Fractions and Decimals
2014-05-01 17:09
This example visually demonstrates the conversion between fractions and decimals using geometric shapes. By utilizing polygon partitioning and sequence commands, it transforms abstract numerical concepts into visual models, helping learners understand their essence and mutual conversion. It is suitable for math classes.
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.47.0" id="858e167e-7537-4bf4-8659-ea981e141f27" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="928" height="710" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.8631465517241379" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 59 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3" size="901" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="216" window="120,102,274,772" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="395" window="153,217,974,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 59 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="901" height="527"/>
<coordSystem xZero="75.88359215718788" yZero="361.1611214538974" scale="201.36162055486795" yscale="201.36162055486906"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.1" distY="0.1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<command name="Corner">
<input a0="5"/>
<output a0="A_1"/>
</command>
<element type="point" label="A_1">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="901.0" y="527.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Sequence[(k, 0), k, 0, 3.6, 0.1]"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1.6000000000000005" y="0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Sequence[(x(A) + 0.1, j), j, 0, 1, 0.1]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false"/>
<condition showObject="(x(A) ≥ 0) ∧ (x(A) < 1) ∨ (x(A) ≥ x(Vertex[poly3, 1])) ∧ (x(A) < x(Vertex[poly3, 1]) + 1) ∨ (x(A) ≥ x(Vertex[poly4, 1])) ∧ (x(A) < x(Vertex[poly4, 1]) + 1)"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-3" y="-4"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.7000000000000006" y="0.5" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="1"/>
</element>
<command name="Polygon">
<input a0="(1.3, 0)" a1="(2.3, 0)" a2="(2.3, 1)" a3="(1.3, 1)"/>
<output a0="poly3" a1="i" a2="j" a3="k" a4="l"/>
</command>
<element type="polygon" label="poly3">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="0.9999999999999998" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-1.0" y="0.0" z="2.3"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="-0.9999999999999998" z="0.9999999999999998"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="1.0" y="0.0" z="-1.3"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="(2.6, 0)" a1="(3.6, 0)" a2="(3.6, 1)" a3="(2.6, 1)"/>
<output a0="poly4" a1="m" a2="n" a3="p" a4="q"/>
</command>
<element type="polygon" label="poly4">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="segment" label="m">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="1.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="n">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-1.0" y="0.0" z="3.6"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="p">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="-1.0" z="1.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="q">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="1.0" y="0.0" z="-2.6"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="If">
<input a0="(x(A) ≥ 1) ∧ (x(A) < x(Vertex[poly3, 1])) ∨ (x(A) ≥ x(Vertex[poly3, 2])) ∧ (x(A) < x(Vertex[poly4, 1])) ∨ x(A) ≟ x(Vertex[poly4, 2])" a1="true" a2="false"/>
<output a0="integer"/>
</command>
<element type="boolean" label="integer">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="A + (0.1, 0)" a2="A + (0.1, If[integer, 0, y(B)])" a3="A + (0, If[integer, 0, y(B)])"/>
<output a0="poly8" a1="j_1" a2="k_1" a3="l_1" a4="m_1"/>
</command>
<element type="polygon" label="poly8">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="(x(A) ≥ 0) ∧ (x(A) < 1) ∨ (x(A) ≥ x(Vertex[poly3, 1])) ∧ (x(A) < x(Vertex[poly3, 1]) + 1) ∨ (x(A) ≥ x(Vertex[poly4, 1])) ∧ (x(A) < x(Vertex[poly4, 1]) + 1)"/>
<objColor r="255" g="0" b="0" alpha="0.2"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="j_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.10000000000000009" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.5" y="0.0" z="0.8500000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-0.10000000000000009" z="0.050000000000000044"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="m_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.5" y="0.0" z="-0.8000000000000003"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="(0, 0)" a1="(Min[x(A), 1], 0)" a2="(Min[x(A), 1], 1)" a3="(0, 1)"/>
<output a0="poly5" a1="r" a2="s" a3="t" a4="a_1"/>
</command>
<element type="polygon" label="poly5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.2"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="segment" label="r">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="1.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="s">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="0.0" z="1.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="t">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-1.0" z="1.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a_1">
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="(x(Vertex[poly3, 1]), 0)" a1="(Max[Min[x(A), x(Vertex[poly3, 1]) + 1], x(Vertex[poly3, 1])], 0)" a2="(Max[Min[x(A), x(Vertex[poly3, 1]) + 1], x(Vertex[poly3, 1])], 1)" a3="(x(Vertex[poly3, 1]), 1)"/>
<output a0="poly6" a1="b_1" a2="c_1" a3="d_1" a4="e_1"/>
</command>
<element type="polygon" label="poly6">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="x(A) > x(Vertex[poly3, 1])"/>
<objColor r="255" g="0" b="0" alpha="0.2"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="b_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.3000000000000005" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="0.0" z="1.6000000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-0.3000000000000005" z="0.3000000000000005"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="0.0" z="-1.3"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="(x(Vertex[poly4, 1]), 0)" a1="(Max[Min[x(A), x(Vertex[poly4, 1]) + 1], x(Vertex[poly4, 1])], 0)" a2="(Max[Min[x(A), x(Vertex[poly4, 1]) + 1], x(Vertex[poly4, 1])], 1)" a3="(x(Vertex[poly4, 1]), 1)"/>
<output a0="poly7" a1="f_1" a2="g_1" a3="h_1" a4="i_1"/>
</command>
<element type="polygon" label="poly7">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="x(A) > x(Vertex[poly4, 1])"/>
<objColor r="255" g="0" b="0" alpha="0.2"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="0.0" z="2.6"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i_1">
<show object="false" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="0.0" z="-2.6"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="(0.8187524918794742, 1.1041021645196354)" a1="(1.818752491879475, 1.1041021645196354)" a2="(1.818752491879475, 2.1041021645196336)" a3="(0.8187524918794742, 2.1041021645196336)"/>
<output a0="poly1" a1="a" a2="b" a3="c" a4="d"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="4" type="0" typeHidden="1"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.05"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="1.0000000000000009" z="-1.1041021645196363"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.9999999999999982" y="0.0" z="1.8187524918794717"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-1.0000000000000009" z="2.1041021645196354"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.9999999999999982" y="0.0" z="-0.8187524918794727"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""= 1""/>
<element type="text" label="text1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="4.0" size="54" style="0"/>
<startPoint x="1.1188572644582426" y="1.7218141104602513" z="1.0"/>
</element>
<command name="Polygon">
<input a0="(0, 0)" a1="(1, 0)" a2="(1, 1)" a3="(0, 1)"/>
<output a0="poly2" a1="e" a2="f" a3="g" a4="h"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="5" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="1.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-1.0" y="0.0" z="1.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="-1.0" z="1.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="1.0" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text2" exp=""→""/>
<element type="text" label="text2">
<show object="true" label="false"/>
<condition showObject="x(A) < 3.6"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="8" style="1"/>
<startPoint exp="A"/>
<labelOffset x="4" y="20"/>
</element>
<expression label="text3" exp=""↑""/>
<element type="text" label="text3">
<show object="true" label="false"/>
<condition showObject="y(B) ≟ 0 ∧ ((x(A) ≥ 0) ∧ (x(A) < 1) ∨ (x(A) ≥ x(Vertex[poly3, 1])) ∧ (x(A) < x(Vertex[poly3, 1]) + 1) ∨ (x(A) ≥ x(Vertex[poly4, 1])) ∧ (x(A) < x(Vertex[poly4, 1]) + 1))"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<startPoint exp="B"/>
<labelOffset x="-6" y="-11"/>
</element>
<command name="Sequence">
<input a0="Segment[(0, j), (1, j)]" a1="j" a2="0" a3="1" a4="0.1"/>
<output a0="list4"/>
</command>
<element type="list" label="list4">
<show object="true" label="false"/>
<condition showObject="(y(B) > 0) ∧ (y(B) < 1) ∧ (x(A) ≥ 0) ∧ (x(A) < 1) ∨ v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(x(Vertex[poly3, 1]), j), (x(Vertex[poly3, 1]) + 1, j)]" a1="j" a2="0" a3="1" a4="0.1"/>
<output a0="list5"/>
</command>
<element type="list" label="list5">
<show object="true" label="false"/>
<condition showObject="(y(B) > 0) ∧ (y(B) < 1) ∧ (x(A) ≥ x(Vertex[poly3, 1])) ∧ (x(A) < x(Vertex[poly3, 1]) + 1) ∨ v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(x(Vertex[poly4, 1]), j), (x(Vertex[poly4, 1]) + 1, j)]" a1="j" a2="0" a3="1" a4="0.1"/>
<output a0="list6"/>
</command>
<element type="list" label="list6">
<show object="true" label="false"/>
<condition showObject="(y(B) > 0) ∧ (y(B) < 1) ∧ (x(A) ≥ x(Vertex[poly4, 1])) ∧ (x(A) < x(Vertex[poly4, 1]) + 1) ∨ v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(i, 0), (i, 1)]" a1="i" a2="0" a3="1" a4="0.1"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="false"/>
<condition showObject="(number > 0) ∧ (number < 1) ∨ v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(x(Vertex[poly3, 1]) + i, 0), (x(Vertex[poly3, 1]) + i, 1)]" a1="i" a2="0" a3="1" a4="0.1"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="false"/>
<condition showObject="(number > 1) ∧ (number < 2) ∨ v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[(x(Vertex[poly4, 1]) + i, 0), (x(Vertex[poly4, 1]) + i, 1)]" a1="i" a2="0" a3="1" a4="0.1"/>
<output a0="list3"/>
</command>
<element type="list" label="list3">
<show object="true" label="false"/>
<condition showObject="(number > 2) ∧ (number < 3) ∨ v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<expression label="text4" exp=""下圖每個大方格代表 1, 著色部分代表多少?""/>
<element type="text" label="text4">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="55" y="51"/>
</element>
<expression label="number" exp="poly5 + poly6 + poly7 + poly8" />
<element type="numeric" label="number">
<value val="1.3500000000000005"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="y(B) < 1" a1="100 * poly8" a2="0"/>
<output a0="hundredthdigit"/>
</command>
<element type="numeric" label="hundredthdigit">
<value val="5.000000000000004"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="unitdigit" exp="floor(number)" />
<element type="numeric" label="unitdigit">
<value val="1.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="tenthdigit" exp="floor(10 * (number - unitdigit))" />
<element type="numeric" label="tenthdigit">
<value val="3.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text5" exp=""" + (LaTeX[unitdigit]) + "\frac{" + (LaTeX[10 * tenthdigit + hundredthdigit]) + "}{100}"" />
<element type="text" label="text5">
<show object="true" label="false"/>
<condition showObject="(unitdigit > 0) ∧ (hundredthdigit > 0) ∧ o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="265" y="385"/>
</element>
<expression label="text6" exp=""\frac{" + (LaTeX[10 * tenthdigit + hundredthdigit]) + "}{100}"" />
<element type="text" label="text6">
<show object="true" label="false"/>
<condition showObject="unitdigit ≟ 0 ∧ (hundredthdigit > 0) ∧ o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="265" y="385"/>
</element>
<expression label="text7" exp=""" + (LaTeX[unitdigit]) + "\frac{" + (LaTeX[tenthdigit]) + "}{10}"" />
<element type="text" label="text7">
<show object="true" label="false"/>
<condition showObject="(unitdigit > 0) ∧ (tenthdigit > 0) ∧ hundredthdigit ≟ 0 ∧ o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="265" y="385"/>
</element>
<expression label="text8" exp=""\frac{" + (LaTeX[tenthdigit]) + "}{10}"" />
<element type="text" label="text8">
<show object="true" label="false"/>
<condition showObject="unitdigit ≟ 0 ∧ (tenthdigit > 0) ∧ hundredthdigit ≟ 0 ∧ o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="265" y="385"/>
</element>
<expression label="text9" exp=""" + number + """ />
<element type="text" label="text9">
<show object="true" label="false"/>
<condition showObject="u"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="610" y="444"/>
</element>
<element type="boolean" label="o">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="117" y="415"/>
<labelMode val="0"/>
<caption val="分數"/>
</element>
<element type="boolean" label="u">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="468" y="415"/>
<labelMode val="0"/>
<ggbscript onUpdate="w=false"/>
<caption val="小數"/>
</element>
<expression label="text10" exp=""" + unitdigit + """ />
<element type="text" label="text10">
<show object="true" label="false"/>
<condition showObject="tenthdigit ≟ 0 ∧ hundredthdigit ≟ 0 ∧ o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="270" y="498"/>
</element>
<element type="boolean" label="v">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="724" y="26"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="顯示100格"/>
</element>
<expression label ="list7" exp="{"一", "二", "三", "四", "五", "六", "七", "八", "九", "零"}"/>
<element type="list" label="list7">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="boolean" label="w">
<value val="false"/>
<show object="true" label="true"/>
<condition showObject="u"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="467" y="485"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="讀法"/>
</element>
<command name="Text">
<input a0="If[unitdigit ≟ 0, "零", Element[list7, unitdigit]] * If[number - unitdigit ≟ 0, "", "點" * If[tenthdigit ≟ 0, "零", Element[list7, tenthdigit]] * If[hundredthdigit ≟ 0, "", Element[list7, hundredthdigit]]]"/>
<output a0="text11"/>
</command>
<element type="text" label="text11">
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="2.0" size="18" style="0"/>
<absoluteScreenLocation x="610" y="513"/>
</element>
</construction>
</geogebra>