Calculator with LOTS of decimals

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SUMMARY

This discussion centers on the need for a calculator capable of handling calculations with significant differences in orders of magnitude without rounding errors. Users specifically mention the limitations of standard calculators and programming languages like Python in providing accurate results for such calculations. Recommendations include using the Windows calculator and the PARI software package, which allows for high precision calculations by setting the precision level with the command \pX, where X can be adjusted to the desired number of decimal places.

PREREQUISITES
  • Understanding of scientific notation and orders of magnitude
  • Familiarity with basic calculator functions and precision settings
  • Knowledge of the PARI software package for number theory
  • Basic command line usage for executing commands in PARI
NEXT STEPS
  • Explore the features of the PARI software package, focusing on precision settings
  • Learn how to use the Windows calculator for scientific calculations
  • Investigate other high-precision calculation tools, such as Mathematica or MATLAB
  • Research best practices for performing calculations with significant digits in programming languages
USEFUL FOR

This discussion is beneficial for mathematicians, scientists, engineers, and anyone requiring precise calculations involving very small or very large numbers without rounding errors.

Usaf Moji
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Hi, I'm trying to do some caculations involving numbers with big differences in their orders of magnitude. Unfortunately, all the cacluclating tools I can find always round off the answers too much to be of any use to me.

For example, if I type 4.5 x 10-12 - (4.5 x 10-12 - 9.2 x 10 -30) I want a calculator that will give me 9.2 x 10 -30. But all the calculators I've used give me 0 due to unwanted rounding during the calculation. Even Python does this.

Does anyone know where I could get a calculator or program that can do the calculation I need? I would prefer something with a simple interface resembling a hand-held calculator (like what Python uses) rather than something that requires any kind of programming.

Thanks.
 
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I think most scientific calculators will give you that answer assuming that you use the exp. button.
 
Usaf Moji said:
Hi, I'm trying to do some caculations involving numbers with big differences in their orders of magnitude. Unfortunately, all the cacluclating tools I can find always round off the answers too much to be of any use to me.

For example, if I type 4.5 x 10-12 - (4.5 x 10-12 - 9.2 x 10 -30) I want a calculator that will give me 9.2 x 10 -30. But all the calculators I've used give me 0 due to unwanted rounding during the calculation. Even Python does this.

Does anyone know where I could get a calculator or program that can do the calculation I need? I would prefer something with a simple interface resembling a hand-held calculator (like what Python uses) rather than something that requires any kind of programming.

Thanks.

The calculator that comes with Windows can do it.

CS
 
stewartcs said:
The calculator that comes with Windows can do it.

CS

Hey, you're right! Thanks!
 
You can use, for free, PARI, the package for number theory. Just look it up on the internet. Normally the program I use goes to 28 decimal places. A little secret here, found in the tutorial is to use \pX to get X places of precision. You can set that for X=50, or X=500 for that matter.

However in the example you gave, depending upon the brackets, it sometimes insists on giving 9.1 followed by a long string of 9s. Even for 500 places its off at the last 7 giving 615927*10^-30.
 
I second the Pari recommendation.

Code:
(15:02)(1+1e-20)^2-1-2e-20
%5 = 9.99999984 E-41

Code:
(15:02)\p 1000
   realprecision = 1001 significant digits (1000 digits displayed)
(15:02)(1+1e-400)^2-1-2e-400
%6 = 9.9999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999526402 E-801
 

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