Calculator Vs computer precision

In summary, the conversation discusses the precision of calculations on a scientific calculator versus a computer calculator. The value of pi is shown to have a slight difference in precision between the two devices, but this difference does not impact real life calculations. An example is given with GPS calculations. Overall, the conversation highlights the capabilities of computers to perform more precise calculations than calculators.
  • #1
mc2_phy
12
0
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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  • #2


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.
 
  • #3


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.
 

1. What is the difference between calculator and computer precision?

The main difference between calculator and computer precision is the level of accuracy in calculations. Calculators typically have a precision of 8-12 digits, while computers can have a precision of up to 16 digits. This means that computers can perform more precise calculations and handle larger numbers than calculators.

2. Why is computer precision important in scientific calculations?

Computer precision is important in scientific calculations because it allows for more accurate and precise results. In fields such as physics or chemistry, even a small difference in decimal places can greatly affect the outcome of an experiment or calculation. Therefore, having a high level of precision is crucial in obtaining reliable and accurate data.

3. How does a computer achieve higher precision than a calculator?

A computer is able to achieve higher precision than a calculator due to its use of floating-point arithmetic. This method allows for the representation of numbers with a larger range and more decimal places, resulting in a higher level of precision. Additionally, computers use more advanced algorithms and can perform multiple operations simultaneously, further increasing their precision.

4. Are there any drawbacks to using high precision in computer calculations?

While high precision in computer calculations may seem advantageous, it can also lead to errors. This is because the calculations involve rounding and approximation, which can introduce small errors in the final result. In some cases, using a lower precision can actually yield more accurate results.

5. How can one ensure accurate results when using a computer for calculations?

To ensure accurate results when using a computer for calculations, it is important to understand the limitations and potential errors associated with high precision. It is also recommended to use multiple methods of calculation and compare the results to verify accuracy. Additionally, using appropriate software and regularly checking for updates can also help maintain accuracy in computer calculations.

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