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<title>Temperature Units and User-Defined Default Units</title>
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<p style="Title" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Temperature Units and User-Defined Default Units</p>
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<f family="Arial" charset="0" size="10">Temperature and Functional Units</f>
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<f family="Arial" charset="0" size="10">User-Defined Default Unit Dialog</f>
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<f family="Verdana" charset="0" size="10">Temperature and Functional Units</f>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Temperature units do not follow a typical multiplicative relationship with other units of the same quantity. The most common examples are the Fahrenheit and Celsius temperature scales; these scales are linear transformations from each other and from the Mathcad base temperature unit, the Kelvin. </p>
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<phrase>Fahrenheit temperature units</phrase>
<phrase>Celsius temperature units</phrase>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">It is always possible to define Celsius and Fahrenheit scaling functions and to use them in the <b>
<u>
<link href=".\..\..\Techniques\opera.xmcd" title="Links to section" popup="false">postfix operator</link>
</u>
</b>. These forward transformations are built into Mathcad so you can enter temperature expressions in natural notation and return results that have the quantity temperature associated with them.</p>
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<phrase>postfix operator</phrase>
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<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">If you type in </p>
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<ml:real>100</ml:real>
<ml:id xml:space="preserve">°C</ml:id>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">you get an error message.</p>
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<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">But if you insert the postfix operator by typing <b>[Ctrl] [Shift] X</b> or open the <b>Evaluation</b> toolbar and click the <b>x f</b> expression and then add °C from the Insert Unit menu: </p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> x f </p>
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<ml:id xml:space="preserve">°F</ml:id>
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<ml:id xml:space="preserve">°F</ml:id>
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<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">When entering a negative temperature, select the <i>entire</i> number before inserting the postfix operator. Otherwise, the entire expression is negated. Note the difference between</p>
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<ml:id xml:space="preserve">°F</ml:id>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">and</p>
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<ml:id xml:space="preserve">°F</ml:id>
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<ml:real>-10</ml:real>
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<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">In the second case, Mathcad automatically adds parentheses around the number to clarify the evaluation.</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">In addition, the <i>units placeholder accepts these same function names</i>, and automatically applies the function inverse, just as the multiplicative units divide by appropriate scaling:</p>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">T1</ml:id>
<ml:unitOverride>
<ml:id xml:space="preserve">°C</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="12"></rendering>
</region>
<region region-id="2108" left="162" top="792.75" width="60" height="15.75" align-x="182.25" align-y="804" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">T1</ml:id>
<ml:unitOverride>
<ml:id xml:space="preserve">°F</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="13"></rendering>
</region>
<region region-id="1608" left="6" top="822.75" width="340.5" height="71.25" align-x="6" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Because you must apply the function inverse, rather than simply dividing by the unit, as with linear units, these functional expressions must be used by themselves in the unit placeholder. The operations required to take the inverse are not necessarily commutative, as they would be in an expression containing multiplicative units.</p>
</text>
</region>
<region region-id="3621" left="6" top="912.75" width="338.25" height="57" align-x="6" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>
<c val="#008080">Note:</c>
</b> To type the degree symbol in a math region, press <b>[Alt]0176 </b>
<inlineAttr font-weight="normal">on the </inlineAttr>
<b>Number </b>
<inlineAttr font-weight="normal">keypad (not the numbers on the main keyboard)</inlineAttr>. You can also use the buttons on the <b>Custom Characters</b> toolbar or choices from the <b>Insert Unit</b> menu.</p>
</text>
</region>
<region region-id="3502" left="0" top="978" width="6000" height="0.75" align-x="0" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1614" left="6" top="986.25" width="135" height="12" align-x="6" align-y="996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Verdana" charset="0" size="10">Temperature Differences</f>
</p>
</text>
</region>
<region region-id="1548" left="6" top="1008.75" width="339.75" height="42.75" align-x="6" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mathcad includes multiplicative units for changes in temperature, <f family="Symbol" charset="2" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">D</inlineAttr>
</f>°<f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">F and </inlineAttr>
</f>
<f family="Symbol" charset="2" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">D</inlineAttr>
</f>°<f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">C. If you convert two Fahrenheit temperatures to Kelvin and take their difference, you get</inlineAttr>
</f>
</p>
</text>
</region>
<region region-id="3633" left="36" top="1066.5" width="342.75" height="33.75" align-x="287.25" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:minus></ml:minus>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:apply>
<ml:div></ml:div>
<ml:real>5</ml:real>
<ml:real>9</ml:real>
</ml:apply>
<ml:parens>
<ml:apply>
<ml:minus></ml:minus>
<ml:id xml:space="preserve">Tα</ml:id>
<ml:real>32</ml:real>
</ml:apply>
</ml:parens>
</ml:apply>
<ml:real>273.16</ml:real>
</ml:apply>
<ml:parens>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:apply>
<ml:div></ml:div>
<ml:real>5</ml:real>
<ml:real>9</ml:real>
</ml:apply>
<ml:parens>
<ml:apply>
<ml:minus></ml:minus>
<ml:id xml:space="preserve">Tβ</ml:id>
<ml:real>32</ml:real>
</ml:apply>
</ml:parens>
</ml:apply>
<ml:real>273.16</ml:real>
</ml:apply>
</ml:parens>
</ml:apply>
<ml:symResult>
<ml:apply>
<ml:minus></ml:minus>
<ml:apply>
<ml:div></ml:div>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>5</ml:real>
<ml:id xml:space="preserve">Tα</ml:id>
</ml:apply>
</ml:parens>
<ml:real>9</ml:real>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:apply>
<ml:div></ml:div>
<ml:real>5</ml:real>
<ml:real>9</ml:real>
</ml:apply>
<ml:id xml:space="preserve">Tβ</ml:id>
</ml:apply>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="14"></rendering>
</region>
<region region-id="1572" left="6" top="1116.75" width="107.25" height="14.25" align-x="6" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The unit <f family="Symbol" charset="2" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">D</inlineAttr>
</f>°<f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">F is equal to</inlineAttr>
</f>
</p>
</text>
</region>
<region region-id="2133" left="36" top="1144.5" width="67.5" height="33.75" align-x="62.25" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Δ°F</ml:id>
</ml:eval>
<resultFormat>
<fraction precision="12" use-mixed-numbers="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"></fraction>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="15"></rendering>
</region>
<region region-id="2137" left="126" top="1152.75" width="42" height="14.25" align-x="143.25" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">similarly, </p>
</text>
</region>
<region region-id="2138" left="192" top="1152.75" width="66" height="15.75" align-x="219.75" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Δ°C</ml:id>
</ml:eval>
</math>
<rendering item-idref="16"></rendering>
</region>
<region region-id="1732" left="6" top="1188.75" width="174.75" height="14.25" align-x="6" align-y="1200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Note that <f family="Symbol" charset="2">D</f>°F is really just 1 Rankine: </p>
</text>
</region>
<region region-id="2019" left="192" top="1188.75" width="56.25" height="15.75" align-x="218.25" align-y="1200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Δ°F</ml:id>
<ml:unitOverride>
<ml:id xml:space="preserve">R</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="17"></rendering>
</region>
<region region-id="2238" left="6" top="1212.75" width="341.25" height="28.5" align-x="6" align-y="1224" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Temperature differences are required to convert results when finding the difference between two temperatures.</p>
</text>
</region>
<region region-id="3642" left="36" top="1254.75" width="25.5" height="14.25" align-x="36" align-y="1266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
<c val="#008080">Right:</c>
</p>
</text>
</region>
<region region-id="3643" left="84" top="1254.75" width="112.5" height="15.75" align-x="155.25" align-y="1266" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:minus></ml:minus>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">Δ°F</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="18"></rendering>
</region>
<region region-id="3644" left="36" top="1278.75" width="33.75" height="14.25" align-x="36" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<c val="#008080">Wrong:</c>
</p>
</text>
</region>
<region region-id="3645" left="84" top="1278.75" width="138.75" height="15.75" align-x="155.25" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:minus></ml:minus>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">°F</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="19"></rendering>
</region>
<region region-id="2233" left="6" top="1308.75" width="332.25" height="28.5" align-x="6" align-y="1320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Temperature differences are required when you add two temperatures, because doing so implies a change from the current temperature. </p>
</text>
</region>
<region region-id="3678" left="36" top="1356.75" width="25.5" height="14.25" align-x="36" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<c val="#008080">Right:</c>
</p>
</text>
</region>
<region region-id="3679" left="84" top="1356.75" width="124.5" height="15.75" align-x="168.75" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>20</ml:real>
<ml:id xml:space="preserve">Δ°F</ml:id>
</ml:apply>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">°F</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="20"></rendering>
</region>
<region region-id="3688" left="252" top="1356.75" width="126.75" height="15.75" align-x="324" align-y="1368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="auto-select" resultMultiplicationStyle="auto-select">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">°F</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="21"></rendering>
</region>
<region region-id="3681" left="36" top="1380.75" width="33.75" height="14.25" align-x="36" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
<c val="#008080">Wrong:</c>
</p>
</text>
</region>
<region region-id="3682" left="84" top="1380.75" width="132.75" height="15.75" align-x="156" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>10</ml:real>
</ml:apply>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°F</ml:id>
<ml:real>20</ml:real>
</ml:apply>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">°F</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="22"></rendering>
</region>
<region region-id="2151" left="0" top="1404" width="6000" height="6" align-x="0" align-y="1404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1778" left="6" top="1410.75" width="338.25" height="57" align-x="6" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Temperature differences <i>can</i> be used in combination with other units. It's important to distinguish between a temperature difference and an absolute temperature when you enter or convert temperature results. For example, calculate the temperature at which an electronic component fails:</p>
</text>
</region>
<region region-id="1858" left="36" top="1482.75" width="72" height="15.75" align-x="70.5" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">Tamb</ml:id>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">°C</ml:id>
<ml:real>25</ml:real>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="23"></rendering>
</region>
<region region-id="1859" left="132" top="1482.75" width="92.25" height="14.25" align-x="132" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">ambient temperature</p>
</text>
</region>
<region region-id="1860" left="36" top="1504.5" width="80.25" height="33.75" align-x="63" align-y="1524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">θJA</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>10</ml:real>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">Δ°C</ml:id>
<ml:id xml:space="preserve">W</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="24"></rendering>
</region>
<region region-id="1861" left="132" top="1512.75" width="113.25" height="14.25" align-x="132" align-y="1524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">temperature rise per watt</p>
</text>
</region>
<region region-id="1862" left="36" top="1542.75" width="62.25" height="15.75" align-x="57" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">Pd</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>13</ml:real>
<ml:id xml:space="preserve">W</ml:id>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="25"></rendering>
</region>
<region region-id="1863" left="132" top="1542.75" width="155.25" height="14.25" align-x="132" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Maximum power rating</p>
</text>
</region>
<region region-id="1799" left="6" top="1572.75" width="267" height="14.25" align-x="6" align-y="1584" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The temperature at which the component fails is given by</p>
</text>
</region>
<region region-id="1864" left="36" top="1596.75" width="117" height="15.75" align-x="63.75" align-y="1608" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">Tfail</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">Tamb</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:id xml:space="preserve">θJA</ml:id>
<ml:id xml:space="preserve">Pd</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="26"></rendering>
</region>
<region region-id="1865" left="36" top="1626.75" width="92.25" height="15.75" align-x="63" align-y="1638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Tfail</ml:id>
</ml:eval>
<resultFormat>
<general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="4"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="27"></rendering>
</region>
<region region-id="1866" left="138" top="1626.75" width="102" height="14.25" align-x="138" align-y="1638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">in degrees Kelvin, or </p>
</text>
</region>
<region region-id="1867" left="36" top="1656.75" width="74.25" height="15.75" align-x="63" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Tfail</ml:id>
<ml:unitOverride>
<ml:id xml:space="preserve">°C</ml:id>
</ml:unitOverride>
</ml:eval>
<resultFormat>
<general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="4"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="28"></rendering>
</region>
<region region-id="1868" left="138" top="1656.75" width="72.75" height="15.75" align-x="165" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Tfail</ml:id>
<ml:unitOverride>
<ml:id xml:space="preserve">°F</ml:id>
</ml:unitOverride>
</ml:eval>
<resultFormat>
<general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="4"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="29"></rendering>
</region>
<region region-id="2256" left="6" top="1680.75" width="341.25" height="85.5" align-x="17.25" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Note that many material properties and component specifications, such as the temperature rise per watt, or the specific heat, and others, are implicitly given as change in temperature per quantity or quantity per change in temperature. If you are doing a calculation with such a property, given in degrees Kelvin, and you wish to convert results into Celsius or Fahrenheit, you may need to use the <f family="Symbol" charset="2" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">D</inlineAttr>
</f>
<f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">°C and </inlineAttr>
</f>
<f family="Symbol" charset="2">D</f>°F unit functions.</p>
</text>
</region>
<region region-id="1706" left="6" top="1784.25" width="245.25" height="12" align-x="6" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Verdana" charset="0" size="10">Building Your Own Scaling and Unit Functions</f>
</p>
</text>
</region>
<region region-id="1707" left="6" top="1800.75" width="327.75" height="57" align-x="6" align-y="1812" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can use the units placeholder with other conversion functions as well. These functions must consist of a defined function and inverse pair, so that Mathcad knows how to apply a function's inverse when used in the placeholder position. </p>
</text>
</region>
<region region-id="1822" left="6" top="1866.75" width="335.25" height="57" align-x="6" align-y="1878" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">It's easy to define your own function pairs. The forward function, used in the postfix operator, is a normal Mathcad function. The "inverse" must have the same name, preceded by the <b>[</b>
<f family="Verdana" charset="0" size="10">
<b>/]</b>
</f> character. For example, below we define one version of the unit decibels. </p>
</text>
</region>
<region region-id="2258" left="0" top="1932" width="6000" height="6" align-x="0" align-y="1932" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1878" left="36" top="1941.75" width="84.75" height="41.25" align-x="84.75" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve" subscript="20">dB</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:pow></ml:pow>
<ml:real>10</ml:real>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>20</ml:real>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="30"></rendering>
</region>
<region region-id="1879" left="126" top="1962.75" width="110.25" height="20.25" align-x="177.75" align-y="1974" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve" subscript="20">/dB</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>20</ml:real>
<ml:apply>
<ml:id xml:space="preserve">log</ml:id>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="31"></rendering>
</region>
<region region-id="2024" left="36" top="1998.75" width="75" height="20.25" align-x="60.75" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">Am</ml:id>
<ml:apply fixity="postfix">
<ml:id xml:space="preserve" subscript="20">dB</ml:id>
<ml:real>23</ml:real>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="32"></rendering>
</region>
<region region-id="2023" left="126" top="1998.75" width="72.75" height="15.75" align-x="150" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Am</ml:id>
</ml:eval>
</math>
<rendering item-idref="33"></rendering>
</region>
<region region-id="2056" left="36" top="2034.75" width="78" height="20.25" align-x="60" align-y="2046" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">Am</ml:id>
<ml:unitOverride>
<ml:id xml:space="preserve" subscript="20">dB</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="34"></rendering>
</region>
<region region-id="2113" left="6" top="2070.75" width="342" height="57" align-x="6" align-y="2082" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">Note: </c>
</b>To start the editing mode that lets you type the <b>[</b>
<f family="Verdana" charset="0" size="10">
<b>/]</b>
</f> character, type <b>[:]</b> and put your cursor in the first placeholder; then type <b>[Ctrl] [Shift] K</b>. You can also enter the /°F and /°C names from the <b>Custom Characters</b> toolbar and backspace over the temperature symbols, leaving just the <b>[</b>
<f family="Verdana" charset="0" size="10">
<b>/]</b>
</f>.</p>
</text>
</region>
<region region-id="1936" left="6" top="2142.75" width="311.25" height="28.5" align-x="6" align-y="2154" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">You can use any of the defined inverse (slash) functions as normal functions as well. Here is one in the postfix operator:</p>
</text>
</region>
<region region-id="1937" left="36" top="2184.75" width="117.75" height="15.75" align-x="105" align-y="2196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">/°C</ml:id>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>450</ml:real>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
</ml:eval>
</math>
<rendering item-idref="35"></rendering>
</region>
<region region-id="1940" left="6" top="2214.75" width="281.25" height="14.25" align-x="6" align-y="2226" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This function is useful if you wish to convert scaling on a graph:</p>
</text>
</region>
<region region-id="1943" left="36" top="2244.75" width="48.75" height="15.75" align-x="46.5" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>10</ml:real>
</ml:range>
</ml:define>
</math>
<rendering item-idref="36"></rendering>
</region>
<region region-id="1944" left="108" top="2244.75" width="81" height="17.25" align-x="131.25" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">T0</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:id xml:space="preserve">i</ml:id>
<ml:real>30</ml:real>
</ml:apply>
</ml:parens>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="37"></rendering>
</region>
<region region-id="1947" left="204" top="2236.5" width="90.75" height="33.75" align-x="225.75" align-y="2256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">R0</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>8.31451</ml:real>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">J</ml:id>
<ml:id xml:space="preserve">K</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="38"></rendering>
</region>
<region region-id="1964" left="114" top="2274.75" width="217.5" height="42.75" align-x="114" align-y="2286" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The expression in the x axis placeholder is the postfix application of the Kelvin to Celsius conversion to the vector T.</p>
</text>
</region>
<region region-id="1955" left="36" top="2271" width="66.75" height="40.5" align-x="53.25" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">P</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:id xml:space="preserve">R0</ml:id>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">T0</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>3</ml:real>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">cm</ml:id>
<ml:real>3</ml:real>
</ml:apply>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="39"></rendering>
</region>
<region region-id="1965" left="36" top="2328" width="264" height="139.5" align-x="36" align-y="2328" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<plot disable-calc="false" item-idref="40"></plot>
<rendering item-idref="41"></rendering>
</region>
<region region-id="2261" left="0" top="2478" width="6000" height="6" align-x="0" align-y="2478" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="2259" left="6" top="2486.25" width="171.75" height="12" align-x="6" align-y="2496" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Verdana" charset="0" size="10">Other Built-in Scaling Functions</f>
</p>
</text>
</region>
<region region-id="2260" left="6" top="2508.75" width="325.5" height="42.75" align-x="6" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Here are some other scaling pairs that are built into Mathcad. As with all the units shown previously, these are functions and must be used in the postfix operator or with normal function call notation.</p>
</text>
</region>
<region region-id="1897" left="6" top="2562.75" width="338.25" height="28.5" align-x="6" align-y="2574" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">FIF, for feet-inches-fraction input and display takes a string of measurements as input or converts measurements of length on the output.</p>
</text>
</region>
<region region-id="1905" left="36" top="2616.75" width="134.25" height="15.75" align-x="108.75" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">FIF</ml:id>
<ml:str xml:space="preserve">9' 6-1/4</ml:str>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">ft</ml:id>
</ml:unitOverride>
</ml:eval>
<resultFormat>
<general precision="5" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="42"></rendering>
</region>
<region region-id="1901" left="210" top="2616.75" width="119.25" height="15.75" align-x="246" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2.6</ml:real>
<ml:id xml:space="preserve">ft</ml:id>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">FIF</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="43"></rendering>
</region>
<region region-id="1904" left="36" top="2646.75" width="150" height="15.75" align-x="96.75" align-y="2658" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">/FIF</ml:id>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>3</ml:real>
<ml:id xml:space="preserve">m</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
</ml:eval>
</math>
<rendering item-idref="44"></rendering>
</region>
<region region-id="2263" left="210" top="2646.75" width="125.25" height="15.75" align-x="290.25" align-y="2658" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">FIF</ml:id>
<ml:str xml:space="preserve">2' 6-1/2</ml:str>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">in</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="45"></rendering>
</region>
<region region-id="2104" left="6" top="2688.75" width="320.25" height="14.25" align-x="22.5" align-y="2700" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">DMS for degrees, minutes and seconds of a given angle. </p>
</text>
</region>
<region region-id="2007" left="36" top="2721.75" width="137.25" height="57.75" align-x="114.75" align-y="2754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply fixity="postfix">
<ml:id xml:space="preserve">DMS</ml:id>
<ml:matrix rows="3" cols="1">
<ml:real>61</ml:real>
<ml:real>1</ml:real>
<ml:real>1.017</ml:real>
</ml:matrix>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">rad</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
<rendering item-idref="46"></rendering>
</region>
<region region-id="2008" left="210" top="2721.75" width="138" height="57.75" align-x="262.5" align-y="2754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2</ml:real>
<ml:id xml:space="preserve">π</ml:id>
</ml:apply>
<ml:real>5.9</ml:real>
</ml:apply>
<ml:id xml:space="preserve">rad</ml:id>
</ml:apply>
<ml:unitOverride>
<ml:id xml:space="preserve">DMS</ml:id>
</ml:unitOverride>
</ml:eval>
</math>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The hours/minutes/seconds function takes a value with dimensions of time and returns the string showing hh:mm:ss when used in the units placeholder. Inversely, you can give it a string (such as time data read from a file) and it returns a time in seconds.</p>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The built-in functions include error checking for appropriate inputs. Click on the equation below to see the error message</p>
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<math error="The argument must be in [hh:mm:ss.sss] format." optimize="false" disable-calc="false">
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<ml:str xml:space="preserve">0:2</ml:str>
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<math error="This value must be a scalar or a matrix." optimize="false" disable-calc="false">
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<ml:matrix rows="3" cols="1">
<ml:str xml:space="preserve">temp</ml:str>
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<ml:real>300</ml:real>
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<ml:real>245</ml:real>
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<ml:id xml:space="preserve">°F</ml:id>
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<pageBreak></pageBreak>
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<region region-id="1698" left="6" top="3086.25" width="178.5" height="12" align-x="16.5" align-y="3096" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="user">
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<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Verdana" charset="0" size="10">User-Defined Default Unit Dialog</f>
</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can use the Unit System tab on the <b>Tools &gt; Worksheet Options</b> dialog to choose which built-in units Mathcad uses to reduce values. Default units for any quantity can be changed to any unit with the same quantity by selecting a "Custom" unit system. The custom unit system can be based around any of the existing systems and modified to suit your work. For example, you can create a custom unit system with all the base default derived units from the SI unit system, except that lengths are returned in inches.</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">There must always be seven base units for each system, but you can have as many or as few derived unit simplification rules as you like. For example, if you wish to simplify every value with units of 1/s to Hertz, simply add Hz to the list of derived units in your custom system. If you no longer wish values with quantity Conductance to display in Siemens, remove the unit S from the list. </p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"></p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can also change the default reduced value to any of the other built-in units for existing quantities, like MPa instead of Pa for pressure. Delete the existing derived unit rule for the quantity of interest and replace it with a new rule that uses the unit you specify. This is convenient if your results in a given document are all of a different scale than the base unit in the current system. There are even derived combination units for quantities such as Torque, which can be expressed in ft·lbf, or energy, in kW·hr.</p>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Unit settings can be made in the Normal Template as well, so they are customized for each new document that you create. </p>
</text>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Look in <b>Help</b> under "Defining your own units" to see how to define your own built-in units in Mathcad. You can define built-in units for unit reduction in your own copy of Mathcad. These will work without a worksheet assignment but will not work in any unmodified copy of Mathcad.</p>
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<phrase>units, defining your own built-in</phrase>
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