<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:x="urn:schemas-microsoft-com:office:excel" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<meta name="ProgId" content="Word.Document">
<meta name="Generator" content="Microsoft Word 15">
<meta name="Originator" content="Microsoft Word 15">
<link rel="File-List" href="cid:filelist.xml@01D8116D.2CBBC400"><!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:SpellingState>Clean</w:SpellingState>
<w:DocumentKind>DocumentEmail</w:DocumentKind>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:EnvelopeVis/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:DoNotExpandShiftReturn/>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="false" DefSemiHidden="false" DefQFormat="false" DefPriority="99" LatentStyleCount="376">
<w:LsdException Locked="false" Priority="0" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index 9"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" Name="toc 9"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Normal Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="footnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="annotation text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="header"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="footer"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="index heading"/>
<w:LsdException Locked="false" Priority="35" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="table of figures"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="envelope address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="envelope return"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="footnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="annotation reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="line number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="page number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="endnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="endnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="table of authorities"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="macro"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="toa heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Bullet"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Bullet 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Bullet 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Bullet 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Bullet 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Number 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Number 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Number 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Number 5"/>
<w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Closing"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Signature"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="true" UnhideWhenUsed="true" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Continue"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Continue 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Continue 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Continue 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="List Continue 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Message Header"/>
<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Salutation"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Date"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text First Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text First Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Note Heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true" UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true" UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Mention"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Smart Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Hashtag"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Unresolved Mention"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" Name="Smart Link"/>
</w:LatentStyles>
</xml><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:roman;
mso-font-pitch:variable;
mso-font-signature:-536869121 1107305727 33554432 0 415 0;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-469750017 -1073732485 9 0 511 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin:0in;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-fareast-font-family:Calibri;}
a:link, span.MsoHyperlink
{mso-style-noshow:yes;
mso-style-priority:99;
color:#0563C1;
text-decoration:underline;
text-underline:single;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-noshow:yes;
mso-style-priority:99;
color:#954F72;
text-decoration:underline;
text-underline:single;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-style-unhide:no;
mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-fareast-font-family:Calibri;}
span.EmailStyle18
{mso-style-type:personal-compose;
mso-style-noshow:yes;
mso-style-unhide:no;
mso-ansi-font-size:11.0pt;
mso-bidi-font-size:11.0pt;
font-family:"Arial",sans-serif;
mso-ascii-font-family:Arial;
mso-hansi-font-family:Arial;
mso-bidi-font-family:"Times New Roman";
color:windowtext;}
span.SpellE
{mso-style-name:"";
mso-spl-e:yes;}
.MsoChpDefault
{mso-style-type:export-only;
mso-default-props:yes;
font-size:10.0pt;
mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;
font-family:"Calibri",sans-serif;
mso-ascii-font-family:Calibri;
mso-fareast-font-family:Calibri;
mso-hansi-font-family:Calibri;
mso-bidi-font-family:"Times New Roman";}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 10]><style>/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Calibri",sans-serif;
mso-ascii-font-family:Calibri;
mso-hansi-font-family:Calibri;
mso-bidi-font-family:"Times New Roman";}
</style><![endif]--><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-US" link="#0563C1" vlink="#954F72" style="tab-interval:.5in;word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">I'm getting questions about the <span class="SpellE">eqn</span> on page 11 for the actual density of water<br>
and <span class="SpellE">s.f.</span> in the calculations, particularly for the error and % error and what<br>
happens when you subtract two numbers and you get zero to the correct<br>
number of <span class="SpellE">s.f.</span> Also, setting <span class="SpellE">s.f.</span> in your data table and graph.<br>
<br>
The <span class="SpellE">eqn</span> on page 11 uses two numbers, -0.00030 and 1.0042. People<br>
have asked if these are exact. No they aren't. Someone took temperature<br>
and density data between 20 and 30 <span class="SpellE">degC</span> and fit the data to a linear eqn.<br>
In doing so the sig. fig. for these numbers were determined from the <span class="SpellE">
s.f.</span><br>
for the temp and density used. You need to use the <span class="SpellE">s.f.</span> in these numbers<br>
and the <span class="SpellE">s.f.</span> for your temperature to determine the proper
<span class="SpellE">s.f.</span> for the<br>
actual density. This can be rather tricky since you need to use the rules<br>
for <span class="SpellE">mult</span>/div and add/<span class="SpellE">subtr</span>. in the same calculation (<span class="SpellE">mult</span>. rule first followed<br>
by add. rule). I can pretty much make assurances you won't get 1 or 1.0.<br>
Just so all of you know, water has it's greatest density of 1.00000 g/mL at<br>
4.0 Celsius. It's density is 1.0 g/mL (two s.f.,1 decimal place) from 0 C to 100 C.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">You actually encountered this in the pre-lab.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><br>
<span style="color:black">You need to report the proper number of <span class="SpellE">
s.f.</span> in the table for all the numbers,</span><br>
<span style="color:black">including the error and % error. This applies even if you use Excel. You will</span><br>
<span style="color:black">have to set decimal places in order to get the correct sig. fig. in Excel since it</span><br>
<span style="color:black">doesn't understand sig. fig. I've explained how to do this on my web page.<o:p></o:p></span></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"> <br>
<span style="color:black">While I'm at it, what happens when you subtract two numbers and you get</span><br>
<span style="color:black">zero? For example, lets say you subtract two numbers and at least one of</span><br>
<span style="color:black">them is only to the 3rd decimal place and the result rounds to 0.000 in the</span><br>
<span style="color:black">third decimal place. This would be the proper way to report it. This means</span><br>
<span style="color:black">"one" <span class="SpellE">s.f.</span>, in the last decimal place. Carry any extra digits to the right of the</span><br>
<span style="color:black">third decimal place to the next calculation, if there is one, remembering if</span><br>
<span style="color:black">you are doing a multiplication or division in the next steps to report the</span><br>
<span style="color:black">final result to 1 <span class="SpellE">s.f.</span> This could very well occur for your error and % error</span><br>
<span style="color:black">columns.</span><br>
<br>
<span style="color:black">You also need to use correct <span class="SpellE">s.f.</span> on the axes for your graphs. The
<span class="SpellE">s.f.</span></span><br>
<span style="color:black">in your density and intercept are determined by the <span class="SpellE">
s.f.</span> in your mass and</span><br>
<span style="color:black">volume being plotted. Since doing a best-fit line averages out the error in</span><br>
<span style="color:black">your actual data points, if you have enough data points you can usually</span><br>
<span style="color:black">gain one <span class="SpellE">s.f.</span> from a graph. For instance, with enough data points, if you</span><br>
<span style="color:black">had 3 <span class="SpellE">s.f.</span> for the mass and 3
<span class="SpellE">s.f.</span> for the volume you could report 4 <span class="SpellE">
s.f.</span> for</span><br>
<span style="color:black">the slope and intercept. Two or three data points is not enough to gain a
</span><br>
<span class="SpellE"><span style="color:black">s.f.</span></span><span style="color:black"> when taking an average or from a graph. Why? Think about this from</span><br>
<span style="color:black">the perspective of plotting a best-fit line. The purpose of a best-fit line is</span><br>
<span style="color:black">to "average out" the error in the data points. If you have only two data</span><br>
<span style="color:black">points the best-fit line will go right through them and will not average out</span><br>
<span style="color:black">the error in the data. Adding one more (total of 3 data points) isn't much</span><br>
<span style="color:black">better. The more data points you have the safer it is to claim an extra
<span class="SpellE">s.f.</span></span><br>
<span style="color:black">in the numbers from the best-fit line (slope, intercept). How many should</span><br>
<span style="color:black">you have before you can say it's safe to gain a <span class="SpellE">
s.f.</span> That's hard to say. It</span><br>
<span style="color:black">depends on the data you have. <b>For our purposes in lab we'll say you</b></span><br>
<b><span style="color:black">need </span><span style="color:red">at least four</span><span style="color:black">.</span></b><br>
<br>
This also applies when taking an average of data. I explained this in lecture<br>
and it's related to what I discussed above. Technically, it's not safe to claim<br>
an extra <span class="SpellE">s.f.</span> when averaging only 2 data points since it really doesn't effectively<br>
average out the experimental error in the data (think about fitting a best-fit<br>
line to only two data points as explained above). Adding a third data point<br>
doesn't help much. Again, for our purposes in lab you can only gain a <span class="SpellE">
s.f.</span> if<br>
you have more than 3 data points., for either an average or numbers from a<br>
<span style="color:black">graph.</span><br>
<br>
<span style="color:black">In reality, this is simplifying error analysis. Error analysis is much more</span><br>
<span style="color:black">complicated than this but beyond the scope of this class. Depending on<o:p></o:p></span></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">your data and the “noise” in your data it could take hundreds of data points<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">in order to safely gain a
<span class="SpellE">s.f.</span></span><span style="font-family:"Arial",sans-serif"><br>
<br>
<span style="color:black">Finally, if you set the <span class="SpellE">s.f.</span> properly in your Excel table before making a graph</span><br>
<span style="color:black">they will carry over to the graph. This is at least true if using the PC version</span><br>
<span style="color:black">of Excel. I'm not sure if this is true if using a version for another operating</span><br>
<span style="color:black">system or a knockoff (Google Docs, OpenOffice, etc.). You can set
<span class="SpellE">s.f.</span></span><br>
<span style="color:black">on the axes by editing the axes.<o:p></o:p></span></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">You also need to use the proper number of
<span class="SpellE">s.f.</span> in the data entry for exp 1 (SCM).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">Do your Excel table first and then just copy those values over to the data<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;color:black">entry program.</span><span style="font-family:"Arial",sans-serif"><br>
<br>
<span style="color:black">Dr. Zellmer</span><o:p></o:p></span></p>
</div>
</body>
</html>