Daniel has identified one of the areas (no pun intended) where some of the
minor prefixes of SI (deci, centi, deka and hecto) are helpful. The one he
identified is AREA (below), But I need to add that, just as he says I forgot
about area, he has forgotten about VOLUME. Volume presents an even MORE
pressing reason to use the minor prefixes or to make some other adjustment
to pure SI. Let me address the two issues separately. First AREA:
> From: "Daniel Bishop" <[EMAIL PROTECTED]>
> Subject: [USMA:8933] Re: Preferred/non-preferred prefixes
>
> You forgot about
> AREA
> Under a strict "powers of 1000" system, the only acceptable and practical
> units for area are mm�, m�, and km�. These differ by a factor of 1 000 000,
> so many measurements would have to be expressed with very large numbers.
It is true, since area is measured in square length units, that when we use
length units which increase (and decrese) by steps of 1000 only, then the
area units will increase (or decrease) by steps of 1000 SQUARED, which is a
million. That does indeed leave a very large gap between consecutive units.
If we use only millimetres, metres and kilometres for lengths then we would
only be able to use square millimetres, square metres and square kilometres
for areas. The lists below show why this is especially awkward for areas.
1000 mm = 1 m
1000 m = 1 km
1 000 000 mm^2 = 1 m^2
1 000 000 m^2 = 1 km^2
Daniel asks what to do here by stating:
> The area of a sheet of A4 paper, for example, has to be described as "62 500
> mm^2." A farm could be "800 000 m^2."
> Now, could someone please explain why that's more suitable than "625 cm^2" or
> "80 ha"?
My response is that, even here, centimetres and hectares are not really
necessary. Daniel's farm example does NOT need to be described
as 800 000 m^2. It could just as well be described
as 0.8 km^2. I don't find this any more difficult to use than 80 ha.
Similarly, his example of 62 500 mm^2 could describe it as 0.0625 m^2. I
agree that both 62 500 and 0.0625 are less simple than we would like. The
question is "Is it worth breaking the pattern of SI prefixes in order to
solve this problem". My answer is "Maybe!" This discussion has caused me to
reconsider my original thoughts on the subject.
But let's compare this to the question of VOLUME measurement.
Here, the basic SI unit is the CUBIC metre, with cubes of the multiples and
submultiples of a metre being available for larger and smaller volumes. But
now, if we restrict ourselves to lengths in steps of 1000 (mm, m, km, etc.)
then the CUBES of these units will go up or down in steps of
1 000 000 000, which is a billion to most Americans (and is known as a
thousand million, I believe, to the British and some other Europeans).
Regardless of the name attached to the number, it is BIG and we have:
1 000 000 000 mm^3 = 1 m^3
1 000 000 000 m^3 = 1 km^3
That is clearly going to be extremely awkward. A normal size bottle of milk
falls between 1 mm^3 and 1 m^3, being of about 10 000 mm^3. That is
probably a number that is inconveniently large. But the alternativewould be
to use 0.000 001 m^3 (or worse yet, 0.000 001 00 m^3, if you wish to
indicate more than one digit precision).
In this case, SI provides a solution, although not a perfect one. It is the
creation of the litre which is NOT recognized as an SI unit but is accepted
for use with SI in order to solve the practical problem of not having a
convenient sized unit between 1 mm^3 and 1 m^3. A litre is defined so that:
1000 L = 1 m^3
and
1 000 000 mm^3 = 1 L
(Yes, I know that it is more commonly referred to as 1000 cm^3 or 1 dm^3,
but I am trying not to use centi and deci here.)
This still leaves an awkwardly large gap between the cubic millimetre and
the litre, but with the use of the millilitre, this gap too is bridged.
Restating the above list:
1000 mm^3 = 1 mL
1000 mL = 1 L
1000 L = 1 m^3
-------------------------
Conclusion: I'm not sure!
In my own mind, I still think it would be better to have fewer prefixes
because, MOST of the time, steps of 1000 do just fine. Thus we could
eliminate centi, deci, deka and hecto. MOST of the opposing arguments I have
heard were based on an imaginary problem of the steps-of-1000 prefixes being
inconvenient. I just don't find the sizes to be inconvenient. However, I
recognize that the problem is quite real when we get to area and volume.
It's a problem that is built into the geometry of our universe and can't be
solved as easily as we'd like. But what's the best way?
I continue to think about it. I appreciate hearing your comments. I my yet
change my mind.
Regards,
Bill Hooper
