Hello!

Got a problem below which has been troubling me for a few days...

I realised I don't know how to round values from thermometers, burettes etc. if the measurement is inbetween the divisions but you have to (because the teacher has said so) have a value which is +-0.05 i.e. the last digit / 2nd d.p ends in 0 or 5 e.g. 25.05cm3, 13.20cm3 are acceptable, 25.04cm3 are NOT.

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If one has to measure a reading on a burette to 0.05 i.e. the last 2nd decimal place number must be a 0 or a 5, but the burette only has divisions every 0.1ml, e.g. 20.0, 20.1, 20.2, then where does one apply the 20.5 reading?

[I have been told by my school that to get the marks in the practical exams, I must read the burette to +-0.05! NOT to 0.01!]

I have heard of a number of different approaches from various people, and was wondering if the chemists here could offer a definitive opinion.

[The following examples assume that the bottom of the meniscus is between the divisions e.g. 20.0 and 20.1cm3] N.B. I have ignored the fact that burettes have their numbers from top down to bottom

Approach A] If the bottom of the meniscus is "below" halfway between the divisions, then you round DOWN to 20.00; else if it is above the halfway point, you round DOWN to 20.05 cm3.

However, another approach suggested by some is: B] If the bottom of the meniscus is "below" halfway between the divisions, then you round UP to 20.05; else if it is above the halfway point (i.e. in the upper half of the region between marked divisions on the burette), you round UP to 20.10 cm3.

Another approach (we'll call it approach C) I have heard is to split the area between 20.0 and 20.1 - i.e. between the divisions -into 3 regions (mentally that is) i.e. in the lower 1/3 you assume that the value is 20.00, in the middle 1/3 you assume that the value is 20.05, in the uppermost 1/3, you assume the value is 20.10.

Last but not least, another approach (which I think is a tad inaccurate), that I have heard from many is the following rule: If it is on the division / line itself, it's 20.00 or 20.10 etc. If it isn't on the line, then it's 20.05,20.15 etc. regardless of how close it may be to the upper or lower regions inbetween the divisions.

If you've read this, thanks, you've got a lot of patience :-)

Here's a picture to help you understand me:

[Some people have suggested the left approach, others have suggested the right

].

Thus, I would be *most grateful* if anyone could tell me which one of these approaches is "official" or the one to use in labs (at least, for secondary school labs).

Thank you. Many thanks.

E