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<!DOCTYPE html>
<html data-require="math graphie word-problems jquery.mobile.vmouse">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Understanding decimals place value</title>
<script src="../khan-exercise.js"></script>
<style>
.column { float: left; height: 430px;
text-align: center;
-webkit-user-select: none;
-khtml-user-select: none;
-moz-user-select: none;
-o-user-select: none;
user-select: none;
}
.columnhead {
font-size: 12px;
font-weight: bold;
}
.coin-column { position: relative; margin: 0px; float: left; left: 1px; z-index: 1; }
.place-value {
width: 67px; margin: 8px; line-height: 30px;
background-color: #eee; border-width: 1px; border-style: solid; border-color: #ddd; color: #ddd;
font-weight: bold; text-align: center; font-size: 20px;
cursor: pointer;
}
.bill {
width: 70px; margin: 10px; line-height: 30px;
background-color: #eee; border-width: 1px; border-style: solid; border-color: #ddd; color: #ddd;
font-weight: bold; text-align: center; font-size: 20px;
cursor: pointer;
}
.bill:hover, .place-value:hover { border-color: #999; }
.coin { width: 51px; margin: 10px; line-height: 32px; color: #ddd; font-size: 20px; font-weight: bold; text-align: center; cursor: pointer; }
.thou-selected { background-color: #ff00af; border-color: #000; color: #fff; }
.hund-selected { background-color: #ffa500; border-color: #000; color: #fff; }
.ten-selected { background-color: #28ae7b; border-color: #000; color: #fff; }
.one-selected { background-color: #6495ed; border-color: #000; color: #fff; }
.tenth-selected { background-color: purple; border-color: #000; color: #fff; }
.hundth-selected { background-color: gray; border-color: #000; color: #fff; }
.thouth-selected { background-color: #a52a2a; border-color: #000; color: #fff; }
.dime { font-size: 17px; }
.dime-selected { color: #fff; }
.penny-selected { color: #fff; }
</style>
</head>
<body>
<div class="exercise">
<div class="vars">
<div data-ensure="!( THOUSANDS === 0 && HUNDREDS === 0 )">
<var id="THOUSANDS">randFromArray([ 0, randRange( 1, 9 ) ])</var>
<var id="HUNDREDS">randRange( 0, 9 )</var>
</div>
<var id="TENS">randRange( 0, 9 )</var>
<var id="ONES">randRange( 0, 9 )</var>
<var id="TENTHS">randRange( 0, 9 )</var>
</div>
<div class="problems">
<div id="place-value">
<div class="vars">
<var id="HUNDREDTHS">randRange( 0, 9 )</var>
<var id="THOUSANDTHS">randRange( 1, 9 )</var>
</div>
<p class="question">
Choose the right number of each place value to make<br />
<code>\Huge{
<span data-if="THOUSANDS !== 0">\color{<var>PINK</var>}{<var>THOUSANDS</var>}</span>
\color{<var>ORANGE</var>}{<var>HUNDREDS</var>}
\color{<var>GREEN</var>}{<var>TENS</var>}
\color{<var>BLUE</var>}{<var>ONES</var>}.
\color{purple}{<var>TENTHS</var>}
\color{gray}{<var>HUNDREDTHS</var>}
\color{#a52a2a}{<var>THOUSANDTHS</var>}
}</code>
</p>
<div class="problem">
<!--
If this didn't exist you would get the following error:
Uncaught TypeError: Cannot read property 'graph' of undefined
Because:
- Both problems use the same .hints.
- .hints uses .graphie.
- The other problem uses graphie so .hints's .graphies must use data-update.
-->
<div class="graphie" id="graph" style="display: none;"></div>
<div class="column">
<span class="columnhead">Thousands</span>
<div data-each="10 times" class="place-value thou">1000</div>
</div>
<div class="column">
<span class="columnhead">Hundreds</span>
<div data-each="10 times" class="place-value hund">100</div>
</div>
<div class="column">
<span class="columnhead">Tens</span>
<div data-each="10 times" class="place-value ten">10</div>
</div>
<div class="column">
<span class="columnhead">Ones</span>
<div data-each="10 times" class="place-value one">1</div>
</div>
<div class="column">
<span class="columnhead">Tenths</span>
<div data-each="10 times" class="place-value tenth">0.1</div>
</div>
<div class="column">
<span class="columnhead">Hundredths</span>
<div data-each="10 times" class="place-value hundth">0.01</div>
</div>
<div class="column">
<span class="columnhead">Thousandths</span>
<div data-each="10 times" class="place-value thouth">0.001</div>
</div>
<var>
(function() {
Khan.scratchpad.disable();
// click handlers
$( "#problemarea .thou" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'thou-selected' );
});
$( "#problemarea .hund" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'hund-selected' );
});
$( "#problemarea .ten" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'ten-selected' );
});
$( "#problemarea .one" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'one-selected' );
});
$( "#problemarea .tenth" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'tenth-selected' );
});
$( "#problemarea .hundth" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'hundth-selected' );
});
$( "#problemarea .thouth" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'thouth-selected' );
});
})()
</var>
<p style="clear: left">&nbsp;</p>
</div>
<div class="solution" data-type="custom">
<div class="instruction">
Click on the numbers in rectangles to select them.
</div>
<div class="guess">digitsToInteger([
$( "#problemarea .thou-selected" ).length,
$( "#problemarea .hund-selected" ).length,
$( "#problemarea .ten-selected" ).length,
$( "#problemarea .one-selected" ).length,
$( "#problemarea .tenth-selected" ).length,
$( "#problemarea .hundth-selected" ).length,
$( "#problemarea .thouth-selected" ).length
]) / 1000
</div>
<div class="validator-function">
if ( guess === 0 ) {
return "";
} else {
return guess === ( digitsToInteger([ THOUSANDS, HUNDREDS, TENS, ONES, TENTHS, HUNDREDTHS, THOUSANDTHS ]) / 1000 );
}
</div>
<div class="show-guess">
var places = digits( guess * 1000 );
// unselect everything
$( "#problemarea .place-value" ).removeClass( 'thou-selected hund-selected ten-selected one-selected tenth-selected, hundth-selected, thouth-selected' );
// select the approprate number of each thing
$( "#problemarea .thou" ).slice( 0, places[6] || 0 ).addClass( 'thou-selected' );
$( "#problemarea .hund" ).slice( 0, places[5] || 0 ).addClass( 'hund-selected' );
$( "#problemarea .ten" ).slice( 0, places[4] || 0 ).addClass( 'ten-selected' );
$( "#problemarea .one" ).slice( 0, places[3] || 0 ).addClass( 'one-selected' );
$( "#problemarea .tenth" ).slice( 0, places[2] || 0 ).addClass( 'tenth-selected' );
$( "#problemarea .hundth" ).slice( 0, places[1] || 0 ).addClass( 'hundth-selected' );
$( "#problemarea .thouth" ).slice( 0, places[0] || 0 ).addClass( 'thouth-selected' );
</div>
<div class="example">click a number to select it</div>
<div class="example">click a number again to deselect it</div>
</div>
</div>
<div id="money">
<div class="vars">
<var id="HUNDREDTHS">randRange( 1, 9 )</var>
<var id="THOUSANDTHS">0</var>
</div>
<p class="question">
Choose the right number of bills and coins to make<br />
<code>\Huge{$
<span data-if="THOUSANDS !== 0">\color{<var>PINK</var>}{<var>THOUSANDS</var>}</span>
\color{<var>ORANGE</var>}{<var>HUNDREDS</var>}
\color{<var>GREEN</var>}{<var>TENS</var>}
\color{<var>BLUE</var>}{<var>ONES</var>}.
\color{purple}{<var>TENTHS</var>}
\color{gray}{<var>HUNDREDTHS</var>}
}</code>
</p>
<div class="problem">
<div class="column">
<span class="columnhead">Thousands</span>
<div data-each="10 times" class="bill thou">$1000</div>
</div>
<div class="column">
<span class="columnhead">Hundreds</span>
<div data-each="10 times" class="bill hund">$100</div>
</div>
<div class="column">
<span class="columnhead">Tens</span>
<div data-each="10 times" class="bill ten">$10</div>
</div>
<div class="column">
<span class="columnhead">Ones</span>
<div data-each="10 times" class="bill one">$1</div>
</div>
<div class="column">
<div class="coin-column">
<span class="columnhead">Tenths</span>
<div data-each="10 times" class="coin dime">10&cent;</div>
</div>
<div class="coin-column">
<span class="columnhead">Hundredths</span>
<div data-each="10 times" class="coin penny">1&cent;</div>
</div>
<div class="graphie" id="graph">
Khan.scratchpad.disable();
init({ range: [ [ 0, 143 ], [ -430, 22 ] ], scale: [ 1, 1 ] });
style({ fill: "#eee", stroke: "#ddd", strokeWidth: 1 });
graph.tenths = [];
graph.hundredths = [];
for ( var i = 0; i &lt; 10; ++i ) {
graph.tenths.push( circle( [ 37, (-42 * i) - 26 ], 18 ) );
graph.hundredths.push( circle( [ 107, (-42 * i) - 26 ], 18 ) );
}
graph.getCoinCircle = function( coinEl ) {
var coins,
coin = $( coinEl );
if ( coin.hasClass( 'dime' ) ) {
coins = KhanUtil.currentGraph.graph.tenths;
} else {
coins = KhanUtil.currentGraph.graph.hundredths;
}
return coins[ coin.index() - 1 ];
}
// click handlers
$( "#problemarea .thou" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'thou-selected' );
});
$( "#problemarea .hund" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'hund-selected' );
});
$( "#problemarea .ten" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'ten-selected' );
});
$( "#problemarea .one" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'one-selected' );
});
$( "#problemarea .dime" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'dime-selected' );
if ( $( this ).hasClass( 'dime-selected' ) ) {
graph.getCoinCircle( this ).attr({ fill: 'purple', stroke: '#000' });
} else {
graph.getCoinCircle( this ).attr({ fill: '#eee', stroke: '#ddd' });
}
});
$( "#problemarea .penny" ).bind( "vmousedown", function( event ) {
event.preventDefault();
$( this ).toggleClass( 'penny-selected' );
if ( $( this ).hasClass( 'penny-selected' ) ) {
graph.getCoinCircle( this ).attr({ fill: 'gray', stroke: '#000' });
} else {
graph.getCoinCircle( this ).attr({ fill: '#eee', stroke: '#ddd' });
}
});
// mouseover handlers
$( "#problemarea .dime" ).bind( "vmouseover", function( event ) {
graph.getCoinCircle( this ).attr({ stroke: '#999' });
});
$( "#problemarea .penny" ).bind( "vmouseover", function( event ) {
graph.getCoinCircle( this ).attr({ stroke: '#999' });
});
// mouseout handlers
$( "#problemarea .dime" ).bind( "vmouseout", function( event ) {
if ( $( this ).hasClass( 'dime-selected' ) ) {
graph.getCoinCircle( this ).attr({ stroke: '#000' });
} else {
graph.getCoinCircle( this ).attr({ stroke: '#ddd' });
}
});
$( "#problemarea .penny" ).bind( "vmouseout", function( event ) {
if ( $( this ).hasClass( 'penny-selected' ) ) {
graph.getCoinCircle( this ).attr({ stroke: '#000' });
} else {
graph.getCoinCircle( this ).attr({ stroke: '#ddd' });
}
});
</div>
</div>
<p style="clear: left">&nbsp;</p>
</div>
<div class="solution" data-type="custom">
<div class="instruction">
Click on the bills and coins to select them.
</div>
<div class="guess">digitsToInteger([
$( "#problemarea .thou-selected" ).length,
$( "#problemarea .hund-selected" ).length,
$( "#problemarea .ten-selected" ).length,
$( "#problemarea .one-selected" ).length,
$( "#problemarea .dime-selected" ).length,
$( "#problemarea .penny-selected" ).length
]) / 100
</div>
<div class="validator-function">
if ( guess === 0 ) {
return "";
} else {
return guess === ( digitsToInteger([ THOUSANDS, HUNDREDS, TENS, ONES, TENTHS, HUNDREDTHS ]) / 100 );
}
</div>
<div class="show-guess">
var places = digits( guess * 100 );
// unselect everything
$( "#problemarea .bill" ).removeClass( 'thou-selected hund-selected ten-selected one-selected' );
$( "#problemarea .dime" ).removeClass( 'dime-selected' );
$( "#problemarea .penny" ).removeClass( 'penny-selected' );
$.each( KhanUtil.currentGraph.graph.tenths, function() {
this.attr({ fill: '#eee', stroke: '#ddd' });
});
$.each( KhanUtil.currentGraph.graph.hundredths, function() {
this.attr({ fill: '#eee', stroke: '#ddd' });
});
// select the approprate number of each thing
$( "#problemarea .thou" ).slice( 0, places[5] || 0 ).addClass( 'thou-selected' );
$( "#problemarea .hund" ).slice( 0, places[4] || 0 ).addClass( 'hund-selected' );
$( "#problemarea .ten" ).slice( 0, places[3] || 0 ).addClass( 'ten-selected' );
$( "#problemarea .one" ).slice( 0, places[2] || 0 ).addClass( 'one-selected' );
$( "#problemarea .dime" ).slice( 0, places[1] || 0 ).addClass( 'dime-selected' );
$( "#problemarea .penny" ).slice( 0, places[0] || 0 ).addClass( 'penny-selected' );
for ( var i = 0; i &lt; places[1]; ++i ) {
KhanUtil.currentGraph.graph.tenths[ i ].attr({ fill: 'purple', stroke: '#000' });
}
for ( var i = 0; i &lt; places[0]; ++i ) {
KhanUtil.currentGraph.graph.hundredths[ i ].attr({ fill: 'gray', stroke: '#000' });
}
</div>
<div class="example">click a bill or coin to select it</div>
<div class="example">click a bill or coin again to deselect it</div>
</div>
</div>
</div>
<div class="hints">
<p>
<code>\Large{
<span data-if="THOUSANDS !== 0">\color{<var>PINK</var>}{<var>THOUSANDS</var>}</span>
\color{<var>ORANGE</var>}{<var>HUNDREDS</var>}
\color{<var>GREEN</var>}{<var>TENS</var>}
\color{<var>BLUE</var>}{<var>ONES</var>}.
\color{purple}{<var>TENTHS</var>}
\color{gray}{<var>HUNDREDTHS</var>}
<span data-if="THOUSANDTHS !== 0">\color{brown}{<var>THOUSANDTHS</var>}</span>
}
</code>
is the same as
<code>\large{
<span data-if="THOUSANDS !== 0">\color{<var>PINK</var>}{<var>THOUSANDS</var>000} + </span>
<span data-if="HUNDREDS !== 0">\color{<var>ORANGE</var>}{<var>HUNDREDS</var>00} + </span>
<span data-if="TENS !== 0">\color{<var>GREEN</var>}{<var>TENS</var>0} + </span>
<span data-if="ONES !== 0">\color{<var>BLUE</var>}{<var>ONES</var>} + </span>
<span data-if="TENTHS !== 0">\color{purple}{0.<var>TENTHS</var>} + </span>
<span data-if="HUNDREDTHS !== 0">\color{gray}{0.0<var>HUNDREDTHS</var>}</span>
<span data-if="THOUSANDTHS !== 0"> + \color{brown}{0.00<var>THOUSANDTHS</var>}</span>
}</code>.
</p>
<div data-if="THOUSANDS !== 0">
<p>
<code>\large{\color{<var>PINK</var>}{<var>THOUSANDS</var>000}}</code> is the same as <code>\large{\color{<var>PINK</var>}{<var>THOUSANDS</var>}}</code>
<var>plural( "thousand", THOUSANDS )</var>, the place value four places to the left of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select thousands.
var thous = $( '#problemarea .thou' );
thous.removeClass( 'thou-selected' );
for ( var i = 0; i &lt; THOUSANDS; i++ ) {
$( thous[ i ] ).addClass( 'thou-selected' );
}
</div>
</div>
<p data-else>
Because there is no number in the <span class="hint_pink">thousands</span> place, you don't need any <span class="hint_pink">thousands</span>.
</p>
<div data-if="HUNDREDS !== 0">
<p>
<code>\large{\color{<var>ORANGE</var>}{<var>HUNDREDS</var>00}}</code> is the same as <code>\large{\color{<var>ORANGE</var>}{<var>HUNDREDS</var>}}</code>
<var>plural( "hundred", HUNDREDS )</var>, the place value three places to the left of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select hundreds.
var hunds = $( '#problemarea .hund' );
hunds.removeClass( 'hund-selected' );
for ( var i = 0; i &lt; HUNDREDS; i++ ) {
$( hunds[ i ] ).addClass( 'hund-selected' );
}
</div>
</div>
<p data-else>
Because the <span class="hint_orange">hundreds</span> place is <code class="hint_orange">\large{0}</code>, you don't need any <span class="hint_orange">hundreds</span>.
</p>
<div data-if="TENS !== 0">
<p>
<code>\large{\color{<var>GREEN</var>}{<var>TENS</var>0}}</code> is the same as <code>\large{\color{<var>GREEN</var>}{<var>TENS</var>}}</code>
<var>plural( "ten", TENS )</var>, the place value two places to the left of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select tens.
var tens = $( '#problemarea .ten' );
tens.removeClass( 'ten-selected' );
for ( var i = 0; i &lt; TENS; i++ ) {
$( tens[ i ] ).addClass( 'ten-selected' );
}
</div>
</div>
<p data-else>
Because the <span class="hint_green">tens</span> place is <code class="hint_green">\large{0}</code>, you don't need any <span class="hint_green">tens</span>.
</p>
<div data-if="ONES !== 0">
<p>
<code>\large{\color{<var>BLUE</var>}{<var>ONES</var>}}</code> is the same as <code>\large{\color{<var>BLUE</var>}{<var>ONES</var>}}</code>
<var>plural( "one", ONES )</var>, the place value one place to the left of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select ones.
var ones = $( '#problemarea .one' );
ones.removeClass( 'one-selected' );
for ( var i = 0; i &lt; ONES; i++ ) {
$( ones[ i ] ).addClass( 'one-selected' );
}
</div>
</div>
<p data-else>
Because the <span class="hint_blue">ones</span> place is <code class="hint_blue">\large{0}</code>, you don't need any <span class="hint_blue">ones</span>.
</p>
<div data-if="TENTHS !== 0">
<p>
<code>\large{\color{purple}{0.<var>TENTHS</var>}}</code> is the same as <code>\large{\color{purple}{<var>TENTHS</var>}}</code>
<var>plural( "tenth", TENTHS )</var>, the place value one place to the right of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select dimes/tenths.
if ( $( '#place-value' ).length === 1 ) {
var tenths = $( '#problemarea .tenth' );
tenths.removeClass( 'tenth-selected' );
for ( var i = 0; i &lt; TENTHS; i++ ) {
$( tenths[ i ] ).addClass( 'tenth-selected' );
}
} else {
var dimes = $( '#problemarea .dime' );
dimes.removeClass( 'dime-selected' );
for ( var i = 0; i &lt; dimes.length; i++ ) {
graph.getCoinCircle( dimes[ i ] ).attr({ fill: '#eee', stroke: '#ddd' });
}
for ( var i = 0; i &lt; TENTHS; i++ ) {
$( dimes[ i ] ).addClass( 'dime-selected' );
graph.getCoinCircle( dimes[ i ] ).attr({ fill: 'purple', stroke: '#000' });
}
}
</div>
</div>
<p data-else>
Because the <span class="hint_purple">tenths</span> place is <code class="hint_purple">\large{0}</code>, you don't need any <span class="hint_purple">tenths</span>.
</p>
<div data-if="HUNDREDTHS !== 0">
<p>
<code>\large{\color{gray}{0.0<var>HUNDREDTHS</var>}}</code> is the same as <code>\large{\color{gray}{<var>HUNDREDTHS</var>}}</code>
<var>plural("hundredth", HUNDREDTHS )</var>, the place value two places to the right of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select pennies/hundredths.
if ( $( '#place-value' ).length === 1 ) {
var hundths = $( '#problemarea .hundth' );
hundths.removeClass( 'hundth-selected' );
for ( var i = 0; i &lt; HUNDREDTHS; i++ ) {
$( hundths[ i ] ).addClass( 'hundth-selected' );
}
} else {
var pennies = $( '#problemarea .penny' );
pennies.removeClass( 'penny-selected' );
for ( var i = 0; i &lt; pennies.length; i++ ) {
graph.getCoinCircle( pennies[ i ] ).attr({ fill: '#eee', stroke: '#ddd' });
}
for ( var i = 0; i &lt; HUNDREDTHS; i++ ) {
$( pennies[ i ] ).addClass( 'penny-selected' );
graph.getCoinCircle( pennies[ i ] ).attr({ fill: 'gray', stroke: '#000' });
}
}
</div>
</div>
<p data-else>
Because the <span class="hint_gray">hundreds</span> place is <code class="hint_gray">\large{0}</code>, you don't need any <span class="hint_gray">hundreds</span>.
</p>
<div data-if="THOUSANDTHS !== 0">
<p>
<code>\large{\color{#a52a2a}{0.00<var>THOUSANDTHS</var>}}</code> is the same as <code>\large{\color{#a52a2a}{<var>THOUSANDTHS</var>}}</code>
<var>plural("thousandth", THOUSANDTHS )</var>, the place value three places to the right of the decimal point.
</p>
<div class="graphie" data-update="graph">
// Select thousandths.
var thouths = $( '#problemarea .thouth' );
thouths.removeClass( 'thouth-selected' );
for ( var i = 0; i &lt; THOUSANDTHS; i++) {
$( thouths[ i ] ).addClass( 'thouth-selected' );
}
</div>
</div>
<!-- no data-else for thousandths since they're only zero if we're dealing with a money problem -->
<p>
Therefore you need
<span data-if="THOUSANDS !== 0"><code>\large{\color{<var>PINK</var>}{<var>THOUSANDS</var>}}</code> <var>plural( "thousand", THOUSANDS )</var>, </span>
<span data-if="HUNDREDS !== 0"><code>\large{\color{<var>ORANGE</var>}{<var>HUNDREDS</var>}}</code> <var>plural( "hundred", HUNDREDS )</var>, </span>
<span data-if="TENS !== 0"><code>\large{\color{<var>GREEN</var>}{<var>TENS</var>}}</code> <var>plural( "ten", TENS )</var>, </span>
<span data-if="ONES !== 0"><code>\large{\color{<var>BLUE</var>}{<var>ONES</var>}}</code> <var>plural( "one", ONES )</var>, </span>
<span data-if="TENTHS !== 0"><code>\large{\color{purple}{<var>TENTHS</var>}}</code> <var>plural( "tenth", TENTHS )</var>, </span>
<span data-if="THOUSANDTHS === 0" data-unwrap>
and <code>\large{\color{gray}{<var>HUNDREDTHS</var>}}</code> <var>plural( "hundredth", HUNDREDTHS )</var>.
</span>
<span data-else data-unwrap>
<span data-if="HUNDREDTHS !== 0"><code>\large{\color{gray}{<var>HUNDREDTHS</var>}}</code> <var>plural( "hundredth", HUNDREDTHS )</var>, </span>
and <code>\large{\color{#a52a2a}{<var>THOUSANDTHS</var>}}</code> <var>plural( "thousandth", THOUSANDTHS )</var>.
</span>
</p>
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