and are ways to show parts of a whole. To write 4.3 as a percent, we multiply by 100 and add the percent symbol %. When doing so, keep in mind that, according to the bar notation, 4.3 is the same as 4.333333.... Let's go!
We found that 4.3 expressed as a percent is 433.3333... % or 433.3 %.
Representing the Decimal Using a Model
Now we want to represent 433.3 % 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 %.
Notice that 433.3 % is 433 and 0.3 parts out of 100 parts. Since 0.3 is equivalent to 13, we will color 433 and a third of a small square.
<jsxgpre id="Solution_269083_3" alt="Model" static=0>
var b = mlg.board([-2.5, 26.5, 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 + 6.5);
var n2 = b.node(0, 10 + 6.5);
var n3 = b.node(10, 10 + 6.5);
var n4 = b.node(10, 0 + 6.5);
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 n13 = b.node(13, 0 + 13);
var n14 = b.node(13, 10 + 13);
var n15 = b.node(23, 10 + 13);
var n16 = b.node(23, 0 + 13);
var n17 = b.node(13 + 13, 0 + 13);
var n18 = b.node(13 + 13, 10 + 13);
var n19 = b.node(23 + 13, 10 + 13);
var n20 = b.node(23 + 13, 0 + 13);
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 pol4 = b.polygon([n13, n14, n15, n16], {
borders: { strokeColor: "darkviolet", opacity: 0.3 },
color: "darkorange",
opacity: 0.5
});
var pol5 = b.polygon([n17, n18, n19, n20], {
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
});
}
/*Grid 4*/
var sp1111 = b.segmentPoints(pol4.borders[0], L, { visible: false });
var sp2111 = b.segmentPoints(pol4.borders[1], L, { visible: false });
var sp3111 = b.segmentPoints(pol4.borders[2], L, { visible: false });
var sp4111 = b.segmentPoints(pol4.borders[3], L, { visible: false });
for (var i = 1; i < sp1.length - 1; i++) {
b.segment(sp1111[i], sp3111[L - 1 - i], {
strokeWidth: 1,
strokeColor: "blue",
opacity: 0.3
});
b.segment(sp2111[i], sp4111[L - 1 - i], {
strokeWidth: 1,
strokeColor: "blue",
opacity: 0.3
});
}
/*Grid 5*/
var sp11111 = b.segmentPoints(pol5.borders[0], L, { visible: false });
var sp21111 = b.segmentPoints(pol5.borders[1], L, { visible: false });
var sp31111 = b.segmentPoints(pol5.borders[2], L, { visible: false });
var sp41111 = b.segmentPoints(pol5.borders[3], L, { visible: false });
for (var i = 1; i < sp1.length - 1; i++) {
b.segment(sp11111[i], sp31111[L - 1 - i], {
strokeWidth: 1,
strokeColor: "blue",
opacity: 0.3
});
b.segment(sp21111[i], sp41111[L - 1 - i], {
strokeWidth: 1,
strokeColor: "blue",
opacity: 0.3
});
}
var Rec = [];
for (var j = 1; j < 4; 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[3].X(), sp1[0].Y()), b.node(sp2[4].X(), sp1[1].Y()), {
fillColor: "darkorange",
fillOpacity: 0.5,
borders:{visible:false},
visible: false
})
);
Rec.push(
b.rectangle(b.node(sp2[3].X(), sp1[1].Y()), b.node(sp2[4].X(), sp1[2].Y()), {
fillColor: "darkorange",
fillOpacity: 0.5,
borders:{visible:false},
visible: false
})
);
Rec.push(
b.rectangle(b.node(sp2[3].X(), sp1[2].Y()), b.node(sp2[4].X(), sp1[3].Y()), {
fillColor: "darkorange",
fillOpacity: 0.5,
borders:{visible:false},
visible: false
})
);
Rec.push(
b.rectangle(
b.node(sp2[3].X(), sp1[3].Y()),
b.node(sp2[4].X(), sp1[3].Y() + 1 / 3),
{
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 per4 = b.segmentText(pol4.borders[1], {
name: "100\\%",
color: "darkorange",
distance: 1.5
});
var per5 = b.segmentText(pol5.borders[1], {
name: "100\\%",
color: "darkorange",
distance: 1.5
});
var f1 = b.polarnode(n1, -90, 2 + 6.5);
var f2 = b.polarnode(n12, -90, 2);
var Per = b.curlyBrace(f2, f1, {
strokeWidth: 1,
label: { text: "400\\%\\text{ or } 4.00", 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);
b.changeText(per1.text, "33.\\bar{3}\\%");
b.changeText(Per.label,"433.\\bar{3}\\% \\text{ or }4.\\bar{3}");
} else {
if(count<=33){
b.changeText(per1.text, count + "\\%");
b.changeText(Per.label,400 + count + "\\% \\text{ or }" + b.round((400 + count) / 100, 2));
}
}
}, 250);
};
var F2 = function () {
b.setAttribute(Rec, { visible: false });
count = 0;
b.changeText(per1.text, count + "\\%");
b.changeText(
Per.label,
400 + 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,
