document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198851>Question 1198851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length and breadth of a rectangular room are 15 m and 12 m respectively. If each of these measurements is liable to a 2% error calculate the absolute error in the area calculated from these values. </SPAN>\n" );
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document.write( "Decrease the \"15 m\" dimension by 2%<BR>\n" );
document.write( "15 - 2% of 15 = 15 - 0.02*15 = 14.7<BR>\n" );
document.write( "or as a shortcut<BR>\n" );
document.write( "98% of 15 = 0.98*15 = 14.7\r<BR>\n" );
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document.write( "This is the smallest possible value the length can be if it is reported as \"15 m\" and there's a 2% error.\r<BR>\n" );
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document.write( "On the other hand, the largest it can be 15*1.02 = 15.3 meters.\r<BR>\n" );
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document.write( "The true length L is somewhere in the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.7+%3C=+L+%3C=+15.3 ALIGN=MIDDLE  ALT=\"14.7+%3C=+L+%3C=+15.3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Through similar calculations, the true width W is somewhere in the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.76+%3C=+W+%3C=+12.24 ALIGN=MIDDLE  ALT=\"11.76+%3C=+W+%3C=+12.24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Scratch work:<BR>\n" );
document.write( "0.98*12 = 11.76<BR>\n" );
document.write( "1.02*12 = 12.24\r<BR>\n" );
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document.write( "In summary so far, the true length (L) and width (W) are found in these respective intervals<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.7+%3C=+L+%3C=+15.3 ALIGN=MIDDLE  ALT=\"14.7+%3C=+L+%3C=+15.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.76+%3C=+W+%3C=+12.24 ALIGN=MIDDLE  ALT=\"11.76+%3C=+W+%3C=+12.24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The smallest possible area occurs when both L and W have been minimized as much as possible. I.e. we pick the smallest value of L and W\r<BR>\n" );
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document.write( "smallest area = (smallest length)*(smallest width)<BR>\n" );
document.write( "smallest area = (14.7)*(11.76)<BR>\n" );
document.write( "smallest area = 172.872\r<BR>\n" );
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document.write( "On the other side of the spectrum we have:<BR>\n" );
document.write( "largest area = (largest length)*(largest width)<BR>\n" );
document.write( "largest area = (15.3)*(12.24)<BR>\n" );
document.write( "largest area = 187.272\r<BR>\n" );
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document.write( "The true area value (A) is somewhere in this interval<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=172.872+%3C=+A+%3C=+187.272 ALIGN=MIDDLE  ALT=\"172.872+%3C=+A+%3C=+187.272\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "note how using the original L and W values gets us<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "A = 15*12<BR>\n" );
document.write( "A = 180\r<BR>\n" );
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document.write( "Let's calculate how far each endpoint of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=172.872+%3C=+A+%3C=+187.272 ALIGN=MIDDLE  ALT=\"172.872+%3C=+A+%3C=+187.272\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is from the 180 value we found just now.\r<BR>\n" );
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document.write( "180-172.872 = 7.128<BR>\n" );
document.write( "187.272-180 = 7.272\r<BR>\n" );
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document.write( "The max absolute error possible is 7.272\r<BR>\n" );
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document.write( "If we knew the true area of this figure, then we could compute the actual absolute error. <BR>\n" );
document.write( "Instead, we can only determine the largest possible max absolute error.<BR>\n" );
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