On Apr 5 , at 10:24 AM, John M. Steele wrote:
I disagree that we should round conversion factors willy-nilly to a
"nice" round number when we know better.
John is right that conversion factors should not be rounded off "willy
nilly", but it does makes sense to round them off to the degree
appropriate for the data to be converted. That's not willy nilly.
For example, even if we know that
1.093 613 298 338 yd = 1 m *
it would be foolish to use that overly precise conversion factor to
convert my
height of 1.81 m into yards.
By simple multiplication, that would give my height to be:
1.979 440 069 991 yd.
or
5.938 320 209 974 ft.
Such overly precise looking results are foolish.
My height (the data being converted) is specified to only three
significant digits so the result cannot have more than three
significant digits. That is, my height MUST be rounded off to
1.98 yd
or
5.94 ft
Consequently, if we're going to round off anyway, it makes sense to
round off earlier and save an awful lot of work.
Realizing that my data (1.81 m) is good to only 3 digits, I round off
my conversion factor to four digits (three might be enough but four
allows some room for round off errors**), thus, instead of the long
value above, I use:
1.094 yd = 1 m
Using this rounded conversion factor, I calculate my 1.81 m height to
be (before rounding):
1.98014 yd.
or
5.94042 ft.
both of which I round off to three significant figures, thus:
1.98 yd.
and
5.94 ft.
These are exactly the same values produced by the earlier, overly-
precise calculations. The answers are the same with a lot less work.
Bill Hooper
1810 mm tall
Fernandina Beach, Florida, USA
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* I don't know how many decimal places there might be in this value. I
calculated it by dividing 1 by 0.9144 which is the EXACT value for the
number of metres in one yard. The division led to a very long decimal.
I am not sure if it is infinitely long (repeating decimal) or if it is
exact once one gets far enough "out" into the decimal digits. Yes, I
could have used the exact conversion factor 0.9144 yd. = 1 m but I
wanted a factor that illustrated my point better. However, these
consideration has nothing to do with the main point above.
** If I rounded off the conversion factor to only 3 digits, my
conversion factor would be 1.09 yd = 1 m and my raw results would be
height = 1.9729 yd. and 5.9187 ft. , which after final rounding would
be height = 1.97 yd. and 5.92 ft. These differ from the previous
values by a quarter to a third of an inch. Quite honestly, those
values would be good enough for most practical purposes, but the
example does show that keeping one more digit in the conversion factor
gives a slightly better answer. However, more than one extra digit
does not give any further changes in the rounded off final value.
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SImplification Begins With SI.
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