and are ways to show parts of a whole.
To write a percent as a decimal, we ignore the percent symbol and move the decimal point two places to the left. Let's do it!
We found that 221 % expressed as a decimal is 2.21.
Representing the Decimal Using a Model
Now we want to represent 2.21 with a model. Begin by constructing a 10 * 10 grid — a total of 100 smaller squares. In this grid one square will correspond to 1 % or 0.01. Then the whole square represents 100 %.
Since 221 % is 221 parts out of 100 parts, we will color 221 small squares.
<jsxgpre id="Solution_269081_3" alt="Model" static=0>
var b = mlg.board([-2.5, 11.5, 38.5,-10], {desktopSize:'medium', style:'usa'});
var bb = b.board.getBoundingBox();
var buttons = [];
var labs = ['Reset', 'Color the Squares'];
var n1 = b.node(0,0);
var n2 = b.node(0,10);
var n3 = b.node(10,10);
var n4 = b.node(10,0);
var n5 = b.node(13,0);
var n6 = b.node(13,10);
var n7 = b.node(23,10);
var n8 = b.node(23,0);
var n9 = b.node(13+13,0);
var n10 = b.node(13+13,10);
var n11 = b.node(23+13,10);
var n12 = b.node(23+13,0);
var pol1 = b.polygon([n1,n2,n3,n4],{borders:{strokeColor:'darkviolet',opacity:0.3}});
var pol2 = b.polygon([n5,n6,n7,n8],{borders:{strokeColor:'darkviolet',opacity:0.3},color:'darkorange',opacity:0.5});
var pol3 = b.polygon([n9,n10,n11,n12],{borders:{strokeColor:'darkviolet',opacity:0.3},color:'darkorange',opacity:0.5});
var L = 11;
/*Grid 1*/
var sp1 = b.segmentPoints(pol1.borders[0],L,{visible:false});
var sp2 = b.segmentPoints(pol1.borders[1],L,{visible:false});
var sp3 = b.segmentPoints(pol1.borders[2],L,{visible:false});
var sp4 = b.segmentPoints(pol1.borders[3],L,{visible:false});
for(var i=1;i<sp1.length-1;i++){
b.segment(sp1[i],sp3[L-1-i],{strokeWidth:1,strokeColor:'blue',opacity:0.3});
b.segment(sp2[i],sp4[L-1-i],{strokeWidth:1,strokeColor:'blue',opacity:0.3});
}
/*Grid 2*/
var sp11 = b.segmentPoints(pol2.borders[0],L,{visible:false});
var sp21 = b.segmentPoints(pol2.borders[1],L,{visible:false});
var sp31 = b.segmentPoints(pol2.borders[2],L,{visible:false});
var sp41 = b.segmentPoints(pol2.borders[3],L,{visible:false});
for(var i=1;i<sp1.length-1;i++){
b.segment(sp11[i],sp31[L-1-i],{strokeWidth:1,strokeColor:'blue',opacity:0.3});
b.segment(sp21[i],sp41[L-1-i],{strokeWidth:1,strokeColor:'blue',opacity:0.3});
}
/*Grid 3*/
var sp111 = b.segmentPoints(pol3.borders[0],L,{visible:false});
var sp211 = b.segmentPoints(pol3.borders[1],L,{visible:false});
var sp311 = b.segmentPoints(pol3.borders[2],L,{visible:false});
var sp411 = b.segmentPoints(pol3.borders[3],L,{visible:false});
for(var i=1;i<sp1.length-1;i++){
b.segment(sp111[i],sp311[L-1-i],{strokeWidth:1,strokeColor:'blue',opacity:0.3});
b.segment(sp211[i],sp411[L-1-i],{strokeWidth:1,strokeColor:'blue',opacity:0.3});
}
var Rec = [];
for(var j=1;j<3;j++){
for(var i=0;i<L-1;i++){
Rec.push(b.rectangle(b.node(sp2[j-1].X(),sp1[i].Y()),b.node(sp2[j].X(),sp1[i+1].Y()),{fillColor:"darkorange",fillOpacity:0.5,borders:{visible:false},visible:false}));
}}
Rec.push(b.rectangle(b.node(sp2[2].X(),sp1[0].Y()),b.node(sp2[3].X(),sp1[1].Y()),{fillColor:"darkorange",fillOpacity:0.5,borders:{visible:false},visible:false}));
/*animation*/
var per1 = b.segmentText(pol1.borders[3],{name:'0\\%',color:"darkorange",distance:1.5});
var per2 = b.segmentText(pol2.borders[3],{name:'100\\%',color:"darkorange",distance:1.5});
var per3 = b.segmentText(pol3.borders[3],{name:'100\\%',color:"darkorange",distance:1.5});
var f1 = b.polarnode(n1,-90,2);
var f2 = b.polarnode(n12,-90,2);
var Per = b.curlyBrace(f2,f1,{strokeWidth:1,label:{text:"200\\%\\text{ or } 2.00",distance:0,color:"darkorange"}});
var count=0;
var F1 = function(){
var interval = setInterval(function(){
b.setAttribute(Rec[count],{visible:true,transitionDuration:250});
count++;
if(count > Rec.length){
clearInterval(interval);
buttons[0].enable();
buttons[0].setLabel(labs[0]);
buttons[0].setDimension(60,30);
}else{
b.changeText(per1.text,count+"\\%");
b.changeText(Per.label,(200+count)+"\\% \\text{ or }"+b.round((200+count)/100,2));
}
},250);
};
var F2 = function(){
b.setAttribute(Rec,{visible:false});
count=0;
b.changeText(per1.text,count+"\\%");
b.changeText(Per.label,(200+count)+"\\% \\text{ or }"+b.round((200+count)/100,2));
buttons[0].enable();
buttons[0].setLabel(labs[1]);
buttons[0].setDimension(125,30);
};
var kk = 0;
var button = function(){
buttons[0].disable();
if(kk%2==0){F1();}
else{F2();}
kk++;
};
buttons.push(b.button(0.5*(bb[0]+bb[2]),bb[3]+0.5, labs[1], button, {mathMode: false,width:125,anchor:"s"}));
</jsxgpre>
