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<div>It appears that there is a need for some re-education in
measurement and conversion arithmetic. Here it is.</div>
<div><br></div>
<div>First, some terminology:</div>
<div> accuracy = how close a measurement is to reality</div>
<div> precision = the smallest unit of measurement used</div>
<div>Accuracy is limited by precision, but not determined by it;
accuracy can be much less than precision. (When that happens,
it's also confusing!)</div>
<div><br></div>
<div>It is theoretically possible to measure the weight of the Olympic
Bell to the nearest microgram, which would be a precision of 11
significant digits. But given the practical limitations of
ordinary measuring equipment, it is unlikely that it could be measured
with an accuracy of more than four or five significant digits.</div>
<div><br></div>
<div>The best weight we have for the Olympic Bell up to now is
Dickon's figure of 22.91 metric tonnes. In the absence of any
accompanying statement as to the accuracy of that measurement, we must
take both the accuracy and the precision of it as "correct to the
fourth significant digit" (which is also, in this case, the
second decimal place). Then the exact weight, if one could
measure it with greater precision, must be in the range</div>
<div> 22.91 plus or minus .005 metric
tonnes</div>
<div>or (adding non-significant trailing zeros and moving the decimal
point)</div>
<div> 22910 plus or minus 5 kilograms</div>
<div>In other words, we presume that it has been measured (weighed) to
the nearest 10 kilograms.</div>
<div><br></div>
<div>Since many of us were originally educated in societies which
did/do not use the metric system of measurement, we are more
comfortable with something else - the Imperial system of weights in
the UK and closely-related countries, and the avoirdupois system of
weights in the USA. So conversion becomes necessary.</div>
<div><br></div>
<div>Conversion factors are widely known, based on international
standards for units of measurements. A few are perfectly
precise; as in the conversion from metric tonnes to kilograms above,
they do not cause any loss of accuracy, because they are based on the
definitions of the units of measurement involved. But most have
some limitation on the precision that they can carry. For
example, the conversion factors in the online calculator which Chris
Pickford referenced have precisions which vary from 8 to 11
significant digits. Those were the best values that I could find
when I developed that calculator several years ago (based on a similar
calculator developed by someone else).</div>
<div><br></div>
<div>When converting a measurement from one system to another, it is
important to use a conversion factor which has at least as much
precision as the measurement being converted, in order to avoid
inadvertent loss of accuracy. In practice, one additional
significant digit is usually enough, though it never hurts to use more
as long as you keep track of accuracy. The online calculator
helps in this regard through the option to specify the number of
significant figures (digits) to be used in presenting the results.
Behind the scenes, it calculates from the initial input value with the
maximum possible precision, and then rounds the results according to
the specified number of significant figures.</div>
<div><br></div>
<div>The conversion factor between kilograms and pounds is 0.45359237
kg/lb.</div>
<div>To convert kilograms to pounds, divide by that factor; to convert
pounds to kilograms, multiply by that factor. To keep track of
the known or presumed accuracy, the "plus or minus" value
must be similarly converted. (The online calculator does NOT do
this automatically; you must figure it for yourself.)</div>
<div><br></div>
<div>Then 22910 plus or minus 5 kilograms (or 22910 +/- 5 kg)</div>
<div>converts to<font face="Lucida Grande" size="-3" color="#000000">
50507.9043</font> +/-<font face="Lucida Grande" size="-3"
color="#000000"> 11.023</font>1 pounds.</div>
<div>Since the size of the accuracy range is so large, it makes no
sense to retain the decimal parts of these values; rounding both
results to the nearest pound, we get</div>
<div> 50508 plus or minus 11 pounds (50508 +/- 11
lb).</div>
<div><br></div>
<div>Since an Imperial ton is 2240 pounds (a precise conversion), this
is equivalent to</div>
<div> 22-10-3-24 +/- 11 in ton-cwt-qtr-lbs form, or</div>
<div> 22.548 +/- 0.005 Imperial tons in decimal
form.</div>
<div>To drop the accuracy range, this should then be stated as</div>
<div> 22.55 Imperial tons</div>
<div><br></div>
<div>In summary, when converting measurements, it is important to
understand (a) what is known or implied about the accuracy and
precision of the original value, (b) what the original system of
measurement was, (c) what conversion factor should be used between the
original system and the target system, and (d) how to apply that
factor to determine the converted value without losing any accuracy or
implying false accuracy. Most of the errors which have been made
in this forum's discussion of the weight of the Olympic Bell have
probably arisen from confusion about (b) or (c).</div>
<div><br></div>
<div>If this essay is TMI (Too Much Information), I shan't apologize,
because you could have hit the Delete button at any time. But I
would welcome correction of any misstatements.</div>
<div><br></div>
<div>Carl</div>
<div><br></div>
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