Burette/Thermom. Readings - Rounding?
B
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. ---
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 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 :-)
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; I'm not at uni btw, so erm... I'm not after
complicated answers, thanks :)).
Thank you. Many thanks. B
Bob
As you suggest, there is a lot of personal taste involved here. The
best answer is to do it the way a particular teacher wants you to --
and see if you can get that person to explain why they want it.
I'm not sure I like any of the options you suggest above -- though
perhaps that is due to the difficulty of describing them in words. I
would say... You have decided to read to the nearest 5 in the last
place. So you judge which 0 or 5 it is _closest_ to.
But I do not particularly like the idea of reading to nearest 5, in
general. You should estimate one digit beyond what the lines show, as
best you can. That is typically to the tenth of a division, though of
course it varies with the scale. Rounding to nearest 5 is throwing
away information, and in general throwing away info is not so good.
bob
faro...@hotmail.com
B wrote:
> 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. ---
This depends as Bob as pointed out on the personal choice of the worker
and the nature of work. Some authors do recommend recoding the volume
to 0.01 ml, so 25.04 ml would be acceptable.
>
> 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?
The last digit is for estimation and applied to the second digit after
the decimal point, your readings could be (say) 20.05 , 20.15 ml,
20.20, 20.25 ml.
Never use sub-divisions in terms of odd numbers.
> 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.
.........
.........
Perhaps there is no universally accepted official method for reading
burette or graduated pipette volumes.
A British analytical chemistry standard text (some 40 years ago)
suggested that "... for common purposes (burette) readings should be
made to 0.05 mL; for precision work, readings should be made to
0.01-0.02 mL..."
So say if you get the meniscus *anywhere between* say 20.0 and 20.1
ml, the only option (for not-so-precise work) by the above rule would
be to record the burette volume as 20.05 ml. If the meniscus exactly
coincides with 20.0 ml or 21.0 division your volume would be 20.00 and
20.10 ml.
For more precise work, you could divide (by imagining) the marks
between 20.0 and 20.1 into 0.02 divisions, i.e. imagine the burette was
marked in 20.00, 20.02, 20.04, 20.06, 20.08 and 20.10 ml. Now if the
mesicus lies in-between the marks 20.0 and 20.1 ml, then you should
record the volume as 20.04, 20.08 etc depending on the position of the
meniscus.
Some authors suggest reading the burette to 0.01 ml, now if the
meniscus is in between the 20.0 and 20.1 mark, then you will need to
note the volume as 20.01, 20.04, 20.07, 20.10 ml depending on the
position of the meniscus and nature of work.
If you go into more details, you will across "drainage time" usually 30
seconds written on good quality burettes & pipettes, this is the time
you should wait before noting the volume, after you finish your
titration etc.
Bob
>
>A British analytical chemistry standard text (some 40 years ago)
>suggested that "... for common purposes (burette) readings should be
>made to 0.05 mL; for precision work, readings should be made to
>0.01-0.02 mL..."
>
>So say if you get the meniscus *anywhere between* say 20.0 and 20.1
>ml, the only option (for not-so-precise work) by the above rule would
>be to record the burette volume as 20.05 ml.
Why is that the only option? That procedure seems to imply that
readings recorded ending in 5 are +/- 4, whereas reading ending in 0
are +/- 1. Not logical?
Why not... If, for whatever reason, readings are to be "made to 0.05
mL", then read to the _nearest_ .05. So anything between .025 and .075
would be recorded as .05.
The idea of distinguishing "common" from "precision" readings is a
good one. But I think one goal in a class is to teach students to read
scales "carefully" -- i.e., as carefully as possible. This is
typically taken to mean to the nearest 1 in the estimated digit.
(Admittedly, that is hard to do with a burette.) But it is better to
try to read to nearest 1, and not do it very well, than to not try.
Information once lost cannot be recovered.
The burette is quite a challenge for students... It is often the first
instrument where they read volume to 0.01 mL; it has a very close line
spacing; and the scale is upside down! With all these issues, I ask
that students have me check their burette readings (at least the first
one or two). It is so much easier when the burette is still there!
bob
(Same Bob, just a different email address -- and news server.
University news server is acting up over the vacation. Private emails
to my old address are fine.)
faro...@hotmail.com
Bob wrote:
> On 28 Dec 2004 23:15:39 -0800, faro...@hotmail.com wrote:
> >A British analytical chemistry standard text (some 40 years ago)
> >suggested that "... for common purposes (burette) readings should be
> >made to 0.05 mL; for precision work, readings should be made to
> >0.01-0.02 mL..."
> >
> >So say if you get the meniscus *anywhere between* say 20.0 and 20.1
> >ml, the only option (for not-so-precise work) by the above rule
would
> >be to record the burette volume as 20.05 ml.
>
> Why is that the only option? That procedure seems to imply that
> readings recorded ending in 5 are +/- 4, whereas reading ending in 0
> are +/- 1. Not logical?
If you remember, I asked posted a question "A Question to English
Speaking Chemists" as to the meaning the very same lines. What I
understand from these statements is that the meniscus could be exactly
on the 20.0 and 20.1 ml marking, then simply we would note the volume
as 20.00 and 20.10 ml or if it is *anywhere in-between these two
divisions", now regardless of the position of meniscus, the volume
should be noted as 20.05 ml.
> Why not... If, for whatever reason, readings are to be "made to 0.05
> mL", then read to the _nearest_ .05. So anything between .025 and
.075
> would be recorded as .05.
Why should we bother the third estimated digit? J.Chem. Ed had an
excellent article IIRC "Principles of Scale Reading", which explained a
lot with diagrams. You might like to give it your students.
> The idea of distinguishing "common" from "precision" readings is a
> good one. But I think one goal in a class is to teach students to
read
> scales "carefully" -- i.e., as carefully as possible. This is
> typically taken to mean to the nearest 1 in the estimated digit.
> (Admittedly, that is hard to do with a burette.) But it is better to
> try to read to nearest 1, and not do it very well, than to not try.
> Information once lost cannot be recovered.
I personally used the 0.01 estimate after waiting for a drainage time
in my notebook, but never mentioned it in the lab reports for the
reasons given in the last paragraph.
>
> The burette is quite a challenge for students... It is often the
first
> instrument where they read volume to 0.01 mL; it has a very close
line
> spacing; and the scale is upside down!
How? The top reads 0 ml and the bottom say 50 ml. Am I missing
somthing?
> With all these issues, I ask
> that students have me check their burette readings (at least the
first
> one or two). It is so much easier when the burette is still there!
Unfortunately the teachers from school to univ. never asked to estimate
burette readings (rather never mentioned estimation for any kind of
scale) and whenvever I asked them about it they discouraged to record
volume the second decimal place. Their argument was "when there is no
division between the two markings how can you record the volume to
second decimal place; for them volume could be 20.0 or 20.1, since
there was no further subdivision...20.04, 20.09 would be meaningless"
Bob
>
>Bob wrote:
>> On 28 Dec 2004 23:15:39 -0800, faro...@hotmail.com wrote:
>> >A British analytical chemistry standard text (some 40 years ago)
>> >suggested that "... for common purposes (burette) readings should be
>> >made to 0.05 mL; for precision work, readings should be made to
>> >0.01-0.02 mL..."
>> >
>> >So say if you get the meniscus *anywhere between* say 20.0 and 20.1
>> >ml, the only option (for not-so-precise work) by the above rule
>would
>> >be to record the burette volume as 20.05 ml.
>>
>> Why is that the only option? That procedure seems to imply that
>> readings recorded ending in 5 are +/- 4, whereas reading ending in 0
>> are +/- 1. Not logical?
>
>If you remember, I asked posted a question "A Question to English
>Speaking Chemists" as to the meaning the very same lines. What I
>understand from these statements is that the meniscus could be exactly
>on the 20.0 and 20.1 ml marking, then simply we would note the volume
>as 20.00 and 20.10 ml or if it is *anywhere in-between these two
>divisions", now regardless of the position of meniscus, the volume
>should be noted as 20.05 ml.
>
I vaguely recall the thread, but do not accept (or remember) that
conclusion, for the reason stated (above).
>
>> Why not... If, for whatever reason, readings are to be "made to 0.05
>> mL", then read to the _nearest_ .05. So anything between .025 and
>.075
>> would be recorded as .05.
>
>Why should we bother the third estimated digit?
Ah. I simply was trying to show that I had divided the interval into
fourths, since that was logically relevant.
There was a long discussion of this in the chemed-L mail list
recently. Some made the point that estimating to nearest fourth (or
perhaps third) is quite reasonable. If one does that, one should write
them as (eg) .25 or .33, not to imply two significant digits, but
simply as an artifact of using decimal numbers.
That point, along with your point above, does serve to emphasize
something several people made there... that the whole system of sig
fig is flawed. Better to explicitly state error bars. (I don't
entirely agree with that, for intro students and informal work, but
they have a point.)
>
>>
>> The burette is quite a challenge for students... It is often the
>first
>> instrument where they read volume to 0.01 mL; it has a very close
>line
>> spacing; and the scale is upside down!
>How? The top reads 0 ml and the bottom say 50 ml. Am I missing
>somthing?
Most any other instrument (incl those used earlier by intro students)
would say 50 at the top. A grad cylinder tells you how much it
contains. A burette tells you how much it has delivered. Besides that
logical distinction, it just looks upside down, compared to an
ordinary volume scale. Students tend to read the line just below 10 as
9.9, rather than as 10.1.
(Some grad cyl show two scales, one reading in each direction.)
>
>
>> With all these issues, I ask
>> that students have me check their burette readings (at least the
>first
>> one or two). It is so much easier when the burette is still there!
>
>Unfortunately the teachers from school to univ. never asked to estimate
>burette readings (rather never mentioned estimation for any kind of
>scale) and whenvever I asked them about it they discouraged to record
>volume the second decimal place. Their argument was "when there is no
>division between the two markings how can you record the volume to
>second decimal place; for them volume could be 20.0 or 20.1, since
>there was no further subdivision...20.04, 20.09 would be meaningless"
>
I know of teachers who follow that procedure. It is a trade-off. But
it is not really fair to say that the estimated digit is meaningless.
A common exercise is to have many students read the same scale. Their
estimated digits are usually close. Say, most are 2,3, or 4. No one
says 8. So the estimated digit has some meaning, but less than a fully
determined digit.
bob
faro...@hotmail.com
Bob wrote:
> Ah. I simply was trying to show that I had divided the interval into
> fourths, since that was logically relevant.
>
> There was a long discussion of this in the chemed-L mail list
> recently. Some made the point that estimating to nearest fourth (or
> perhaps third) is quite reasonable. If one does that, one should
write
> them as (eg) .25 or .33, not to imply two significant digits, but
> simply as an artifact of using decimal numbers.
Bob
An email discussion of chemistry education. That is, people post to
the list, and all messages are then sent to all members of the list.
The list is open to anyone, so feel free to give it a try. It is
another good way to get involved in some good discussions. No risk; it
is as easy to unsubscribe as to subscribe:
http://mailer.uwf.edu/archives/chemed-l.html
where the thing after the hyphen is an "el" (not a "one").
bob