[...] If your meter should be one order of magnitude better than your specification you get to 0.005% - these are 4 1/2 digits [...]
depending on how you view things, the above (0.005% for a 4.5 digit meter) may be out by a factor of 10, or even 100...
consider my 3.5 digit meter: it can at best be used to measure an
arbitrary input to a 0.5% resolution. the limiting factor is where i want to measure, for example, 2.01 volts. this is too much to measure using the 2v range, so i need to use the 20v range instead. this can yield readings of 2.00 (a little low) or 2.01 (spot on) or 2.02 (a little high), giving a 0.5% usable resolution. while i could have my 3.5 digit meter adjusted to significantly better than 0.5% accuracy, this would be relatively pointless as the meter is unable to display results to anything better than 1 part in 200 (0.5%).
my 4.5 digit meter can, by extension, resolve an arbitrary input to within 0.05%, and hence is it pointless to have it adjusted to anything significantly better. my 5.5 digit meter can do 0.005%, while my 6.5 digit meter can do 0.0005%
now lets work the numbers backwards. lets say i want to measure something that is between 1.9 and 2.1 volts using my 3.5 digit meter.
if i see the number "2.01" displayed, what can i confidently say about the measurement that i am observing? it is fair to say that the actual voltage being measured could be anywhere between (just over) 2.005 and (just under) 2.015 volts -
assuming the meter is spot on (0.0% accuracy error). but then we need to factor in the 0.5% level of accuracy we already arrived at above - this gives us an
expanded range of 1.994975 to 2.025075 volts for what we are trying to measure, and possible displays of "1.99", "2.00", "2.01", "2.02", or "2.03".
this rather wide range gives me little confidence in that ".01" i'm seeing! i feel that i need at least to see one more digit to be confident - or that i need to downgrade the accuracy i'm willing to ascribe to my measurements by a factor of 2. i would be far more comfortable if i was looking at a display showing "1.990", as then i can happily dismiss the last digit and say "this is within 0.5% of 1.99 volts" with an air of certainty!
hence, when making arbitrary measurements, we really would like a 'guard digit' that we can throw out. while this
could be a half-digit on the right (where the rightmost digit on our meter can only be either "0" or "5"), the marketing department prefers that every displayed digit beyond the first can cover the full range of "0".."9". instead, when we see the display of "2.01" we need to take that as being something between "1.99" and "2.03" - even if the reference and resistor divider of our meter is good for 0.5% accuracy, the reading we
see displayed only has a +/-1% useful accuracy (what we might decide to call 'confidence').
by extension:
our 4.5 digit meter has a maximum useful accuracy of 0.1%,
our 5.5 digit meter has a maximum useful accuracy of 0.01%,
our 6.5 digit meter has a maximum useful accuracy of 0.001%.
and in cases of there being a little noise within our measurement system (as happens with 5.5 and more digit meters), we may wish to instead take a full decimal digit as the 'guard'. then we get:
our 5.5 digit meter having a maximum useful accuracy of 0.05%,
our 6.5 digit meter having a maximum useful accuracy of 0.005%.
cheers,
rob :-)