1. significant digits
I forget who said they were working on a string math library, but here is a
useless
exercize for it: how many angstroms are in a parsec?
Kat
2. Re: significant digits
> I forget who said they were working on a string math library, but here is a
useless
> exercize for it: how many angstroms are in a parsec?
Kat makes a "significant" joke, right... 
Has anyone investigated the possible use of BCD math for things like this.
'BCD', is, at least in the x387 'kernel', and should be a lot faster than any
string math.
Assembly "pros" might check around for bcdasm.zip, by Morten Elling, which
claims up to 48k. integer digits possible.
( a 'major' project ahead ? )
Wolf
3. Re: significant digits
About 9,467,280,000,000,000,000,000
----- Original Message -----
From: Kat <gertie at PELL.NET>
To: EUforum <EUforum at topica.com>
Sent: Wednesday, February 21, 2001 10:07 AM
Subject: significant digits
> I forget who said they were working on a string math library, but here is
a useless
> exercize for it: how many angstroms are in a parsec?
>
> Kat
>
>
>
4. Re: significant digits
Kat wrote:
>
> I forget who said they were working on a string math library, but here is a
> useless
> exercize for it: how many angstroms are in a parsec?
>
> Kat
>
1 pc = 3.085677580*10^16m,
1 A = 10^-10m,
hence 1pc/1A = 3.085677580*10^26, which is the number of angstroems in a
pc.
Have a nice, rolf
5. Re: significant digits
Oops
I forgot to multiply light years by 3.26 to get parsecs
so I get now
1 parsec = 3.08633 * 10^14
1 angstrom = 10^-10
Product of the two is 3.08633 * 10^24
which is 3,086,330,000,000,000,000,000,000 angstroms per parsec
(approximately)
Bye
Martin
----- Original Message -----
From: Rolf Schroeder <r.schr at T-ONLINE.DE>
To: EUforum <EUforum at topica.com>
Sent: Wednesday, February 21, 2001 12:36 PM
Subject: Re: significant digits
> Kat wrote:
> >
> > I forget who said they were working on a string math library, but here
is a useless
> > exercize for it: how many angstroms are in a parsec?
> >
> > Kat
> >
> 1 pc = 3.085677580*10^16m,
> 1 A = 10^-10m,
>
> hence 1pc/1A = 3.085677580*10^26, which is the number of angstroems in a
> pc.
>
> Have a nice, rolf
>
>
>
6. Re: significant digits
On 21 Feb 2001, at 11:59, simulat wrote:
> About 9,467,280,000,000,000,000,000
Not precise enough, need all significant digits. 
Kat
>
> ----- Original Message -----
> From: Kat <gertie at PELL.NET>
> To: EUforum <EUforum at topica.com>
> Sent: Wednesday, February 21, 2001 10:07 AM
> Subject: significant digits
>
>
> > I forget who said they were working on a string math library, but here is
> a useless
> > exercize for it: how many angstroms are in a parsec?
> >
> > Kat
> >
> >
> >
>
>
>
7. Re: significant digits
Kat wrote:
>
> On 21 Feb 2001, at 11:59, simulat wrote:
>
> > About 9,467,280,000,000,000,000,000
>
> Not precise enough, need all significant digits.
>
Kat, excuse me, but except the above number if totally wrong, your
request makes no sense! It means: for the length of a parsec in meters,
[m], is not known more accurate then up to 11 decimal digits
(1pc=3.0856775807e+016[m]+-4.0e+005[m]), the number of Angstroms per
parsecs is also only accurate up to 11 decimal digits, the value is:
3.0856775807e+026[A/pc]+-4.0e015[A/pc] (all units are written in
brackets). For multiplications and divisions the accuracy in decimal
digits will not change. For differences or additions one has to decide
if the expression still makes sense.
Have a nice day, Rolf
8. Re: significant digits
On 22 Feb 2001, at 3:06, rolf.schroeder at DESY.DE wrote:
> Kat wrote:
> >
> > On 21 Feb 2001, at 11:59, simulat wrote:
> >
> > > About 9,467,280,000,000,000,000,000
> >
> > Not precise enough, need all significant digits.
> >
> Kat, excuse me, but except the above number if totally wrong, your
> request makes no sense! It means: for the length of a parsec in meters,
> [m], is not known more accurate then up to 11 decimal digits
> (1pc=3.0856775807e+016[m]+-4.0e+005[m]), the number of Angstroms per
> parsecs is also only accurate up to 11 decimal digits, the value is:
> 3.0856775807e+026[A/pc]+-4.0e015[A/pc] (all units are written in
> brackets). For multiplications and divisions the accuracy in decimal
> digits will not change. For differences or additions one has to decide
> if the expression still makes sense.
Ok, it looked to me like he had simply used " 9.46728Esomething" and written out
all
the zeros. You have used "3.0856775807etc", making it inherently more accurate,
for
the same number of places to the left of the decimal point. If the phrase
"significant
digits" is not appropriate, then what is the phrase to use to describe the
difference
in accuracy between "3.14" vs "3.1415" or "1.234E10" vs "1.23456789E10"?
Kat
9. Re: significant digits
Kat wrote:
> Ok, it looked to me like he had simply used " 9.46728Esomething" and written
> out all
> the zeros. You have used "3.0856775807etc", making it inherently more
> accurate, for
> the same number of places to the left of the decimal point. If the phrase
> "significant
> digits" is not appropriate, then what is the phrase to use to describe the
> difference
> in accuracy between "3.14" vs "3.1415" or "1.234E10" vs "1.23456789E10"?
>
OK, let's take your example of "3.14" vs "3.1416" (I assume it should
represent PI=4*atan(1), I took 3.1416 instead of your 3.1415 for 3.1416
is the exact rounded number to the 5th decimal for PI). The last
significant digit of the first number (3.14) is of course the digit 4,
the number PI is given up to 3 significant decimal digits. It means (in
case the representation is rounded) that 3.135 <= PI <= 3.145, the
accuracy is +-0.005. The second number representing PI is of higher
accuracy, it means that 3.14155 <= PI <= 3.14165, the accuracy is
+-0.00005. The actual value of PI (to keep our example) can not be given
in decimal representation, but it is between 3.141592653589793 and
3.141592653589794. Behind the last significant digit of an physically
measured quantity you may write any numbers you like, it means nothing
concerning accuracy, but it makes no sense to write digits with no
meaning!
By the way: often it's better to give the relative accuracy (the smaller
the better!), that is the interval of uncertainy of the given value
divided by the value itself, in our case: for the first example:
+-0.005/3.14=+-0.0016, in the second one: +-0.00005/3.1416=+-0.000016,
which is far smaller and therefor better.
Have a nice day, Rolf
10. Re: significant digits
How significant is 22 / 7
Euman
11. Re: significant digits
At 03:50 22/02/01 -0800, you wrote:
>How significant is 22 / 7
>
22/7 is an absolute value and is accurate
to a theoreticly infinate No. of digits.
As an approximation of Pi, it's pretty
rough: - say 4 or 5 sig figs.
12. Re: significant digits
Euman, 22/7 is *very* significant, because it cannot be represented in binary
computers as a native binary numeral. In the formula:
C = pi * D
how many digits does one need to define the planet Pluto's position with enough
accuracy to hit it with a satellite, considering you also must slingshot the
satalite off
several other planets first, over a time period of several years?
Not that i expect anyone to use Eu to do this, but i *did* say it was a useless
exercize
of a string math library with my first post on this topic.
Kat
