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In summary, the speaker is having trouble evaluating their gamma factor for their special relativity homework because they need to compute 1 minus a very small number. Their calculator and Mathematica treat this value as simply 1. They are wondering if there are any methods they could do by hand for this problem. The listener suggests using Mathematica's floating point precision capabilities to get a more accurate result. The speaker thanks them for the solution.

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BOAS

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Hello,

i'm having trouble evaluating my gamma factor for my special relativity homework, because I need to compute 1 minus a very small number (8.57*10^-13). My calculator treats this value as simply 1, as does Mathematica. Although I don't know much about it, and maybe there's a way to force it to consider the small number.

Are there any methods that I could do by hand?

(I am also looking for a computer method elsewhere, but I figured this might be interesting).

Thanks!

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SteamKing

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Evaluating such a difference will be a problem with a standard calculator. Mathematica however should be able to handle floating point calculations to such a precision that you don't get a value of 1 for the difference.

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BOAS

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SteamKing said:

Evaluating such a difference will be a problem with a standard calculator. Mathematica however should be able to handle floating point calculations to such a precision that you don't get a value of 1 for the difference.

Thanks, that solves the problem at hand.

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Vanadium 50

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(1+x)^(1/2) is approximately 1 + x/2.

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CellCoree

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Hello,

I can understand the difficulty in evaluating your gamma factor with such a small number. In situations like this, it is important to use high precision methods for calculating square roots. One method you could use by hand is the Babylonian method, also known as the Heron's method, which involves taking an initial guess and iteratively refining it until you reach the desired level of precision. However, this may be quite time consuming and may not be feasible for your homework assignment.

For computer methods, you can try using libraries or functions specifically designed for high precision calculations, such as the GMP library or the mpmath module in Python. These tools allow you to specify the desired level of precision and can handle very small numbers without rounding them off.

I hope this helps. Best of luck with your homework!

## Related to How Can I Compute High Precision Square Roots for Special Relativity Homework?

## What is a high precision square root?

High precision square root is the process of finding the square root of a number with a high level of accuracy, often to many decimal places. This is achieved by using advanced mathematical algorithms and computer calculations.

## Why is high precision square root important?

High precision square root is important because it allows for more accurate and precise calculations in scientific and mathematical applications. It also helps to reduce rounding errors and improve the overall accuracy of the solution.

## How is high precision square root calculated?

High precision square root is calculated using various mathematical algorithms and methods, such as the Newton's method, the bisection method, or the continued fraction method. These methods use iterative processes to find the square root to a desired level of precision.

## What are some common uses for high precision square roots?

High precision square roots are commonly used in fields such as engineering, physics, and finance, where accurate calculations are crucial. They are also used in computer programming and data analysis to improve the accuracy of mathematical operations.

## Are there any limitations to high precision square roots?

While high precision square roots can provide very accurate results, they are limited by the precision of the computer or calculator used for the calculations. Additionally, some numbers, such as irrational numbers, may not have an exact square root and can only be approximated to a certain level of precision.

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