# What is the lowest mass measurable using a 4 decimal point analytical balance?

I think it is 1 mg, but I've heard people saying 0.1 mg. As 0.1 mg = 0.0001 g, which is the uncertain digit, I think such a measurement is not reliable at all.

Any opinions ? Thanks.

Keep in mind that for many analytical instruments, you cannot assume that the uncertainty is ± the last digit. It's usually necessary to look at the specifications in the manual or on a sticker to find the measured uncertainty. For instance, one of our balances, a Sartorius CPA225D (manual), is readable to 0.01 mg (i.e. the display can display increments of 0.01 mg), but the specifications list the repeatability as only ±0.05 mg (±1 s.d.). This means that repeated measurements of the same mass will be (ideally) normally distributed with a standard deviation of 0.05 mg and that even though the instrument has the resolution to report in 0.01 mg increments, the uncertainty in a measurement is higher.

• This precisely! – Jan Jan 25 '16 at 22:29

I think that by 4-digit analytical balance; you mean 4 decimal places. in which case the error would be ±0.0001 g.

If you were correct in that it was actually a 4-digit balance then the uncertainty would be ±0.001 g. However, this would mean that the balance only weighs up to 9.999g and balances usually allow more than that by my understanding. Hence why I think it would be 4 decimcal places and correct to ±0.0001 g.

EDIT

The scales I use have a repeatability of ±0.0001 g. My understanding is that if I have 5.0006 ±0.0001 g then there is doubt about the last digit. For every reading we take there will always be a measure of doubt. In this case it is important to highlight how big that doubt is, so it cannot simply be ignored. we have an uncertainty of ±0.0001 g meaning the true value could read 5.0005-5.0007 g. If you thought the uncertainty was 0.001g of the balance reading then our uncertainty would become 5.000-5.001 g. But the balance is certain that it doesn't weigh 5.000 g.

• Sorry about that. I meant 4 decimal points. I've corrected the question. – chemkatku Jan 25 '16 at 14:06
• i'll edit my answer about the reliability of the measurement – LiamH Jan 25 '16 at 14:07
• @jan I have seen analytical balances with 7 decimal places in the pharmaceutical industry – LiamH Jan 25 '16 at 14:08
• @jan ah I think I understand you. are we agreeing that the last value is the uncertainty? – LiamH Jan 25 '16 at 14:12
• @LiamH Please explain "if I have 5.0006 ±0.0001 g then the last digit has some reliability because I know i don't have 5.007 g". – chemkatku Jan 25 '16 at 14:44