= span style=3D'mso-hansi-font-family:"Times New Roman";display:none'>

1)Count the zeros in the divisor

2)Move the decimal point that many places to the left

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Examples

p18.23 ¸ 1000

<= span style=3D'visibility:hidden'>p

p.0537 ¸ 100,000

p.0537 ¸ 10

<= span style=3D'visibility:hidden'>p

p1900 ¸ 1,000,000

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Dividing by .1, .01, .001, etc.

pConsider

p9.226 ¸ .01

<= span style=3D'visibility:hidden'>p

pCount the decimals in the divisor

<= span class=3DBB style=3D'position:absolute;left:-3.79%;top:.3em'>pMove the decimal point t= hat many places to the right

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Examples

p58.19 ¸ .001

<= span style=3D'visibility:hidden'>p

p7800 ¸ .000001

p.00321 ¸ .01

<= span style=3D'visibility:hidden'>p

p6.0032 ¸ .1

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Solving Equation & Order of Opera= tions with Decimals

pSame as before

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Converting Fractions to Decim= als

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Converting Fractions to Decimals

pDivide the numerator by the denominator

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Examples

p5/8

<= span style=3D'visibility:hidden'>p

p3/2

p3/4

<= span style=3D'visibility:hidden'>p

p7/16

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Examples (cont.)

p3/8

<= span style=3D'visibility:hidden'>p

p3/20

p7/8

<= span style=3D'visibility:hidden'>p

p13/20

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Note

pAll denominators had only 2’s and 5’s as factors

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Repeating Decimals

pWhen the denominator has factors other than 2’s <= /span>and/or 5’s, the de= cimal repeats (never ends)

pWe often use a bar to indicate the repeating pattern

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Examples

p2/3

<= span style=3D'visibility:hidden'>p

p6/11

<= span style=3D'visibility:hidden'>p

p8/11

p5/12

<= span style=3D'visibility:hidden'>p

p3/7

<= span style=3D'visibility:hidden'>p

p4/14

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Ratio

pA comparison of unlike quantities, often represented in fraction form<= /span>

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Examples

pJill was paid $350 for 28 hours of work. The ratio of dollars to hour worked is her wage. Find her wage per hour.<= /div>

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Examples (cont.)

pJim drove his car 552 miles on 26 gallons of gas. The ratio of miles driven to= gas used is gas mileage. Find Jim’s miles per ga= llon.

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Calculations with Fractions and Decim= als

pEither

pConvert all numbers to fractions

pOR

pConvert all numbers to decimals

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Examples

p2/5 x .235= 3;

<= span style=3D'visibility:hidden'>p

p.4 x .235 = OR 2/5 x = 235/1000=

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Examples (cont.)

p1.38 ¸ 3/4

<= span style=3D'visibility:hidden'>p

p1.38 ¸ .75 OR 138/100 ¸ 3/4

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Examples (cont.)

p5.82 x 1/3

pTo get an exact answer with a non-repeating decimal, must keep in fractions&#= 13;

p582/100 x = 1/3

<= span style=3D'visibility:hidden'>p

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Examples (cont.)

p3/8 x 326.8&#= 13;

<= span style=3D'visibility:hidden'>p

p4/9 x 12.6

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Estimating

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Estimating

pUseful as a substitution for an exact answer

pIt can also be helpful to check if your exact answer is= “in the ballpark”

<= span class=3DBB style=3D'position:absolute;left:-3.78%;top:.3em'>pWhen estimating in calculations, you usually want to round each number so it has 1 or 2 non-zero digits =

pThis makes calculations much easier

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Examples

pEstimate 249.2 ¸ 52.132 by rounding each = number to the nearest ten

<= span style=3D'visibility:hidden'>p

pEstimate 13462.5 x 2849.76 by rounding each number to the nearest th= ousand

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Examples (cont.)

pEstimate $129.95 + $189.95 by rounding each number to the nearest ten dollars

<= span style=3D'visibility:hidden'>p

pGeorge gets 19.6 miles per gallon. = His tank holds 15.3 gallons of gas. Approximatel= y how many miles can George travel on one tank of gas?

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MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D46, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0241.htm",1,-1,1),new hrefList(= "slide0001.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("= slide0010.htm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("s= lide0238.htm",1,-1,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("sl= ide0027.htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("sli= de0033.htm",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slid= e0041.htm",1,-1,1),new hrefList("slide0044.htm",1,-1,1),new hrefList("slide= 0063.htm",1,-1,1),new hrefList("slide0069.htm",1,-1,1),new hrefList("slide0= 077.htm",1,-1,1),new hrefList("slide0085.htm",1,-1,1),new hrefList("slide00= 87.htm",1,-1,1),new hrefList("slide0098.htm",1,-1,1),new hrefList("slide009= 7.htm",1,-1,1),new hrefList("slide0101.htm",1,-1,1),new hrefList("slide0102= .htm",1,-1,1),new hrefList("slide0150.htm",1,-1,1),new hrefList("slide0157.= htm",1,-1,1),new hrefList("slide0159.htm",1,-1,1),new hrefList("slide0166.h= tm",1,-1,1),new hrefList("slide0168.htm",1,-1,1),new hrefList("slide0172.ht= m",1,-1,1),new hrefList("slide0174.htm",1,-1,1),new hrefList("slide0176.htm= ",1,-1,1),new hrefList("slide0240.htm",1,-1,1),new hrefList("slide0178.htm"= ,1,-1,1),new hrefList("slide0180.htm",1,-1,1),new hrefList("slide0183.htm",= 1,-1,1),new hrefList("slide0187.htm",1,-1,1),new hrefList("slide0189.htm",1= ,-1,1),new hrefList("slide0191.htm",1,-1,1),new hrefList("slide0193.htm",1,= -1,1),new hrefList("slide0200.htm",1,-1,1),new hrefList("slide0202.htm",1,-= 1,1),new hrefList("slide0203.htm",1,-1,1),new hrefList("slide0206.htm",1,-1= ,1),new hrefList("slide0209.htm",1,-1,1),new hrefList("slide0211.htm",1,-1,= 1),new hrefList("slide0215.htm",1,-1,1),new hrefList("slide0219.htm",1,-1,1= )); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('

' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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1	Decimals
2	Decimal Notation= , Order
3	Definitions<= /font> Decimal Notation: Repr= esents parts of whole numbers with place values to the right of the decimal point Decimal Point: Separat= es whole numbers from parts of whole numbers.
4	Place-Value Char= t
5	Converting from = Decimals to Fractions The decimal portion is the numerator of the fraction The place value of the farthest right digit is the denominator Reduce as necessary
6	Examples .8 15.25 .6252.02 1.005 1.36 .75 2.02 .0001
7	Converting from Fractions to Decimals Move the decimal in the numerator to the left the number of zeros in= the denominator
8	Examples ¹⁶/₁₀₀ ¹⁸/₁₀ ⁵⁸⁶/₁₀₀ ³²⁸/₁₀₀₀₀ ¹⁹/₁₀₀₀ ³/₁₀₀₀₀
9	Order= Compare the first different digit
10	Examples 1.6 □ 1.8 12.3952 □ 12.3948 23.6941 □ 23.695 3.65 □ 3.62 82.346 □ 82.351 14.3875 □ 13.3885
11	Rounding Decima= ls Locate (circle) the digit in the appropriate place Consider the digit to the right:&nb= sp; If 5 or higher, round circled digit up. If 4 or lower, leave circled digit unchanged. Delete all digits to right of circled digit
12	Examples Round 4.972 to the nearest hundredth Round 6.4951 to the nearest tenth Round 18.345 to the nearest hundredth Round.000316 to the nearest ten-thousandth
13	Solving Equatio= ns Addition and Subtraction
14	Solving Equatio= ns Examples x + 23.29 =3D 48.75 10.1 + x =3D 100. 01 5.823 =3D x – .03962 x – 1.436 =3D 5.2 .9999 + x =3D 1 x + .0123 =3D .09
15	Multiplication<= br> Powers of Ten
16	Multiplying by = .1, .01, .001, etc. Consider 368.54 15.039 x .001 x .0001 Count the decimal places Move the decimal point that many places to the left
17	Examples .013 · .01 2.079 · .00001 58.12 · .0001 .962 · .1
18	Multiplying by = 10, 100, 1000, etc. Consider 368.54 15.039 x 10 x 10000 Count the number of zeros Move the decimal point that many places to the right
19	Examples 12.62 · 10000 .0037 · 100 1.0025 · 1000 12.461 · 1000000
20	Powers of Ten Large numbers are often written as powers of ten (a ten with an exponent)
21	Write as a Powe= r of Ten 100 10,000 1,000,000 1000 100,000 1,000,000,000
22	Write as a Numb= er 10⁵ 10⁷ 10¹² 10⁴
23	Dividing by 10,= 100, 1000 etc. Consider 5234 ¸	24	Examples 18.23 ¸ 1000 .0537 ¸ 100,000 .0537 ¸ 10 1900 ¸	25	Dividing by .1,= .01, .001, etc. Consider 9.226 ¸ .01 Count the decimals in the divisor Move the decimal point that many places to the right
26	Examples 58.19 ¸ .001 7800 ¸ .01 6.0032 ¸ .1
27	Solving Equatio= n & Order of Operations with Decimals Same as before
28	Converting Frac= tions to Decimals
29	Converting Frac= tions to Decimals Divide the numerator by the denominator
30	Examples ⁵/₈ ³/₂ ³/₄ ⁷/₁₆
31	Examples (cont.= ) ³/₈ ³/₂₀ ⁷/₈ ¹³/₂₀
32	Note= All denominators had only 2’s and 5’s as factors
33	Repeating Decim= als When the denominator has factors other than 2’s and/or 5’= ;s, the decimal repeats (never ends) We often use a bar to indicate the repeating pattern
34	Examples ²/₃ ⁶/₁₁ ⁸/₁₁ ⁵/₁₂ ³/₇ ⁴/₁₄
35	Ratio A comparison of unlike quantities, often represented in fraction for= m
36	Examples Jill was paid $350 for 28 hours of work. The ratio of dollars to hour worked is her wage. Fi= nd her wage per hour.
37	Examples (cont.= ) Jim drove his car 552 miles on 26 gallons of gas. The ratio of miles driven t= o gas used is gas mileage. F= ind Jim’s miles per gallon.
38	Calculations wi= th Fractions and Decimals Either Convert all numbers to fractions OR Convert all numbers to decimals
39	Examples ²/₅ x .235 .4 x .235 OR ²/₅ x ²³⁵/₁₀₀₀
40	Examples (cont.= ) 1.38 ¸ ³/₄
41	Examples (cont.= ) 5.82 x ¹/₃ To get an exact answer with a non-repeating decimal, must keep in fractions ⁵⁸²/₁₀₀ x ¹/₃
42	Examples (cont.= ) ³/₈ x 326.8 ⁴/₉ x 12.6
43	Estimating<= /font>
44	Estimating<= /font> Useful as a substitution for an exact answer It can also be helpful to check if your exact answer is “in the ballpark” When estimating in calculations, you usually want to round each numb= er so it has 1 or 2 non-zero digits This makes calculations much easier
45	Examples Estimate 249.2 ¸ 52.132 by rounding each number to the near= est ten Estimate 13462.5 x 2849.76 by rounding each number to the nearest thousand
46	Examples (cont.= ) Estimate $129.95 + $189.95 by rounding each number to the nearest ten dollars George gets 19.6 miles per gallon.&= nbsp; His tank holds 15.3 gallons of gas. Approximately how many mile= s can George travel on one tank of gas?

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