format a measurement result and its error in "scientific" way

[Daniel Fetchinson]

Hi folks, often times in science one expresses a value (say
1.03789291) and its error (say 0.00089) in a short way by parentheses
like so: 1.0379(9)

One can vary things a bit, but let's take the simplest case when we
only keep 1 digit of the error (and round it of course) and round the
value correspondingly. I've been searching around for a simple
function that would take 2 float arguments and would return a string
but didn't find anything although something tells me it's been done a
gazillion times.

What would be the simplest such function?

Cheers,
Daniel

 

[jmfauth]

Hi folks, often times in science one expresses a value (say
1.03789291) and its error (say 0.00089) in a short way by parentheses
like so: 1.0379(9)

Before swallowing any Python solution, you should
realize, the values (value, error) you are using are
a non sense :

1.03789291 +/- 0.00089

You express "more precision" in the value than
in the error.

---

As ex, in a 1.234(5) notation, the "()" is usually
used to indicate the accuracy of the digit in "()".

Eg 1.345(7)

Typographically, the "()" is sometimes replaced by
a bold digit ou a subscripted digit.

jmf

 

[Daniel Fetchinson]

Hi folks, often times in science one expresses a value (say

Before swallowing any Python solution, you should
realize, the values (value, error) you are using are
a non sense :

1.03789291 +/- 0.00089

You express "more precision" in the value than
in the error.

My impression is that you didn't understand the original problem:
given an arbitrary value to arbitrary digits and an arbitrary error,
find the relevant number of digits for the value that makes sense for
the given error. So what you call "non sense" is part of the problem
to be solved.

Cheers,
Daniel

 

[Ulrich Eckhardt]

Am 16.02.2012 01:18, schrieb Daniel Fetchinson:

Hi folks, often times in science one expresses a value (say
1.03789291) and its error (say 0.00089) in a short way by parentheses
like so: 1.0379(9)

Just so that I understand you, the value of the last "digit" is
somewhere between 9-9 and 9+9, right? So the value itself is rounded so
that its last digit has the same value as the only digit to which the
error is rounded.

One can vary things a bit, but let's take the simplest case when we
only keep 1 digit of the error (and round it of course) and round the
value correspondingly.

First step is to format the values as decimal string ('{0:f}'.format).
Then, pad both values to the same number of digits before and after the
radix separator. Then, iterate over the strings, those digits where the
error digits are zero are those that are taken verbatim for the value.
The following digit is rounded and then added to the result. The
according digit in the error is also rounded and added in brackets.

Note that you can not compute these "values", since the definition of
the rounding depends on a decimal representation. If you have decimal
floating point numbers, where 0.1 is representable without loss, you
could actually do that. In order to allow common treatment as decimal as
required for this algorithm, the first step above was the conversion to
a decimal string.

Write tests that make sure this works, e.g. I ignored any sign and you
also can't use str() to format the value because that could give you
"123.45e+5" as a result.

Good luck!

Uli

 

[jmfauth]

My impression is that you didn't understand the original problem:
given an arbitrary value to arbitrary digits and an arbitrary error,
find the relevant number of digits for the value that makes sense for
the given error. So what you call "non sense" is part of the problem
to be solved.

I do not know where these numbers (value, error) are
coming from. But, when the value and the error
have not the same "precision", there is already
something wrong somewhere.
And this, *prior* to any representation of these
values/numbers.

jmf