Uncertainty help

[Guest Jar Jar D'oh!]

Hi!

I'm trying to consolidate what I know about uncertainties, so tell me if I'm either missing anything or whether I'm doing anything wrong:

Uncertainties for analog instruments is +/- 0.5 the last decimal place ( 0.12 +/- 0.05)

Uncertainties for digital instruments is +/- 1 eh? ( 0.12 +/- 1)

But why is it that the uncertainties are halved?

Oh, I just remembered another thing I wanted to know: For an electronic scale measuring up to 1 mg or 0.001g Is the uncertainty +/- 1 g or 0.001g. I got into an argument with a teacher over this, I really need to know.

I'm really bad a uncertainties and I really haven't got these and some other queries cleared, can you help out?

Edited February 27, 2012 by Jar Jar D'oh!

[Victorious]

I'm not sure. They're probably halved because of a probability chance.. Like there might be a possibility whereby this number can be between 1 and 0.5. It allows a larger chancing point.

I believe it's 0.0001g. Although, I'm not sure.

[CkyBlue]

For analog instruments, the uncertainty is half the smallest division.

Your example is incorrect. If the measurement was 0.12, it would be 0.120 +/- 0.005.

This reading of the apparatus is such that we cannot determine the precision of the an instrument to more decimal places. As an example, assume we record the reading 0.12 for an instrument. The instrument and the recording value tell us the smallest divisions are by 0.01; therefore the divisions we see are 0.10, 0.11, 0.12, 0.13 ... However when we record the value 0.12, we cannot be certain the value is at exactly 0.12. The actual measurement must be in between the uncertainty, with a value of 0.005 because if otherwise, we would not have recorded 0.12.

Given the same instruments, if the actual value was 0.123, we record it as 0.12.

If the actual value was 0.117, we record it as 0.12.

The uncertainty must be 0.005 because if the actual value must fall in between the value in which you have interpreted.

If the actual value was 0.126, you would have recorded it as 0.13, not 0.12 0.126 does not fall within the uncertainty of 0.12.

In an electronic scale, the uncertainty is one of the smallest scale division.

For example, if the scale measured up to 3 decimal places, the uncertainty would be 0.001.

Hope that helped, and I was not rambling too much

[Guest Jar Jar D'oh!]

For analog instruments, the uncertainty is half the smallest division.

Your example is incorrect. If the measurement was 0.12, it would be 0.120 +/- 0.005.

This reading of the apparatus is such that we cannot determine the precision of the an instrument to more decimal places. As an example, assume we record the reading 0.12 for an instrument. The instrument and the recording value tell us the smallest divisions are by 0.01; therefore the divisions we see are 0.10, 0.11, 0.12, 0.13 ... However when we record the value 0.12, we cannot be certain the value is at exactly 0.12. The actual measurement must be in between the uncertainty, with a value of 0.005 because if otherwise, we would not have recorded 0.12.

Given the same instruments, if the actual value was 0.123, we record it as 0.12.

If the actual value was 0.117, we record it as 0.12.

The uncertainty must be 0.005 because if the actual value must fall in between the value in which you have interpreted.

If the actual value was 0.126, you would have recorded it as 0.13, not 0.12 0.126 does not fall within the uncertainty of 0.12.

In an electronic scale, the uncertainty is one of the smallest scale division.

For example, if the scale measured up to 3 decimal places, the uncertainty would be 0.001.

Hope that helped, and I was not rambling too much

I really appreciate the effort so I'm going to rep you for that, but all the same my brain's tied in a knot because Drake answered with the exact opposite of what you've written to another thread of mine on uncertainty in Chem.

Check it out here.

[CkyBlue]

I'm not sure what exactly what we're opposing of each other, but I'm guessing it's the uncertainty for an electronic balance?

If so, I was just stating what the Pearson Baccalaureate textbook for HL chem was saying in my own word. That rule for uncertainty does not make sense to me either. But it's better to go with what is required of the syllabus, right?

[Guest Jar Jar D'oh!]

True that, but its 4 AM here, I'll reason later :'D