Example: Converting Units in Plots

Plots > Working with Plots > Example: Converting Units in Plots

Change the units in an axis expression.

1. Define a range variable and a function with units.

2. Plot the function.

<region id="ID0EQWTIB" actualWidth="596.2" actualHeight="312" top="249.60000000000002" left="19.200000000000003" height="312" width="596.2" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white" origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="12">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <graph-size width="442.6" height="254.4" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="5">
          <axisLine position="origin" positionticmark="0" legendWidth="60.93" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="5">
          <axisLine position="origin" positionticmark="0" legendWidth="110.68" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve">dist</id>
                  <id xml:space="preserve">x</id>
                </apply>
              </math>
              <math>
                <id labels="UNIT" xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">m</id>
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

The tick mark values are displayed in terms of the base units of the unit system that you are using, regardless of the units entered.

3. Change the units in which the y-axis expression is plotted by deleting the meter abbreviation m from the unit placeholder and inserting the inch abbreviation in in the empty placeholder.

<region id="ID0E6YTIB" actualWidth="595.2" actualHeight="312" top="883.20000000000016" left="19.200000000000003" height="312" width="595.2" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white" origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="13">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <graph-size width="441.6" height="254.4" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="5">
          <axisLine position="origin" positionticmark="0" legendWidth="60.93" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="200">
          <axisLine position="origin" positionticmark="0" legendWidth="111.65" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve">dist</id>
                  <id xml:space="preserve">x</id>
                </apply>
              </math>
              <math>
                <id labels="UNIT" xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">in</id>
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

4. Replot the same function but this time add a scaling factor in the unit placeholder instead of converting the units.

<region id="ID0EQ1TIB" actualWidth="587.488263343793" actualHeight="312" top="1286.4" left="19.200000000000003" height="312" width="587.488263343793" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="14">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
        <trace resultRef="15">
          <traceStyle color="#FF008000" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <graph-size width="414.688263343793" height="254.4" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="5">
          <axisLine position="origin" positionticmark="0" legendWidth="60.93" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="200">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="136.416666666667" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve">dist</id>
                  <id xml:space="preserve">x</id>
                </apply>
              </math>
              <math>
                <id labels="UNIT" xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">in</id>
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve">dist</id>
                  <id xml:space="preserve">x</id>
                </apply>
              </math>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <scale />
                  <real>0.1</real>
                  <id labels="UNIT" xml:space="preserve">m</id>
                </apply>
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

The traces represent equivalent numbers. For example, the second point on the first trace is at 79 in = 2 meters. On the second trace, it is as 20 * 0.1 m = 2 meters.

5. Insert two horizontal markers to mark the above two data points.

<region id="ID0EF3TIB" actualWidth="594.488263343793" actualHeight="312" top="1766.4000000000003" left="19.200000000000003" height="312" width="594.488263343793" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot background-type="white">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace resultRef="16">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
        <trace resultRef="17">
          <traceStyle color="#FF008000" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <graph-size width="421.688263343793" height="254.4" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="5">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="60.93" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <plotEquations>
            <plotEquation>
              <math>
                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">x</id>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="200">
          <axisLine position="ticknumberlock" positionticmark="0" legendWidth="136.416666666667" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers>
            <marker resultRef="18" display="true" color="#FFFF0000" line-style="Dot" line-weight="2" value="20">
              <real xmlns="http://schemas.mathsoft.com/math50">20</real>
            </marker>
            <marker resultRef="19" display="true" color="#FF800080" line-style="Dot" line-weight="2" value="79">
              <real xmlns="http://schemas.mathsoft.com/math50">79</real>
            </marker>
          </markers>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve">dist</id>
                  <id xml:space="preserve">x</id>
                </apply>
              </math>
              <math>
                <id labels="UNIT" xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">in</id>
              </math>
            </plotEquation>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id xml:space="preserve">dist</id>
                  <id xml:space="preserve">x</id>
                </apply>
              </math>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <scale />
                  <real>0.1</real>
                  <id labels="UNIT" xml:space="preserve">m</id>
                </apply>
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

Tick marks and the callout values are unitless. Only axis expressions can have units.