In alt.engineering.electrical Don Kelly wrote:

| Just a bitch that we have dealt with befo
|
| Phil- please realize that 207.846096....... is meaningless except that it is
| "about 208". 208V is correct to 3 significant figures which is actually
| better than one can assume to be true in practice. If the voltage line to
| neutral is actually 120.V (note the decimal) then we have 3 significant
| digits implying something between 119.5 Vand 120.5.V
| Then all you can truly claim is 208.V
| If it is 120.0V then there is reason to assume 208.0 V but no more decimals
| than that.
| If you have a meter which gives you 120.000000V with less than 1 part in 120
| million error then you can claim 207.846097V for line to line voltage Do
| you have such a meter?
|
| Engineering and physics students who ignore the principle of "significant
| digits" lose marks for this "decimal inflation".
|
| Sure- you can let the calculator carry the extra digits (as it will do
| internally) but accepting these as gospel truth to the limit of the
| calculator or computer display is simply not on as you can't get better
| accuracy from a calculation than the accuracy of the original data (actually
| you will lose a bit). All that you get rid of is round off errors in
| calculations.
|
| Since, as you say, precise voltage is not really practical, then
| multi-decimal point numbers are meaningless. If we say 120V +/-10% then we
| are talking about 108-132V which for line to line becomes 187-229V (average
| 208V) and any extra decimal points don't mean anything.

You didn't notice the :-) I put on the number?

We've been over this. I know the practice of significant digits, and how
the voltages are designated (two different reasons you can get 208). I do
follow the practice of carrying exactly the result of calculations into
other calculations. I also use over significance in comparison of numbers.

But I also know that rounding is a form of noise. So I avoid it until the
time I end up with the final result. So if I multiply 120 by the square
root of three I do get a number like 207.84609690826527522329356 which is
either carried as-is into the next calculation, or rounded if it is the
final answer. If some other strange calculation happens to give me the
value 207.84609690826527522329356 then I know it is effectively equivalent
to 120 times the square root of three in some way. But if what I get is
208.455732193971783228 then I know it has nothing to do with 120 times the
square root of three, even though it, too, would end up as 208 if rounded
to 3 significant digits.

When it comes to _measured_ amounts, as opposed to synthetic ones, then the
significance rules dictate how to round the results. With synthetic numbers
(e.g. numbers I can just pick), I can also pick the rounding rules for the
final results. But if I don't know that the calculations are done (e.g. I
am not merely giving a designation for a voltage system), where someone else
may take those numbers and do more calculations and round the results, then
I do use more significance. But that is no different to me than just carrying
that number from one calculation stage to another.

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| Phil Howard KA9WGN (email for humans: first name in lower case at ipal.net) |