Sciencemadness Discussion Board - Do electronic balances round the mass off or down?

Do electronic balances round the mass off or down?

fusso - 13-10-2018 at 04:55

Assume I have 1.005g of anything on a 2 decimal place balance.
Will it round the mass off to 1.01g or round down to 1.00g?

12thealchemist - 13-10-2018 at 05:36

When a balance has flickered between one weight and another, I always take that to be halfway between the two. So, if I had 1.005 g of something on a balance, it would flick between 1.00 g and 1.01 g.

fusso - 13-10-2018 at 06:05

Quote: Originally posted by 12thealchemist

When a balance has flickered between one weight and another, I always take that to be halfway between the two. So, if I had 1.005 g of something on a balance, it would flick between 1.00 g and 1.01 g.

What about 1.008g?

12thealchemist - 13-10-2018 at 06:10

That would display as 1.01 g, I would assume

Sulaiman - 13-10-2018 at 06:15

Usually the resolution of digital scales is better than their linearity, repeatability and accuracy,
so it does not matter if it rounds up or down or alternates between the two

P.S. Digitally it is easiest to use the next least significant binary digit
so <0.5 would be rounded down and >=0.5 rounded up,
which is also how it is generally handled in mathematics

[Edited on 13-10-2018 by Sulaiman]

Heptylene - 13-10-2018 at 06:44

I agree with Sulaiman. Unless you have a good quality scale with calibration weights, the resolution is probably better than the actual precision of the scale.

To illustrate this, just take 10 consecutive measurements of the same object on your scale: the measured weight will likely not be the same every time.

And the scale will be inaccurate depending on where you are on the earth, which is why you need the calibration weights. The gravitational acceleration varies depending on where you are on the earth by a fraction of a percent, so if you measure something at 100.000 g, the thing might actually have a mass of 100.067 g or 99.978g. Think about it if you bought the scale from another continent.

The scale might also drift off over time or due to transport.

fusso - 22-10-2018 at 13:25

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wg48 - 22-10-2018 at 13:47

Quote: Originally posted by Sulaiman

Usually the resolution of digital scales is better than their linearity, repeatability and accuracy,
so it does not matter if it rounds up or down or alternates between the two

In the presence of measurement noise with a zero mean distribution you have to round that way or you will introduce a bias in your readings.

AJKOER - 31-10-2018 at 04:47

Quote: Originally posted by Sulaiman

........
so <0.5 would be rounded down and >=0.5 rounded up,
which is also how it is generally handled in mathematics

[Edited on 13-10-2018 by Sulaiman]

Actually, I recently was surprised to learn that the above generally cited rounding randomization rule is not taught in all states in America (like in Florida, an increasingly pro-business state).

My take on the rationale of such randomization rule is that if you adds a large number of rounded numbers together, where the digit subject to rounding is an assumed random deviate of some distribution, the result should demonstrate, on repetition, minor deviation bias from an unrounded number total or average. However, this logic is off if the data was transformed and one is working with numbers having a non-symmetric distribution (for example, ratio statistics).

I somehow doubt an underlying mathematical rationalization and a more likely reason for a bias rounding rule is due to some presumed educational or legal or financial benefit (like it is OK for a bank to round down on interest payment to customers, or credit card companies can round up interest payments due, as long as there is a disclosure document).

I speculate that existing laws probably cite generally taught standards. So, by changing to a bias rounding rule in schools, such hypothetical suspect practices may have a legal foundation.

So, do electronic balances round the mass up or down? Well, that may depend on your zip code.

[Edited on 31-10-2018 by AJKOER]

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[Edited on 31-10-2018 by AJKOER]