james.jones@firstinvestors.com wrote:
I suspect this idea, while clever, does not cover the problem domain sufficiently well to be superior to lists.
Please have a look at the attached list. (I hope sending attachments works.) This is a list of all SI units I could find on a quick search. The first two columns are nominator and denominator a corresponding rational number would have. Of course, this is not a proof, but the numbers suggest that for practical purposes we're not even getting near a range that's likely to be dangerous. By the way, there's no need to worry about growing intermediate results: a/b * c/d is equal to a/d * c/b and these two factors can be normalized before the multiplication is carried out. If that's done and a/b and c/d were in normal form, then so will be the result and there's no intermediate result growing larger then the final product. Andreas 9 1 3^2 m^2 area square metre m2 27 1 3^3 m^3 volume cubic metre m3 3 2 3/2 m/s speed, velocity metre per second m/s 3 4 3/2^2 m/s^2 acceleration metre per second squared m/s2 1 3 1/3 1/m wavenumber reciprocal metre m1 5 27 5/3^3 kg/m^3 mass density kilogram per cubic metre kg/m3 5 9 5/3^2 kg/m^2 surface density kilogram per square metre kg/m2 27 5 3^3/5 m^3/kg specific volume cubic metre per kilogram m3/kg 7 9 7/3^2 A/m^2 current density ampere per square metre A/m2 7 3 7/3 A/m magnetic field strength ampere per metre A/m 13 27 13/3^3 mol/m^3 concentration mole per cubic metre mol/m3 5 27 5/3^3 kg/m^3 mass concentration kilogram per cubic metre kg/m3 17 9 17/3^2 cd/m^2 luminance candela per square metre cd/m2 1 2 1/2 1/s frequency hertz (d) Hz 15 4 5*3/2^2 kg*m/s^2 force newton N 5 12 5/(3*2^2) kg/m*s^2 pressure, stress pascal Pa N/m2 45 4 5*3^2/2^2 kg*m^2/s^2 energy, work, heat joule J N m 45 8 5*3^2/2^3 kg*m^2/s^3 power, radiant flux watt W J/s 14 1 7*2 A*s electric charge coulomb C 45 56 5*3^2/(7*2^3) kg*m^2/A*s^3 electric potential volt V W/A 784 45 7^2*2^4/(5*3^2) A^2*s^4/kg*m^2 capacitance farad F C/V 45 392 5*3^2/(7^2*2^3) kg*m^2/A^2*s^3 electric resistance ohm V/A 392 45 7^2*2^3/(5*3^2) A^2*s^3/kg*m^2 electric conductance siemens S A/V 45 28 5*3^2/(7*2^2) kg*m^2/A*s^2 magnetic flux weber Wb V s 5 28 5/(7*2^2) kg/A*s^2 magnetic flux density tesla T Wb/m2 45 196 5*3^2/(7^2*2^2) kg*m^2/A^2*s^2 inductance henry H Wb/A 11 1 11 K Celsius temperature degree Celsius (e) °C 17 1 17 cd luminous flux lumen lm cd sr (c) 17 9 17/3^2 cd/m^2 illuminance lux lx lm/m2 1 2 1/2 1/s activity referred to a radionuclide (f) becquerel (d) Bq 9 4 3^2/2^2 m^2/s^2 absorbed dose, specific energy (imparted), kerma gray Gy J/kg 5 6 5/(3*2) kg/m*s dynamic viscosity pascal second Pa s 45 4 5*3^2/2^2 kg*m^2/s^2 moment of force newton metre N m 5 4 5/2^2 kg/s^2 surface tension newton per metre N/m 5 8 5/2^3 kg/s^3 heat flux density, watt per square metre W/m2 45 44 5*3^2/(11*2^2) kg*m^2/K*s^2 heat capacity, entropy joule per kelvin J/K 9 44 3^2/(11*2^2) m^2/K*s^2 specific heat capacity, joule per kilogram kelvin J/(kg K) 9 4 3^2/(2^2) m^2/s^2 specific energy joule per kilogram J/kg 15 88 5*3/(11*2^3) kg*m/K*s^3 thermal conductivity watt per metre kelvin W/(m K) 5 12 5/(3*2^2) kg/m*s^2 energy density joule per cubic metre J/m3 15 56 5*3/(7*2^3) kg*m/A*s^3 electric field strength volt per metre V/m 14 27 7*2/(3^3) A*s/m^3 electric charge density coulomb per cubic metre C/m3 14 9 7*2/3^2 A*s/m^2 surface charge density coulomb per square metre C/m2 14 9 7*2/3^2 A*s/m^2 electric flux density, coulomb per square metre C/m2 784 135 7^2*2^4/(5*3^3) A^2*s^4/kg*m^3 permittivity farad per metre F/m 15 196 5*3/(7^2*2^2) kg*m/A^2*s^2 permeability henry per metre H/m 45 52 5*3^2/(13*2^2) kg*m^2/mol*s^2 molar energy joule per mole J/mol 45 572 5*3^2/(13*11*2^2) kg*m^2/mol*K*s^2 molar entropy joule per mole kelvin J/(mol K) 14 5 7*2/5 A*s/kg exposure coulomb per kilogram C/kg 9 8 3^2/2^3 m^2/s^3 absorbed dose rate gray per second Gy/s 13 54 13/(3^3*2) mol/m^3*s catalytic activity katal per cubic metre kat/m3