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        <a href="http://www.w3.org/"><img width="72" height="48" alt="W3C" src="http://www.w3.org/Icons/w3c_home"></a>
      </p>
      <h1>
        <a id="title"></a>Units in MathML</h1>
      <h2>
        <a id="w3c-doctype"></a>W3C Working Group Note 10 November 2003</h2>
      <dl>
        <dt>This version:</dt>
        <dd>
          <a href="http://www.w3.org/TR/2003/NOTE-mathml-units-20031110/">http://www.w3.org/TR/2003/NOTE-mathml-units-20031110/</a>
        </dd>
        <dt>Latest version:</dt>
        <dd>
          <a href="http://www.w3.org/TR/mathml-units/">http://www.w3.org/TR/mathml-units/</a>
        </dd>
        <dt>Previous version:</dt>
        <dd>
          <span>This is the first version of this Note.</span>
        </dd>
        <dt>Editors:</dt>
        <dd>Douglas Wilhelm Harder - Invited Expert, University of Waterloo</dd>
        <dd>Stan Devitt - Invited Expert, StratumTek</dd>
      </dl>
      <p class="copyright">
        <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a>&nbsp;&copy;&nbsp;2003&nbsp;<a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>&reg;</sup> (<a href="http://www.lcs.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.org/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. W3C <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a>, <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> and <a href="http://www.w3.org/Consortium/Legal/copyright-software">software licensing</a> rules apply.</p>
    </div>
    <hr>
    <div>
      <h2>
        <a id="abstract"></a>Abstract</h2>
      <p>MathML is an XML application for describing mathematical
      notation, capturing both its structure and content. As such, its
      scope does not extend to include units - determinate quantities
      adopted as standards of measure - which nevertheless, by their
      very nature, occur in an applied mathematical setting.  This
      Note makes recommendations and suggestions for how units can be
      incorporated into MathML.</p>
    </div>
    <div>
      <h2>
        <a id="status"></a>Status of this Document</h2>
      <p>
        <em>This section describes the status of this document
            at the time of its publication. Other documents may
            supersede this document. A list of current W3C
            publications and the latest revision of this technical
            report can be found in the <a href="http://www.w3.org/TR/">W3C technical reports
            index</a> at http://www.w3.org/TR/.</em>
      </p>
      <p> This document makes recommendations and suggestions for how
      to work with units in MathML.  Please report comments and errors
      in this document to <a href="mailto:www-math@w3.org">www-math@w3.org</a>.</p>
      <p>This document has been produced by the W3C Math Working
	 Group as part of the <a href="http://www.w3.org/Math/">W3C
	 Math Activity</a> (<a href="http://www.w3.org/Math/Activity">Activity
	 statement</a>).  The goals of the Working Group are
	 discussed in the <a href="http://www.w3.org/Math/Documents/Charter2001.html">
	 Working Group Charter</a>.  A list of <a href="http://www.w3.org/TR/2003/REC-MathML2-20031021/appendixi.html">participants
	 in the W3C Math Working Group</a> is available.</p>
      <p>Publication as a Working Group Note does not imply
	 endorsement by the W3C Membership. This is a draft document
	 and may be updated, replaced or obsoleted by other documents
	 at any time. It is inappropriate to cite this document as
	 other than work in progress. Patent disclosures relevant to
	 this Note may be found on the Math Working Group's <a href="http://www.w3.org/Math/Disclosures">patent disclosure
	 page</a>.</p>
    </div>
    <div class="toc">
      <h2>
        <a id="contents"></a>Table of Contents</h2>
      <p class="toc">1 <a href="#introduction">Introduction</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;1.1 <a href="#goals">Goals</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;1.2 <a href="#definitions">Definitions</a>
        <br>
2 <a href="#display_in_presentation">Display of Units in Presentation MathML</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;2.1 <a href="#exceptions">Exceptions</a>
        <br>
3 <a href="#inclusion_in_content">Inclusion of Units in Content MathML</a>
        <br>
4 <a href="#identifying_in_presentation">Identifying Units in Presentation MathML</a>
        <br>
5 <a href="#identifying_in_content">Identifying Unit Symbols in Content MathML</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;5.1 <a href="#content">Element Content</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;5.2 <a href="#encoding">Encoding Attribute</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;5.3 <a href="#definitionURL">Definition URL Attribute</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.3.1 <a href="#base">Base</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.3.2 <a href="#name">Unit Name</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.3.3 <a href="#context">Context</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.3.4 <a href="#country_code">Country Code</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5.3.5 <a href="#prefix">Prefix</a>
        <br>
6 <a href="#compound_in_content">Facilitating the Conversion of Units in MathML</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;6.1 <a href="#dimension">Dimension</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;6.2 <a href="#SI-equivalent-unit">SI Equivalent Unit</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;6.3 <a href="#system">System</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;6.4 <a href="#fps">Foot-Pound-Second System of Units</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;6.5 <a href="#SI-conversion-factor">SI Conversion Factor</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;6.5.1 <a href="#N4004AF">Examples</a>
        <br>
7 <a href="#conversions">Conversions Using Semantic Information</a>
        <br>
8 <a href="#examples">Examples</a>
        <br>
9 <a href="#acknowledgements">Acknowledgements</a>
        <br>
      </p>
      <h3>
        <a id="appendices"></a>Appendices</h3>
      <p class="toc">A <a href="#bibliography">Bibliography</a>
        <br>
B <a href="#prefixes">SI and IEC Prefixes</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;B.1 <a href="#SI-prefixes">SI Prefixes</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;B.2 <a href="#IEC-prefixes">IEC Prefixes</a>
        <br>
C <a href="#dimensions">Dimensions</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;C.1 <a href="#base_derived_dimensions">Dimensions with SI Base or Derived Units</a>
        <br>
&nbsp;&nbsp;&nbsp;&nbsp;C.2 <a href="#compound_dimensions">Dimensions with Compound SI Units</a>
        <br>
      </p>
    </div>
    <hr>
    <div class="body">
      <div class="div1">
        <h2>
          <a id="introduction"></a>1 Introduction</h2>
        <p>The support of units within MathML <a href="#MathML2">[MathML2]</a> is of primary interest
      to those wishing to use MathML to encode measured data. This Note presents a recommendation
      for how to include units in any MathML
    expression. It deals with both the presentation and content representations of units.</p>
        <p>The primary reference for this document is the IEEE/ASTM SI 10-1997
    <em>Standard for the Use of the International System of Units (SI): The Modern Metric
    System</em><a href="#ieee-astm">[ieee-astm]</a>,
        hereafter referred to as <em>the standard</em>.
    This Note only interprets what is defined in the standard and should not be used as a
    replacement.</p>
        <div class="div2">
          <h3>
            <a id="goals"></a>1.1 Goals</h3>
          <p>The goals of this Note are to provide suggestions and recommendations
        for encoding the presentation, identification, and inclusion of units in both Presentation
        and Content MathML.</p>
        </div>
        <div class="div2">
          <h3>
            <a id="definitions"></a>1.2 Definitions</h3>
          <p>The term
    <em>unit name</em>
     refers to the actual name of a unit (for example, meter, feet, torr), while
    <em>unit symbol</em>
     refers to usually a smaller number of characters used to represent the associated unit
     (for example, m, ft, Torr). Unit symbols are not abbreviations, and abbreviations should never
     be used as symbols.
     For example, use <em>A</em> and not <em>amp</em>.  For archaic units with no defined symbol,
    use the unit name as the unit symbol.</p>
          <p>A <em>compound unit</em> is a unit which is written as a product of powers of unit symbols
        and constants.</p>
        </div>
      </div>
      <div class="div1">
        <h2>
          <a id="display_in_presentation"></a>2 Display of Units in Presentation MathML</h2>
        <p>Section 3.5 of the standard is
      devoted to the style and usage of writing unit names and symbols. The following highlights
      the most relevant points brought up in this section and suggests
    possible interpretations in MathML.</p>
        <p>When writing compound unit names, the standard recommends that they be written in
      full English with standard pluralization and spacing, for example,
    <em>kilograms per cubic meter</em>
     and
    <em>meters per second squared</em>. MathML is concerned with the incorporation of
    units into mathematical expressions, and so the unit names are often inappropriate.
It is recommended instead that the unit symbols are used at all times.</p>
        <p>Unit symbols are written in roman (upright) type, are not altered in the plural,
      are not followed by a period except at the end of a sentence, and no space
      is left between a prefix
    and a unit symbol.  This is accomplished in MathML by using the
    <code>mi</code> element. Single character symbols must be qualified by setting the
    <code>mathvariant</code> attribute to <code>normal</code> as otherwise they would be italicized.
     For example,</p>
        <div class="exampleInner">
          <pre>&lt;mi mathvariant='normal'&gt;m&lt;/mi&gt; </pre>
        </div>
        <p>The standard recommends that a raised dot is used to
        indicate the product of two units. In Presentation MathML, this may be done through
        the use of the mathematical operator <code>&lt;mo&gt;&amp;middot;&lt;/mo&gt;</code>.
        For example, the newton meter may be expressed as</p>
        <div class="exampleInner">
          <pre>&lt;mrow&gt;
  &lt;mi mathvariant='normal' class='MathML-Unit'&gt;N&lt;/mi&gt;
  &lt;mo&gt;&amp;middot;&lt;/mo&gt;
  &lt;mi mathvariant='normal' class='MathML-Unit'&gt;m&lt;/mi&gt;
&lt;/mrow&gt; </pre>
        </div>
        <p>A quotient of two or more units may be expressed in one of the following ways:</p>
        <table cellpadding="2" border="2">
          <tbody>
            <tr>
              <th rowspan="1" colspan="1">MathML Source</th><th rowspan="1" colspan="1">Display</th><th rowspan="1" colspan="1">Description</th>
            </tr>
            <tr>
              <td rowspan="1" colspan="1"><code>&lt;mi mathvariant='normal' class='MathML-Unit'&gt;J&lt;/mi&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mi mathvariant='normal' class='MathML-Unit'&gt;kg&lt;/mi&gt;</code></td><td rowspan="1" colspan="1"><img src="units/eq_1.png" alt="J/kg"></td><td rowspan="1" colspan="1">J/kg</td>
            </tr>
            <tr>
              <td rowspan="1" colspan="1"><code>&lt;mi mathvariant='normal' class='MathML-Unit'&gt;J&lt;/mi&gt; &lt;mo&gt;&amp;middot;&lt;/mo&gt; &lt;msup&gt;&lt;mi mathvariant='normal' class='MathML-Unit'&gt;kg&lt;/mi&gt; &lt;mn&gt;-1&lt;/mn&gt;&lt;/msup&gt;&lt;mfrac&gt;</code></td><td rowspan="1" colspan="1"><img src="units/eq_2.png" alt="J*kg^-1"></td><td rowspan="1" colspan="1">J&middot;kg<sup>-1</sup></td>
            </tr>
            <tr>
              <td rowspan="1" colspan="1"><code>&lt;mfrac&gt;&lt;mi mathvariant='normal' class='MathML-Unit'&gt;J&lt;/mi&gt; &lt;mi mathvariant='normal' class='MathML-Unit'&gt;kg&lt;/mi&gt;&lt;/mfrac&gt;</code></td><td rowspan="1" colspan="1"><img src="units/eq_3.png" alt="J over Kg"></td><td rowspan="1" colspan="1">the ratio of J over kg</td>
            </tr>
          </tbody>
        </table>
        <p>In representing a quotient, do not use more than one solidus (/) in the same expression unless
      parentheses are inserted to avoid ambiguity.</p>
        <p>In expressing a quantity containing a value and a unit symbol, a space shall be left
      between them. In MathML this is achieved by using the mathematical operator
    <code>&lt;mo rspace="thickmathspace"&gt;&amp;InvisibleTimes;&lt;/mo&gt;</code>. If the
    default spacing used for <code>&amp;InvisibleTimes;</code> is not acceptable (it is
     often zero), extra space is added in MathML with the
    <code>rspace</code>
     attribute. For example, <code>35 mm</code> may be expressed as</p>
        <div class="exampleInner">
          <pre>&lt;mrow&gt;
  &lt;mn&gt;35&lt;/mn&gt; &lt;mo rspace='thickmathspace'&gt;&amp;InvisibleTimes;&lt;/mo&gt;
  &lt;mi mathvariant='normal' class='MathML-Unit'&gt;mm&lt;/mi&gt;
&lt;/mrow&gt; </pre>
        </div>
        <p>In expressing a quantity containing a value and a compound unit, the unit should remain
      distinct from the value. For example, in expressing 10 kg&middot;m/s, one would use:</p>
        <div class="exampleInner">
          <pre>&lt;mrow&gt;
  &lt;mn&gt;10&lt;/mn&gt; &lt;mo rspace='thickmathspace'&gt;&amp;InvisibleTimes;&lt;/mo&gt;
  &lt;mfrac&gt;
    &lt;mrow&gt;
      &lt;mi mathvariant='normal' class='MathML-Unit'&gt;kg&lt;/mi&gt; &lt;mo&gt;&amp;middot;&lt;/mo&gt; &lt;mi
      mathvariant='normal' class='MathML-Unit'&gt;m&lt;/mi&gt;
    &lt;/mrow&gt; &lt;mi mathvariant='normal' class='MathML-Unit'&gt;s&lt;/mi&gt;
  &lt;/mfrac&gt;
&lt;/mrow&gt;</pre>
        </div>
        <p>and not</p>
        <div class="exampleInner">
          <pre>&lt;mfrac&gt;
  &lt;mrow&gt;
    &lt;mn&gt;10&lt;/mn&gt; &lt;mo rspace='thickmathspace'&gt;&amp;InvisibleTimes;&lt;/mo&gt;
    &lt;mi&gt;kg&lt;/mi&gt; &lt;mo&gt;&amp;middot;&lt;/mo&gt; &lt;mi mathvariant='normal'&gt;m&lt;/mi&gt;
  &lt;/mrow&gt; &lt;mi mathvariant='normal'&gt;s&lt;/mi&gt;
&lt;/mfrac&gt; </pre>
        </div>
        <p>For both unit symbols and compound units, the unit should be the last term in the product.</p>
        <div class="div2">
          <h3>
            <a id="exceptions"></a>2.1 Exceptions</h3>
          <p>As MathML may be used in the display of intermediate steps of a calculation, not all
        of the above rules may apply. For example, in finding the speed of a body which moved
	thirty meters in five seconds, the Presentation MathML markup may be:


</p>
          <div class="exampleInner">
            <pre>&lt;mrow&gt;
  &lt;mfrac&gt;
    &lt;mrow&gt;
      &lt;mn&gt;30&lt;/mn&gt;
      &lt;mo rspace='thickmathspace'&gt;&amp;InvisibleTimes;&lt;/mo&gt;
      &lt;mi mathvariant='normal' class='MathML-Unit'&gt;m&lt;/mi&gt;
    &lt;/mrow&gt;
    &lt;mrow&gt;
      &lt;mn&gt;5&lt;/mn&gt;
      &lt;mo rspace='thickmathspace'&gt;&amp;InvisibleTimes;&lt;/mo&gt;
      &lt;mi mathvariant='normal' class='MathML-Unit'&gt;s&lt;/mi&gt;
    &lt;/mrow&gt;
  &lt;/mfrac&gt;
  &lt;mo&gt;=&lt;/mo&gt;
  &lt;mn&gt;6&lt;/mn&gt;
  &lt;mo rspace='thickmathspace'&gt;&amp;InvisibleTimes;&lt;/mo&gt;
  &lt;mfrac&gt;
    &lt;mi mathvariant='normal' class='MathML-Unit'&gt;m&lt;/mi&gt;
    &lt;mi mathvariant='normal' class='MathML-Unit'&gt;s&lt;/mi&gt;
  &lt;/mfrac&gt;
&lt;/mrow&gt; </pre>
          </div>
          <p> which displays as <img src="units/eq_4.png" alt="30 meters in 5 seconds"></p>
          <p>Certain non-SI units have, through common usage, symbols which differ in the
        plural. For example, the pound may be represented by the symbol
    <code>lb</code>
     or
    <code>lbs</code> , depending on the amount being measured. Similarly, 3.2 yards is often
    written 3.2 yds.</p>
          <p>The symbol kWh for the kilowatthour instead of kW&middot;h is also acceptable.</p>
          <p>Exceptions to the requirement that a space separate the quantity and unit are
        the symbols for degree, minute, and second of plane angle. In this case, it would be
        appropriate to use the
    <code>mo</code>
     operator. For example,</p>
          <div class="exampleInner">
            <pre>&lt;mn&gt;32&lt;/mn&gt;
&lt;mo&gt;&amp;InvisibleTimes;&lt;/mo&gt;
&lt;mi mathvariant='normal' class='MathML-Unit'&gt;&deg;&lt;/mi&gt;
&lt;mn&gt;18&lt;/mn&gt;
&lt;mo&gt;&amp;InvisibleTimes;&lt;/mo&gt;
&lt;mi mathvariant='normal' class='MathML-Unit'&gt;'&lt;/mi&gt;
&lt;mn&gt;54&lt;/mn&gt;
&lt;mo&gt;&amp;InvisibleTimes;&lt;/mo&gt;
&lt;mi mathvariant='normal' class='MathML-Unit'&gt;"&lt;/mi&gt;</pre>
          </div>
        </div>
      </div>
      <div class="div1">
        <h2>
          <a id="inclusion_in_content"></a>3 Inclusion of Units in Content MathML</h2>
        <p>In expressing a quantity with units,
      as with Presentation MathML, it is recommended that the unit be the last child of an
    <code>apply</code>
     element which has a
    <code>times</code>
     element as the first child.  It is also preferable if compound units are kept
     separate as a nested apply at the end of a product.</p>
      </div>
      <div class="div1">
        <h2>
          <a id="identifying_in_presentation"></a>4 Identifying Units in Presentation MathML</h2>
        <p>The presentation element
    <code>mi</code>
     does not take any attributes which may be used to indicate that it represents a unit. Content
     MathML must be used to identify individual or compound units.</p>
      </div>
      <div class="div1">
        <h2>
          <a id="identifying_in_content"></a>5 Identifying Unit Symbols in Content MathML</h2>
        <p>MathML 2.0 introduced externally
      defined symbols with the
    <code>csymbol</code>
     element. This element allows the author to use identifiers with externally defined semantics.</p>
        <p>The attribute
    <code>definitionURL</code>
     is a pointer to the external definition of the semantics of the symbol. The attribute
    <code>encoding</code>
     gives the syntax of the definition pointed to by the definition URL. Thus, the
    <code>csymbol</code>
     content element as such is the appropriate tool for identifying a symbol as being a unit.</p>
        <p>The
    <code>csymbol</code>
     element should not be used to encapsulate a compound unit. For example, the following unit
     of speed should not be constructed using a single <code>csymbol</code> element:
    <code>&lt;csymbol&gt;centimeters per second&lt;/csymbol&gt;</code>
     or
    <code>&lt;csymbol&gt;cm/s&lt;/csymbol&gt;</code>.</p>
        <p>Such compound units should be represented by explicit products or quotients of
simple units.</p>
        <div class="div2">
          <h3>
            <a id="content"></a>5.1 Element Content</h3>
          <p>The content of the <code>csymbol</code> element may consist of any
        encoding which is desired to represent the unit and is not restricted in any way beyond
        those already set in the MathML 2.0
    specification.</p>
          <p>The symbol g<sub>0</sub>
     or g<sub>n</sub>
     is often used to represent the unit of acceleration due to freefall. The semantics are
     already defined by the attributes, and thus the content may be used to indicate the display
     of this unit.
    For example,</p>
          <div class="exampleInner">
            <pre>&lt;csymbol definitionURL='http://.../units/gravity'&gt;&lt;msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;/csymbol&gt;</pre>
          </div>
        </div>
        <div class="div2">
          <h3>
            <a id="encoding"></a>5.2 Encoding Attribute</h3>
          <p>The <code>encoding</code> attribute is optional and is used to help parse the actual defintion.
It is only needed if the intention is to actually interpret the definitions by machine.</p>
        </div>
        <div class="div2">
          <h3>
            <a id="definitionURL"></a>5.3 Definition URL Attribute</h3>
          <p>The
    <code>definitionURL</code>
     attribute may be used to uniquely identify a unit. The following is a recommendation for
     a unique definition URL.</p>
          <p>The definition URL is made up of two to five parts:</p>
          <div class="exampleInner">
            <pre>http://<em>base</em>/units/<em>unit name</em>[/<em>context</em>][/<em>country</em>][#<em>prefix</em>]</pre>
          </div>
          <p>where the context, country, and prefix are optional. The use of these parts is
        described below:</p>
          <div class="div3">
            <h4>
              <a id="base"></a>5.3.1 Base</h4>
            <p>To this point, no fixed URL has been chosen to represent the
          base of these definition URLs, so for the remainder of this Note, the base will be
          indicated by ellipsis:
    <code>...</code>. For example,</p>
            <div class="exampleInner">
              <pre>&lt;csymbol definitionURL='http://.../units/meter'&gt;m&lt;/csymbol&gt;</pre>
            </div>
          </div>
          <div class="div3">
            <h4>
              <a id="name"></a>5.3.2 Unit Name</h4>
            <p>The unit name is spelled in full without any prefix. With
          the myriad of spellings available for each unit name, even within SI, it is recommended
          that the American English spelling with
    standard translations to lower case ASCII characters be used wherever possible. For
    example, the German Fu&szlig; and the &Aring;ngstr&ouml;m should use the definition URLs
    <code>http://.../units/foot/de</code>
     and
    <code>http://.../units/angstrom</code>, respectively.</p>
            <p>In cases where the (nonstandard) unit symbol is an abbreviation of a compound unit name, the
          unit symbol should be used in place of the unit name. For example,
    <em>gallons per minute</em>
     and
    <em>revolutions per minute</em>
     should use the definition URLs should use the definition URLs
    <code>http://.../units/gpm</code>
     and
    <code>http://.../units/rpm</code> , respectively.</p>
            <p>The unit name was chosen over the unit symbol for the definition URL as the name is
          less likely to conflict with other unit names, and unit names tend to be more easily
          converted to ASCII. For example, the symbol for the ohm is &Omega; (&amp;Omega;).</p>
          </div>
          <div class="div3">
            <h4>
              <a id="context"></a>5.3.3 Context</h4>
            <p>The context is used only where the name is insufficient to
          properly qualify the unit either through common usage or an international or scientific
          agreement. No SI base units, derived units
    with special names and symbols, or derived units with special names admitted for reasons of
    safeguarding human health requires a context as they are understood to be the default. Of
    the units in use with and in temporary use with SI, the only which require a context are
    the angular minute and second, <code>http://.../units/minute/angular</code>
     and
    <code>http://.../units/second/angular</code>, respectively.</p>
            <p>An example of where a context is necessary is the U.S. survey mile. The default
          international mile has the definition URL
    <code>http://.../units/mile</code>
     whereas the U.S. survey mile would use the definition URL
    <code>http://.../units/mile/survey/us</code>. In this case, the context is necessary as the standard U.S. mile is equal to the international
 mile.</p>
            <p>Over the years, the definitions of the various SI units have been modified. In most
          cases, the definitions have been made more exact, so previous measurements are
          still valid up to the
    precision of the former definition. The one exception to this is the definition of the
    liter. In 1901, the liter was defined as <em>the unit of volume occupied by a mass of one
    kilogram of pure water at its maximum density and at standard atmospheric pressure.</em>
     The definition of the liter was changed in 1964 to be a special name for the cubic
     decimeter. These two definitions differ by approximately 28 parts per million, and thus
     it is necessary to
    differentiate between these two units. The context of the original liter could be the year the
    definition was made, so the definition URL would be <code>http://.../units/liter/1901</code>.</p>
            <p>A date may be used in other cases where a definition has changed, where the date
          refers to the year the definition in question was made.</p>
            <p>In some cases, a unit
          may have multiple definitions which may be differentiated by the dimension. In this
          case, the dimension could be used as the context. For example, the langley may either
    be defined as
<img src="units/eq_5.png" alt="cal/cm^2">

     (surface energy density) or

<img src="units/eq_6.png" alt="cal/(cm^2 &times; min)">

     (surface power density). The definition URLs for these two units may be
    <code>http://.../units/langley/surface_energy_density</code>
     and
    <code>http://.../units/langley/surface_power_density</code>, respectively.</p>
          </div>
          <div class="div3">
            <h4>
              <a id="country_code"></a>5.3.4 Country Code</h4>
            <p>By default, the country is referred to by the ISO 3166
          country codes. In the case of historical units, where possible, the modern successor
          of that country should be used.  Where this is not possible,
    ISO 3166-2 Regional codes may be used, again, if possible.</p>
            <p>For example, the definition URL of the Scottish mile would be
    <code>http://.../units/mile/gb-sct</code>.</p>
            <p>This breaks down when referring to ancient units. It would be nonsensical to
          refer to the Roman mile as an Italian mile. In these cases, the adjective form of
          the civilization is used. Some examples are given below:</p>
            <ul>
              <li>
                <p>arabic</p>
              </li>
              <li>
                <p>athenian</p>
              </li>
              <li>
                <p>egyptian</p>
              </li>
              <li>
                <p>greek</p>
              </li>
              <li>
                <p>hebrew</p>
              </li>
              <li>
                <p>ionian</p>
              </li>
              <li>
                <p>persian</p>
              </li>
              <li>
                <p>prussian</p>
              </li>
              <li>
                <p>rabbinical</p>
              </li>
              <li>
                <p>roman</p>
              </li>
              <li>
                <p>talmudic</p>
              </li>
            </ul>
          </div>
          <div class="div3">
            <h4>
              <a id="prefix"></a>5.3.5 Prefix</h4>
            <p>SI accomodates decimal multiples and submultiples of units
          to be represented by placing prefixes in front of the symbols.  The IEC introduced
          prefixes to represent binary multiples of units. A unit with a prefix is represented by
          appending the prefix to the
    definition URL using the fragment identifier <code>#</code>. For the prefix <code>&mu;</code> (micro)
     use the recommended ASCII equivalent,
    <code>u</code>.</p>
            <p>Examples:</p>
            <table cellpadding="2" border="2">
              <tbody>
                <tr>
                  <th rowspan="1" colspan="1">Unit Name</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">Recommended Definition URL</th>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">centimeter</td><td rowspan="1" colspan="1">cm</td><td rowspan="1" colspan="1"><code>http://.../units/meter#c</code></td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">micrometer</td><td rowspan="1" colspan="1">&mu;m</td><td rowspan="1" colspan="1"><code>http://.../units/meter#u</code></td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">kilogram</td><td rowspan="1" colspan="1">kg</td><td rowspan="1" colspan="1"><code>http://.../units/gram#k</code></td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">kibibyte (1024 bytes)</td><td rowspan="1" colspan="1">KiB</td><td rowspan="1" colspan="1"><code>http://.../units/byte#Ki</code></td>
                </tr>
              </tbody>
            </table>
            <p>A full list of prefixes are given in <a href="#IEC-prefixes"><b>B.2 IEC Prefixes</b></a>. Unlike other parts of the
          definition URL, the prefixes should be capitalized where necessary.</p>
          </div>
        </div>
      </div>
      <div class="div1">
        <h2>
          <a id="compound_in_content"></a>6 Facilitating the Conversion of Units in MathML</h2>
        <p>A unit is
      a standard of measurement. In order to convert, for example, 1.35 dynes to newtons, two
      pieces of information are necessary:</p>
        <ol class="1">
          <li>
            <p>The dimension of the unit, and</p>
          </li>
          <li>
            <p>Either:
      </p>
            <ol class="a">
              <li>
                <p>The associated system of units, or</p>
              </li>
              <li>
                <p>The conversion to a known system of units.</p>
              </li>
            </ol>
          </li>
        </ol>
        <p>At this point, the measurement can be converted to any other unit of equal dimension.</p>
        <p>Suppose we wish to convert 15.3 kilometers per hour to feet
      per second. Both are measurements of speed, the second being the unit of speed in the
      foot-pound-second system of units. If we know
    that the conversion of km/h to SI is approximately 0.277778 m/s, then the conversion from m/s
    is the conversion of m to ft over the conversion of s to s, that is, 3.28084. Thus,
    the conversion is 15.3&times;0.277778&times;3.28084 ft/s = 13.9436 ft/s.</p>
        <p>Suppose we want to convert 3.532 calorie hours to erg seconds. This problem may be reduced
      to converting the first unit to a common system of units, say SI, and then converting the
    corresponding SI unit to cgs system of units.</p>
        <p>Given that cal&middot;h and erg&middot;s are units of action (the dimension), if we know that
      the conversion of 1 cal&middot;s to SI is 15062.4 kg&middot;m<sup>2</sup>/s. The conversion from SI to cgs is a multiplication by 10<sup>7</sup>. Thus
    3.532 cal&middot;h = 3.532&times;15062.4&times;10<sup>7</sup>erg&middot;s = 5.32e11
    erg&middot;s.</p>
        <p>Again, consider converting 83.7 statvolts per centimeter to volts per meter. This
      problem may be reduced to converting a unit in the electrostatic system of units (emu)
      to SI.</p>
        <p>Given that sV/cm is a unit of electric field strength, we may take the
      product of the conversions of corresponding units of mass, length time, and electric
      current to get the conversion to SI.
    This product is 10<sup>-3</sup>&times;10<sup>-2</sup>/(1<sup>3</sup>&times;2997924580<sup>-1</sup>) = 29979.2458, and therefore the conversion to SI of 87.3 statV/cm is 29979.2458
    V/m.</p>
        <p>It is always possible to determine all of this information by interpreting
      the MathML appropriately, although by transmitting plain MathML the task may be quite
      difficult. Even a unit as simple as cm/s may be stored in any of three ways:</p>
        <div class="exampleInner">
          <pre>&lt;apply&gt;
  &lt;divide/&gt;
  &lt;csymbol definitionURL='http://.../units/meter#c&gt;cm&lt;/csymbol&gt;
  &lt;csymbol definitionURL='http://.../units/second&gt;s&lt;/csymbol&gt;
&lt;/apply&gt;

&lt;apply&gt;
  &lt;times/&gt;
  &lt;csymbol definitionURL='http://.../units/meter#c&gt;cm&lt;/csymbol&gt;
  &lt;apply&gt;
    &lt;power/&gt;
    &lt;csymbol definitionURL='http://.../units/second&gt;s&lt;/csymbol&gt;
    &lt;cn type='integer'&gt;-1&lt;/cn&gt;
  &lt;/apply&gt;
&lt;/apply&gt;

&lt;csymbol definitionURL='http://.../units/kyne'&gt;kyn&lt;/csymbol&gt;</pre>
        </div>
        <p>In general, it is quite difficult to pick a unit from an expression. This section
      describes a method for facilitating the transmission of unit information by making use of the
    <code>semantics</code>
     element.</p>
        <p>Each <code>semantics</code> element would contain the attribute
    <code>definitionURL="http://.../units/"</code>. The first
    child element would be the unit encoded in either Content or Presentation MathML.</p>
        <p>The remaining annotations may be used to facilitate interpretation and conversion of
      the given unit.</p>
        <ul>
          <li>
            <p>dimension</p>
          </li>
          <li>
            <p>SI-equivalent-unit</p>
          </li>
          <li>
            <p>system</p>
          </li>
          <li>
            <p>SI-conversion-factor</p>
          </li>
        </ul>
        <div class="div2">
          <h3>
            <a id="dimension"></a>6.1 Dimension</h3>
          <p>A dimension is something which may be measured. Within the
        scientific community, most objects may be measured in units of length, mass, time,
        electric current, thermodynamic temperature,
    amount of substance, or luminous intensity (base dimensions) or as products of powers of
    these (derived dimensions). Currency may also be taken to be a base dimension in some fields
    such as economics.</p>
          <p>A system of units is a collection of units which assign specific standards of measure
        (units) to a set of base and derived dimensions. Knowing the dimension of that which
        is being measured
    already goes a long way to helping conversions of units. The International System of Units
    (SI) is one such system of units used to describe physical phenomena and has been chosen
    to be the standard of such measurement.</p>
          <p>If the dimension of a unit and the conversion of that unit to SI (see
    <a href="#SI-conversion-factor">SI conversion factor</a> ) are known, then converting
    the given information to any other system of units is straight forward so long as the
    conversion from SI to the target unit is known.</p>
          <p>For example, 4.37 yds may be encoded as:</p>
          <div class="exampleInner">
            <pre>&lt;apply&gt;
  &lt;times/&gt;
  &lt;cn type='real'&gt;4.37&lt;/cn&gt;
  &lt;semantics definitionURL='http://.../units/'&gt;
    &lt;csymbol definitionURL='http://.../units/yard'&gt;yds&lt;/csymbol&gt;
    &lt;annotation definitionURL='http://.../dimension/length'/&gt;
    &lt;annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'&gt;
      &lt;cn type='real'&gt;0.9144&lt;/cn&gt;
    &lt;/annotation-xml&gt;
  &lt;/semantics&gt;
&lt;/apply&gt; </pre>
          </div>
          <p>Thus, any application reading this data and wishing to convert it to cgs need only
        extract the dimension, the conversion factor, and look up the appropriate conversion
        of the unit of length in
    SI (m) to the unit of length in cgs (cm) to get 4.37 yds = 400 cm.</p>
          <p>The dimension may also be used to encode information which may be lost in the
        representation. For example, while a reasonable SI unit of torque is the
    <code>J/rad</code>, it is common to use the unit <code>N m</code>
     where the second unit is understood to be a radial measure. Some other examples of units
     which may be used to represent different quantites are:</p>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">Unit</th><th rowspan="1" colspan="1">Possible
              Quantities</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">coulomb</td><td rowspan="1" colspan="1">electric
              charge, quantity of electricity</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">volt</td><td rowspan="1" colspan="1">electric
              potential difference, electromotive force</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">watt</td><td rowspan="1" colspan="1">power, radiant
              flux</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">newton meter</td><td rowspan="1" colspan="1">energy,
              torque</td>
              </tr>
            </tbody>
          </table>
          <p>A list of possible dimensions is given in <a href="#dimensions"><b>C Dimensions</b></a>.</p>
        </div>
        <div class="div2">
          <h3>
            <a id="SI-equivalent-unit"></a>6.2 SI Equivalent Unit</h3>
          <p>In this case, the <code>annotation-xml</code> element is the SI equivalent unit, and
        gives a MathML encoding of the equivalent SI unit. This annotation is redundant if the
        dimension of the unit is given, as the conversion from
    the dimension to the equivalent unit is a matter of a table look up, though it may be used
    if an unnamed dimension is being used. For example, the rate of change of power per unit
    of time is an unnamed dimension, thus, for example, one encoding of 30.523 Hp/min may be:</p>
          <div class="exampleInner">
            <pre>&lt;apply&gt;
  &lt;times/&gt;
  &lt;cn type='real'&gt;30.523&lt;/cn&gt;
  &lt;semantics definitionURL='http://.../units/'&gt;
    &lt;apply&gt;
      &lt;divide/&gt;
      &lt;csymbol definitionURL='http://.../units/horsepower'&gt;Hp&lt;/csymbol&gt;
      &lt;csymbol definitionURL='http://.../units/minute'&gt;min&lt;/csymbol&gt;
    &lt;/apply&gt;
    &lt;annotation-xml encoding='MathML' definitionURL='http://.../SI-equivalent-unit'&gt;
      &lt;apply&gt;
        &lt;divide/&gt; &lt;csymbol
        definitionURL='http://.../units/watt'&gt;W&lt;/csymbol&gt; &lt;csymbol
        definitionURL='http://.../units/second'&gt;s&lt;/csymbol&gt;
      &lt;/apply&gt;
    &lt;/annotation-xml&gt;
    &lt;annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'&gt;
      &lt;cn type='real'&gt;12.428331193037837&lt;/cn&gt;
    &lt;/annotation-xml&gt;
  &lt;/semantics&gt;
&lt;/apply&gt; </pre>
          </div>
        </div>
        <div class="div2">
          <h3>
            <a id="system"></a>6.3 System</h3>
          <p>A system of units is a collection of base units and products of
        powers of those units used to measure various physical phenomena.</p>
          <p>A system of
        units is said to be self-consistent if any two products of units within that system which
        have the same dimensions are equal. For example, SI is consistent while UK and US systems
    systems of units are not. For example, in either system, the unit of power, the Hp, is not
    equal to the compound unit lb&middot;ft<sup>2</sup>/s<sup>3</sup>. Neither is the unit of
    force, the pound-force, equal to the compound unit lb&middot;ft/s<sup>2</sup>.</p>
          <p>In general, the system annotation should only be used when the system is
        self-consistent. The following systems are self consistent:</p>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">System Name</th><th rowspan="1" colspan="1">Annotation</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">International System of Units</td><td rowspan="1" colspan="1"><code>&lt;annotation definitionURL='http://.../system/SI'/&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Centimeter-Gram-Second</td><td rowspan="1" colspan="1"><code>&lt;annotation definitionURL='http://.../system/cgs'/&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Electrostatic System of Units</td><td rowspan="1" colspan="1"><code>&lt;annotation definitionURL='http://.../system/esu'/&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Electromagnetic System of Units</td><td rowspan="1" colspan="1"><code>&lt;annotation definitionURL='http://.../system/emu'/&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Atomic System of Units</td><td rowspan="1" colspan="1"><code>&lt;annotation definitionURL='http://.../system/atomic'/&gt;</code></td>
              </tr>
            </tbody>
          </table>
          <p>The system annotation should be used if the unit is either the default
        unit in the given system for the particular dimension, or is equal to that unit.</p>
          <p>For example, the system annotation may be used for either J or kg&middot;m<sup>2</sup>/s<sup>2</sup>
     but should not be used for kJ. All three could use the energy dimension annotation, but the
     first two would use the SI system annotation whereas the latter would use the SI conversion
     factor XML
    annotation with content <code>&lt;cn type="integer"&gt;1000&lt;/cn&gt;</code>.</p>
        </div>
        <div class="div2">
          <h3>
            <a id="fps"></a>6.4 Foot-Pound-Second System of Units</h3>
          <p>Due to the ubiquitous nature of the
        foot-pound-second system of units in some countries some mention of this system of
        units is necessary. It is recommended that the dimension and SI
    conversion factor annotations be used. Some conversion factors between the fps system and
    SI are provided in the following table. Exact conversions are marked in bold.</p>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">Name</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">SI Equivalent Unit</th><th rowspan="1" colspan="1">Conversion           Factor</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">foot</td><td rowspan="1" colspan="1">ft</td><td rowspan="1" colspan="1">m</td><td rowspan="1" colspan="1"><code>0.3048</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">pound</td><td rowspan="1" colspan="1">lb</td><td rowspan="1" colspan="1">kg</td><td rowspan="1" colspan="1"><code>0.45359237</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">poundal</td><td rowspan="1" colspan="1">pdl</td><td rowspan="1" colspan="1">N</td><td rowspan="1" colspan="1"><code>0.138254954376</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">pound-force</td><td rowspan="1" colspan="1">lbf</td><td rowspan="1" colspan="1">N</td><td rowspan="1" colspan="1"><code>4.4482216152605</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">horsepower</td><td rowspan="1" colspan="1">Hp</td><td rowspan="1" colspan="1">W</td><td rowspan="1" colspan="1"><code>745.69987158227022</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">pound(-force)s per square inch</td><td rowspan="1" colspan="1">psi</td><td rowspan="1" colspan="1">Pa</td><td rowspan="1" colspan="1"><code>6894.757293</code></td>
              </tr>
            </tbody>
          </table>
          <p>The conversions of most other fps units may be found by taking products of
        powers of the above conversion factors.</p>
        </div>
        <div class="div2">
          <h3>
            <a id="SI-conversion-factor"></a>6.5 SI Conversion Factor</h3>
          <p>The SI conversion factor <code>annotation-xml</code> encoding
        is a MathML encoding of the conversion factor between that unit and the equivalent SI
        unit of the same dimension. In the previous example, the
    conversion from lbf&middot;ft to J/rad is 3389544870828501/2500000000000000 = 1.3558179483314004.</p>
          <div class="div3">
            <h4>
              <a id="N4004AF"></a>6.5.1 Examples</h4>
            <p>Some examples of using units with the semantics encoding
          are:</p>
            <p>980.665 cm/s</p>
            <div class="exampleInner">
              <pre>&lt;apply&gt;
    &lt;times/&gt;
    &lt;cn type='real'&gt;980.665&lt;/cn&gt;
    &lt;semantics definitionURL='.../units'&gt;
      &lt;apply&gt;
        &lt;times/&gt;
        &lt;csymbol definitionURL='.../units/meter#c'&gt;cm&lt;/csymbol&gt;
        &lt;csymbol definitionURL='.../units/second'&gt;s&lt;/csymbol&gt;
      &lt;/apply&gt;
      &lt;annotation definitionURL='http://.../dimension/speed'/&gt;
      &lt;annotation definitionURL='http://.../system/cgs'/&gt;
      &lt;annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'&gt;
        &lt;cn type='rational'&gt;1&lt;/sep&gt;100&lt;/cn&gt;
      &lt;/annotation-xml&gt;
    &lt;/semantics&gt;
  &lt;/apply&gt;</pre>
            </div>
            <p>1 atm = 103.325 kPa</p>
            <div class="exampleInner">
              <pre>&lt;apply&gt;
  &lt;eq/&gt;
  &lt;apply&gt;
    &lt;times/&gt;
    &lt;cn type='integer'&gt;1&lt;/cn&gt;
    &lt;semantics  definitionURL='http://.../units/'&gt;
      &lt;csymbol definitionURL='http://.../units/atmosphere'&gt;atm&lt;/csymbol&gt;
      &lt;annotation definitionURL='http://.../dimension/pressure'/&gt;
      &lt;annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'&gt;
        &lt;cn type='integer'&gt;101325&lt;/cn&gt;
      &lt;/annotation-xml&gt;
    &lt;/semantics&gt;
    &lt;cn type='integer'&gt;1&lt;/cn&gt;
  &lt;/apply&gt;
  &lt;apply&gt;
    &lt;times/&gt;
    &lt;cn type='real'&gt;101.325&lt;/cn&gt;
    &lt;semantics definitionURL='http://.../units/'&gt;
      &lt;csymbol definitionURL='http://.../units/pascal#k'&gt;kPa&lt;/csymbol&gt;
      &lt;annotation definitionURL='http://.../dimension/pressure'/&gt;
      &lt;annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'&gt;
        &lt;cn type='integer'&gt;1000&lt;/cn&gt;
      &lt;/annotation-xml&gt;
    &lt;/semantics&gt;
  &lt;/apply&gt;
&lt;/apply&gt;</pre>
            </div>
          </div>
        </div>
      </div>
      <div class="div1">
        <h2>
          <a id="conversions"></a>7 Conversions Using Semantic Information</h2>
      </div>
      <div class="div1">
        <h2>
          <a id="examples"></a>8 Examples</h2>
        <p>The fuel efficency of some cars is as good as 4.4 L/(100 km).</p>
        <div class="exampleInner">
          <pre>&lt;mrow&gt;
  &lt;mn&gt;4.4&lt;/mn&gt;
  &lt;mo&gt;&amp;InvisibleTimes;&lt;/mo&gt;
  &lt;mfrac&gt;
    &lt;mi&gt;L&lt;/mi&gt;
    &lt;mrow&gt;
      &lt;mn&gt;100&lt;/mn&gt;
      &lt;mo&gt;&amp;InvisibleTimes;&lt;/mo&gt;
      &lt;mi mathvariant='normal' class='MathML-Unit'&gt;km&lt;/mi&gt;
    &lt;/mrow&gt;
  &lt;/mfrac&gt;
&lt;/mrow&gt; </pre>
        </div>
        <div class="exampleInner">
          <pre>&lt;apply&gt;
  &lt;times/&gt;
  &lt;cn type='real'&gt;4.4&lt;/cn&gt;
  &lt;semantics&gt;
    &lt;apply&gt;
      &lt;divide/&gt;
      &lt;csymbol definitionURL='http://.../units/liter'&gt;L&lt;/csymbol&gt;
      &lt;apply&gt;
        &lt;times/&gt;
        &lt;cn type='integer'&gt;100&lt;/cn&gt;
        &lt;csymbol definitionURL='http://.../units/meter#k'&gt;km&lt;/csymbol&gt;
      &lt;/apply&gt;
    &lt;/apply&gt;
  &lt;/semantics&gt;
&lt;/apply&gt; </pre>
        </div>
      </div>
      <div class="div1">
        <h2>
          <a id="acknowledgements"></a>9 Acknowledgements</h2>
        <p>The first editor would like to thank Stan Devitt, Robert Miner, Max
      Froumentin, Laurent Bernardin, and Jacques Carette for helping me with this Note. In
      particular, Dr. Devitt suggested the use of the
    <code>semantics</code>
     element for isolating a unit, and Dr. Miner helped initiate the Note. The first editor would also like to
     thank Jeff Giles for additional comments.</p>
      </div>
    </div>
    <div class="back">
      <div class="div1">
        <h2>
          <a id="bibliography"></a>A Bibliography</h2>
        <dl>
          <dt class="label">
            <a id="ieee-astm"></a>ieee-astm</dt>
          <dd>IEEE/ASTM SI 10-1997
      <em>Standard for Use of the International System of Units (SI): The Modern Metric
      System</em>, IEEE Inc., New York, 1997.</dd>
          <dt class="label">
            <a id="MathML2"></a>MathML2</dt>
          <dd>David Carlisle, Patrick Ion, Robert Miner, Nico Poppelier, <a href="http://www.w3.org/TR/2003/REC-MathML2-20031021/">Mathematical Markup Language (MathML) Version 2.0, second edition</a>, W3C Recommendation 21 October 2003</dd>
        </dl>
      </div>
      <div class="div1">
        <h2>
          <a id="prefixes"></a>B SI and IEC Prefixes</h2>
        <p>Prefixes are used to form names and symbols
      of decimal or binary multiples and decimal submultiples of units. These prefixes or their
      symbols are attached to names or symbols, forming what are
      called <em>multiples and submultiples of units</em>.</p>
        <p>SI prefixes are used to represent decimal multiples and submultiples of units. As 10<sup>3</sup>
     = 1000 &tilde; 1024 is approximately equal to 2<sup>10</sup>, it has been common to use SI prefixes to represent binary multiples of
    information units, though this is not universal. For example, in referring to the bit
    rates of a modem, the prefixes indicate powers of 10, not 2. The IEC introduced binary
    prefixes in 1998 to correct the confusion resulting from this.</p>
        <div class="div2">
          <h3>
            <a id="SI-prefixes"></a>B.1 SI Prefixes</h3>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">Multiplication Factor</th><th rowspan="1" colspan="1">Prefix</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">Example</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">10<sup>24</sup></td><td rowspan="1" colspan="1">yotta</td><td rowspan="1" colspan="1">Y</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#Y"&gt;Ym&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>21</sup></td><td rowspan="1" colspan="1">zetta</td><td rowspan="1" colspan="1">Z</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#Z"&gt;Zm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>18</sup></td><td rowspan="1" colspan="1">exa</td><td rowspan="1" colspan="1">E</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#E"&gt;Em&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>15</sup></td><td rowspan="1" colspan="1">peta</td><td rowspan="1" colspan="1">P</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#P"&gt;Pm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>12</sup></td><td rowspan="1" colspan="1">tera</td><td rowspan="1" colspan="1">T</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#T"&gt;Tm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>9</sup></td><td rowspan="1" colspan="1">giga</td><td rowspan="1" colspan="1">G</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#G"&gt;Gm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>6</sup></td><td rowspan="1" colspan="1">mega</td><td rowspan="1" colspan="1">M</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#M"&gt;Mm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>3</sup>
           = 1000</td><td rowspan="1" colspan="1">kilo</td><td rowspan="1" colspan="1">k</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#k"&gt;km&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>2</sup>
           = 100</td><td rowspan="1" colspan="1">hecto</td><td rowspan="1" colspan="1">h</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#h"&gt;hm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>1</sup>
           = 10</td><td rowspan="1" colspan="1">deka</td><td rowspan="1" colspan="1">da</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#da"&gt;dam&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-1</sup>
           = 0.1</td><td rowspan="1" colspan="1">deci</td><td rowspan="1" colspan="1">d</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#d"&gt;dm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-2</sup>
           = 0.01</td><td rowspan="1" colspan="1">centi</td><td rowspan="1" colspan="1">c</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#c"&gt;cm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-3</sup>
           = 0.001</td><td rowspan="1" colspan="1">milli</td><td rowspan="1" colspan="1">m</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#m"&gt;mm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-6</sup></td><td rowspan="1" colspan="1">micro</td><td rowspan="1" colspan="1">&mu;</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#u"&gt;&mu;m&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-9</sup></td><td rowspan="1" colspan="1">nano</td><td rowspan="1" colspan="1">n</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#n"&gt;nm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-12</sup></td><td rowspan="1" colspan="1">pico</td><td rowspan="1" colspan="1">p</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#p"&gt;pm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-15</sup></td><td rowspan="1" colspan="1">femto</td><td rowspan="1" colspan="1">f</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#f"&gt;fm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-18</sup></td><td rowspan="1" colspan="1">atto</td><td rowspan="1" colspan="1">a</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#a"&gt;am&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-21</sup></td><td rowspan="1" colspan="1">zepto</td><td rowspan="1" colspan="1">z</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#z"&gt;zm&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">10<sup>-24</sup></td><td rowspan="1" colspan="1">yocto</td><td rowspan="1" colspan="1">y</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/meter#y"&gt;ym&lt;/csymbol&gt;</code></td>
              </tr>
            </tbody>
          </table>
        </div>
        <div class="div2">
          <h3>
            <a id="IEC-prefixes"></a>B.2 IEC Prefixes</h3>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">Multiplication Factor</th><th rowspan="1" colspan="1">Full
           Technical               Name</th><th rowspan="1" colspan="1">Prefix</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">Example</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">2<sup>60</sup></td><td rowspan="1" colspan="1">exabinary</td><td rowspan="1" colspan="1">exbi</td><td rowspan="1" colspan="1">Ei</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/byte#Ei"&gt;EiB&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2<sup>50</sup></td><td rowspan="1" colspan="1">petabinary</td><td rowspan="1" colspan="1">pebi</td><td rowspan="1" colspan="1">Pi</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/byte#Pi"&gt;PiB&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2<sup>40</sup></td><td rowspan="1" colspan="1">terabinary</td><td rowspan="1" colspan="1">tebi</td><td rowspan="1" colspan="1">Ti</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/byte#Ti"&gt;TiB&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2<sup>30</sup></td><td rowspan="1" colspan="1">gigabinary</td><td rowspan="1" colspan="1">gibi</td><td rowspan="1" colspan="1">Gi</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/byte#Gi"&gt;GiB&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2<sup>20</sup></td><td rowspan="1" colspan="1">megabinary</td><td rowspan="1" colspan="1">mebi</td><td rowspan="1" colspan="1">Mi</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/byte#Mi"&gt;MiB&lt;/csymbol&gt;</code></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">2<sup>10</sup></td><td rowspan="1" colspan="1">kilobinary</td><td rowspan="1" colspan="1">kibi</td><td rowspan="1" colspan="1">Ki</td><td rowspan="1" colspan="1"><code>&lt;csymbol definitionURL="http://.../units/byte#Ki"&gt;KiB&lt;/csymbol&gt;</code></td>
              </tr>
            </tbody>
          </table>
        </div>
      </div>
      <div class="div1">
        <h2>
          <a id="dimensions"></a>C Dimensions</h2>
        <p>This appendix contains a list
      of suggested values for the <code>definitionURL</code> element for dimensions which may be used in the dimension annotation
      of a semantics group. Also listed is the standard SI unit of that dimension.</p>
        <p>Fragment identifiers are not used, as indices into the dimension pages may later be
      used to identify, for example, the SI unit, e.g., <code>http://.../dimension/length#SI</code>
        </p>
        <div class="div2">
          <h3>
            <a id="base_derived_dimensions"></a>C.1 Dimensions with SI Base or Derived Units</h3>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">Dimension</th><th rowspan="1" colspan="1">Definition URL</th><th rowspan="1" colspan="1">SI Unit</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">length</td><td rowspan="1" colspan="1">http://.../dimension/length</td><td rowspan="1" colspan="1">m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">mass</td><td rowspan="1" colspan="1">http://.../dimension/mass</td><td rowspan="1" colspan="1">kg</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">time</td><td rowspan="1" colspan="1">http://.../dimension/time</td><td rowspan="1" colspan="1">s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric current</td><td rowspan="1" colspan="1">http://.../dimension/electric_current</td><td rowspan="1" colspan="1">A</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">thermodynamic temperature</td><td rowspan="1" colspan="1">http://.../dimension/thermodynamic_temperature</td><td rowspan="1" colspan="1">K</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">amount of substance</td><td rowspan="1" colspan="1">http://.../dimension/amount_of_substance</td><td rowspan="1" colspan="1">mol</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">luminous intensity</td><td rowspan="1" colspan="1">http://.../dimension/luminous_intensity</td><td rowspan="1" colspan="1">cd</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">amount of information</td><td rowspan="1" colspan="1">http://.../dimension/amount_of_information</td><td rowspan="1" colspan="1">B</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">plane angle</td><td rowspan="1" colspan="1">http://.../dimension/plane_angle</td><td rowspan="1" colspan="1">rad</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">solid angle</td><td rowspan="1" colspan="1">http://.../dimension/solid_angle</td><td rowspan="1" colspan="1">sr</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric capacitance</td><td rowspan="1" colspan="1">http://.../dimension/electric_capacitance</td><td rowspan="1" colspan="1">F</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric charge</td><td rowspan="1" colspan="1">http://.../dimension/electric_charge</td><td rowspan="1" colspan="1">C</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric conductance</td><td rowspan="1" colspan="1">http://.../dimension/electric_conductance</td><td rowspan="1" colspan="1">S</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric inductance</td><td rowspan="1" colspan="1">http://.../dimension/electric_inductance</td><td rowspan="1" colspan="1">H</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric potential difference</td><td rowspan="1" colspan="1">http://.../dimension/electric_potential_difference</td><td rowspan="1" colspan="1">V</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric resistance</td><td rowspan="1" colspan="1">http://.../dimension/electric_resistance</td><td rowspan="1" colspan="1">&Omega;</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">energy</td><td rowspan="1" colspan="1">http://.../dimension/energy</td><td rowspan="1" colspan="1">J</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">force</td><td rowspan="1" colspan="1">http://.../dimension/force</td><td rowspan="1" colspan="1">N</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">frequency</td><td rowspan="1" colspan="1">http://.../dimension/frequence</td><td rowspan="1" colspan="1">Hz</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">illuminance</td><td rowspan="1" colspan="1">http://.../dimension/illuminance</td><td rowspan="1" colspan="1">lx</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">luminous flux</td><td rowspan="1" colspan="1">http://.../dimension/luminous_flux</td><td rowspan="1" colspan="1">lm</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">magnetic flux</td><td rowspan="1" colspan="1">http://.../dimension/magnetic_flux</td><td rowspan="1" colspan="1">Wb</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">magnetic flux density</td><td rowspan="1" colspan="1">http://.../dimension/magnetic_flux_density</td><td rowspan="1" colspan="1">T</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">power</td><td rowspan="1" colspan="1">http://.../dimension/power</td><td rowspan="1" colspan="1">W</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">pressure</td><td rowspan="1" colspan="1">http://.../dimension/pressure</td><td rowspan="1" colspan="1">Pa</td>
              </tr>
            </tbody>
          </table>
        </div>
        <div class="div2">
          <h3>
            <a id="compound_dimensions"></a>C.2 Dimensions with Compound SI Units</h3>
          <table border="1" cellpadding="3">
            <thead>
              <tr>
                <th rowspan="1" colspan="1">Dimension</th><th rowspan="1" colspan="1">Definition URL</th><th rowspan="1" colspan="1">Example Compound SI Unit</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">absorbed dose rate</td><td rowspan="1" colspan="1">http://.../dimension/absorbed_dose_rate</td><td rowspan="1" colspan="1">Gy/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">acceleration</td><td rowspan="1" colspan="1">http://.../dimension/acceleration</td><td rowspan="1" colspan="1">m/s<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">action</td><td rowspan="1" colspan="1">http://.../dimension/action</td><td rowspan="1" colspan="1">kg&middot;m<sup>2</sup>/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">angular acceleration</td><td rowspan="1" colspan="1">rad/s<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">angular speed</td><td rowspan="1" colspan="1">http://.../dimension/angular_speed</td><td rowspan="1" colspan="1">rad/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">area</td><td rowspan="1" colspan="1">http://.../dimension/area</td><td rowspan="1" colspan="1">m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">concentration</td><td rowspan="1" colspan="1">http://.../dimension/concentration</td><td rowspan="1" colspan="1">mol/m<sup>3</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">current density</td><td rowspan="1" colspan="1">http://.../dimension/current_density</td><td rowspan="1" colspan="1">A/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">dynamic viscosity</td><td rowspan="1" colspan="1">http://.../dimension/dynamic_viscosity</td><td rowspan="1" colspan="1">Pa&middot;s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric charge density</td><td rowspan="1" colspan="1">http://.../dimension/electric_charge_density</td><td rowspan="1" colspan="1">C/m<sup>3</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric field strength</td><td rowspan="1" colspan="1">http://.../dimension/electric_field_strength</td><td rowspan="1" colspan="1">V/m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">electric flux density</td><td rowspan="1" colspan="1">http://.../dimension/electric_flux_density</td><td rowspan="1" colspan="1">C/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">energy density</td><td rowspan="1" colspan="1">http://.../dimension/electric_density</td><td rowspan="1" colspan="1">J/m<sup>3</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">entropy</td><td rowspan="1" colspan="1">http://.../dimension/entropy</td><td rowspan="1" colspan="1">J/K</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">exposure</td><td rowspan="1" colspan="1">http://.../dimension/exposure</td><td rowspan="1" colspan="1">C/kg</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">heat capacity</td><td rowspan="1" colspan="1">http://.../dimension/heat_capacity</td><td rowspan="1" colspan="1">J/K</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">heat flux density</td><td rowspan="1" colspan="1">http://.../dimension/heat_flux_density</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">irradiance</td><td rowspan="1" colspan="1">http://.../dimension/irradiance</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">kinematic viscosity</td><td rowspan="1" colspan="1">http://.../dimension/kinematic_viscosity</td><td rowspan="1" colspan="1">m<sup>2</sup>/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">linear frequency</td><td rowspan="1" colspan="1">http://.../dimension/linear_frequence</td><td rowspan="1" colspan="1">1/(m&middot;s)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">linear mass density</td><td rowspan="1" colspan="1">http://.../dimension/linear_mass_density</td><td rowspan="1" colspan="1">kg/m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">luminance</td><td rowspan="1" colspan="1">http://.../dimension/luminance</td><td rowspan="1" colspan="1">cd/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">magentic field strength</td><td rowspan="1" colspan="1">http://.../dimension/magentic_field_strength</td><td rowspan="1" colspan="1">A/m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">mass density</td><td rowspan="1" colspan="1">http://.../dimension/mass_density</td><td rowspan="1" colspan="1">kg/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">molar energy</td><td rowspan="1" colspan="1">http://.../dimension/molar_energy</td><td rowspan="1" colspan="1">J/mol</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">molar entropy</td><td rowspan="1" colspan="1">http://.../dimension/molar_entropy</td><td rowspan="1" colspan="1">J/(mol&middot;K)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">molar heat capacity</td><td rowspan="1" colspan="1">http://.../dimension/molar_heat_mass</td><td rowspan="1" colspan="1">J/(mol&middot;K)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">moment of force</td><td rowspan="1" colspan="1">http://.../dimension/moment_of_force</td><td rowspan="1" colspan="1">J/rad</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">moment of inertia</td><td rowspan="1" colspan="1">http://.../dimension/moment_of_inertia</td><td rowspan="1" colspan="1">kg&middot;m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">momentum</td><td rowspan="1" colspan="1">http://.../dimension/momentum</td><td rowspan="1" colspan="1">kg&middot;m/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">permeability</td><td rowspan="1" colspan="1">http://.../dimension/permeability</td><td rowspan="1" colspan="1">H/m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">permittivity</td><td rowspan="1" colspan="1">http://.../dimension/permittivity</td><td rowspan="1" colspan="1">F/m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">power density</td><td rowspan="1" colspan="1">http://.../dimension/power_density</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">radiance</td><td rowspan="1" colspan="1">http://.../dimension/radiance</td><td rowspan="1" colspan="1">W/(m<sup>2</sup>&middot;sr)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">radiant intenstiy</td><td rowspan="1" colspan="1">http://.../dimension/radiant_intensity</td><td rowspan="1" colspan="1">W/sr</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">specific heat capacity</td><td rowspan="1" colspan="1">http://.../dimension/specific_heat_capacity</td><td rowspan="1" colspan="1">J/(kg&middot;K)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">specific energy</td><td rowspan="1" colspan="1">http://.../dimension/specific_energy</td><td rowspan="1" colspan="1">J/kg</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">specific entropy</td><td rowspan="1" colspan="1">http://.../dimension/specific_entroy</td><td rowspan="1" colspan="1">J/(kg&middot;K)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">specific volume</td><td rowspan="1" colspan="1">http://.../dimension/specific_volume</td><td rowspan="1" colspan="1">m<sup>3</sup>/kg</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">surface energy density</td><td rowspan="1" colspan="1">http://.../dimension/surface_energy_density</td><td rowspan="1" colspan="1">J/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">surface power density</td><td rowspan="1" colspan="1">http://.../dimension/surface_power_density</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">surface tension</td><td rowspan="1" colspan="1">http://.../dimension/surface_tension</td><td rowspan="1" colspan="1">N/m</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">thermal conductivity</td><td rowspan="1" colspan="1">http://.../dimension/thermal_conductivity</td><td rowspan="1" colspan="1">W/(m&middot;K)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">speed</td><td rowspan="1" colspan="1">http://.../dimension/speed</td><td rowspan="1" colspan="1">m/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">volume</td><td rowspan="1" colspan="1">http://.../dimension/volume</td><td rowspan="1" colspan="1">m<sup>3</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">volume flow</td><td rowspan="1" colspan="1">http://.../dimension/volume_flow</td><td rowspan="1" colspan="1">m<sup>3</sup>/s</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">wave number</td><td rowspan="1" colspan="1">http://.../dimension/wave_number</td><td rowspan="1" colspan="1">1/m</td>
              </tr>
            </tbody>
          </table>
        </div>
      </div>
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