Derived Units Question

Why are derived units defined in terms of unity, for example speed of 1 miles/hour is defined as something which covers 1 mile in one hour. Why not 60 miles in 60 hours. (Its more accurate to measure the later).

Maybe speed is not such a good example, maybe capacitance or resistance units are better.

Well, why don’t you tell me how long it takes to drive 14 miles at a speed of 120 mp60h.

grienspace makes a good point. In addition, giving speed as 60mi/60h is not more accurate, however, it may be more precise if you consider the final zero for the top 60 to be significant, and the 60 on the bottom to be exact. But you could just as easily say 1.0 miles/hour (the implied 1 hour is considered to be exact, I believe) to get two significant digits.

It seems like capacitance or resistance units are worse examples, because they do not use ratios. How else can you say 1 farad? Or 1 ohm?

[rant]I hate when people say that time passes at the rate of 1 second per second.[/rant]

Capacitance: One farad is one coulomb per volt.
Resistance: One ohm is one volt per ampere.

Chava

Thank you Chava. Exactly my point, if you did’nt realize by now - it is almost impossible to have 1 coulomb of charge !!! So why not define Capacitance as say 1 (mu) Coulomb / 1 (mu) volts

After you divide, what’s the difference?

If they weren’t derived with respect to unity you’d have to keep track of it in your mind. It is SO much easier to have it in terms of unity rather than, say 60 because that’s just a natural multiplicative unit and when you convert from one unit to another you naturally multiply.

It would be downright foolhardy to make things more complicated than you need to. Foolhardy.

By the way, measured values are done so that they are the most accurate…whether that be a billion times or a billionth of the time, whatever is the most accurate is what is used. As cornflakes points out, after you divide there is no point to sticking with the more cumbersome “measured” quantities. For example you could use “one second” or you could use 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom. The latter is, in principle, more accurate but the former is easier to manipulate. If you need to be precise, you can always refer to the definition later.