Re: precision of a measurement (documentation related question)

• To: mathgroup at smc.vnet.net
• Subject: [mg61609] Re: precision of a measurement (documentation related question)
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sun, 23 Oct 2005 05:46:25 -0400 (EDT)
• References: <acbec1a40510221346r2cee06c3led071a9eeb92d58b@mail.gmail.com> <acbec1a40510221456i64c176d7s73cd5110ac614ba1@mail.gmail.com> <acbec1a40510221537h4df0a645h1824fdb52b9f54b@mail.gmail.com> <acbec1a40510221544xac5ed8bu638b96de6cc51ed5@mail.gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

```It is also puzzling to compare:
Solve[2\[Equal]-Log[10,dx/30],dx]//N
Interval[30`2]//FullForm
Interval[Sig[30,0.5]]//FullForm
The intervals are the same, even with two different precisions...
however, one can see that the "precision of the interval endpoints"
are different.

On 10/22/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> Can someone explain:
> Interval@Sig[30,0.5]//FullForm
> Interval at Sig[0.183,0.0005]//FullForm
>
> Notice how the interval seems to be correct for 30+ or - 0.5, but not
> for 0.183 + or - 0.0005
>
> On 10/22/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> > To follow up, here is a function that people could use to compactly
> > enter in measurements and their (half) error range to obtain a number
> > in Mathematica that will have the appropriate significance attached to
> > it (no, I haven't really thought of handling complex numbers yet, but
> > I am sure someone smarter than myself could extend it).
> > Sig[x_,dx_]:=SetPrecision[x,-Log[10,Abs[dx/x]]]
> >
> > Following my previous question:
> > Sig[30,0.5]
> > is the answer I was looking for earlier.
> >
> > This Sig function could be combined with the Notation package to make
> > input even more tidy looking. One could also write a Notation to make
> > numbers with significance show error ranges by default...
> >
> > Regards,
> >
> > On 10/22/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> > > Thanks to a Mention by Maxim in this thread:
> > > and the documentation for Interval,
> > > I was able to figure out the answer to my question:
> > > FullForm@Interval[SetPrecision[x,-Log[10,dx/x]]]/.{{x\[Rule]30,
> > >       dx\[Rule]0.5},{x\[Rule]30,dx\[Rule]1}
> > >
> > > On 10/22/05, Chris Chiasson <chris.chiasson at gmail.com> wrote:
> > > > Hi Mathgroup,
> > > > If I know that a number (say in inches, measured on a ruler that only
> > > > has marks for inches) and its error are:
> > > > 30 + or - 0.5,
> > > > then looking at the help file for Precision, I see that the precision is:
> > > > -Log[10,dx/x]
> > > > In this case, is dx = 0.5 or is it equal to 1.0??
> > > > I have noticed that in either case, the number of significant
> > > > digits/the precision is less than 2.
> > > >
> > > > Your thoughts?
> > > > --
> > > > Chris Chiasson
> > > > http://chrischiasson.com/contact/chris_chiasson
> > > >
> > >
> > >
> > > --
> > > Chris Chiasson
> > > http://chrischiasson.com/contact/chris_chiasson
> > >
> >
> >
> > --
> > Chris Chiasson
> > http://chrischiasson.com/contact/chris_chiasson
> >
>
>
> --
> Chris Chiasson
> http://chrischiasson.com/contact/chris_chiasson
>

--
Chris Chiasson
http://chrischiasson.com/contact/chris_chiasson

```

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