Calculator Vs computer precision

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SUMMARY

The discussion compares the precision of calculations between scientific calculators and computer calculators, specifically focusing on the value of π. A scientific calculator provides π as 3.141592654, while a computer calculator offers it as 3.14159265359. The percentage error between these two values is calculated as approximately 4.1 x 10-10. While this difference is negligible for everyday calculations, it becomes significant in advanced applications such as GPS, where higher precision is crucial. Tools like y-cruncher can compute millions of digits of π, demonstrating the superior capability of computers over traditional calculators.

PREREQUISITES
  • Understanding of basic mathematical concepts, including percentage error
  • Familiarity with the value of π and its applications
  • Knowledge of computational tools like WolframAlpha
  • Awareness of advanced calculation software such as y-cruncher
NEXT STEPS
  • Research the use of precision in GPS calculations and its impact on accuracy
  • Explore y-cruncher for high-precision calculations of π and other constants
  • Learn about the limitations of scientific calculators in advanced mathematical applications
  • Investigate the differences between various computational tools and their precision capabilities
USEFUL FOR

This discussion is beneficial for mathematicians, engineers, computer scientists, and anyone interested in the implications of numerical precision in calculations.

mc2_phy
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Calculator Vs computer...precision

Im doing a simple research to find out which device is better for calculations

Valueof π
On scientific calculator = 3.141592654
on computer calculator = 3.14159265359


How do I find percent error?

And would this difference have any impact on calculations performed in rel life? An example would be nice thanks
 
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Welcome to PF, mc2_phy! :smile:

How about WolframAlpha: http://m.wolframalpha.com/input/?i=pi&x=0&y=0
Not that you can click on More digits if you are not satisfied with the precision.

The percentage error is the error divided by the number.
On your scientific calculator that is ##{3.141592654 - 3.14159265359 \over 3.14159265359} = 4.1 \times 10^{-10}##.

For real life calculations, the difference won't matter.
For more exotic calculations, such as in advanced physics, it does matter.
An example is GPS. For the calculations involved you need more precision than either your scientific or computer calculator gives.
 


What do you mean by "computer calculator" ? Computers have much more power than any calculators so in principle you can write better calculation software even on the worst computers today.
Also there are pi calculating programs out there like y-cruncher with which you can compute million digits of pi for seconds( I think its limited to trillion digits) on the cheapest PC you can buy today.
In real life scenario so many digits would be absolutely useless.
 

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