Statistical Physics: very large and very small numbers

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Homework Help Overview

The discussion revolves around a problem in statistical physics involving the expression p = (1/44)^(10^5) and its comparison to the value 10^(-164345). Participants are exploring how to analytically derive the latter from the former, particularly in the context of handling very large and very small numbers.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to compare two expressions with different bases and consider how to convert them to a common base for comparison. There is also mention of the limitations of calculators in handling very small numbers.

Discussion Status

Some participants have offered guidance on converting (1/44) to a power of 10 as a potential approach. The discussion appears to be productive, with participants actively engaging in reasoning and exploring different methods without reaching a definitive conclusion.

Contextual Notes

There is an acknowledgment that the calculator's output may not be exact and that the expression (1/44)^(10^5) leads to a very small number that challenges typical computational tools.

PhysicsGirl90
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Working on statistical physics i came across this expression:

p = (1/44)^(10^5) = 10^(-164345)

However TI-83 calculator is unable to verify it (gives answer 0). Can someone tell me how to get from (1/44)^(10^5) to 10^(-164345) analytically?
 
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You are still going to need to use a calculator at some point (their answer of 10^(-164345) is not exact, it has been rounded off). But yes, there is a way to find the answer which the calculator can cope with.

To start with, what is the main difference between the expressions (1/44)^(10^5) and 10^(-164345) ? Like if you wanted to compare the two numbers, what would be the first thing you would do?
 
They have a different base. So if we wanted to compare them we they would both have to have the same base.
 
exactly. So what can you do to get them both to have the same base?
 
Thank you for your comment Bruce...i figured it out...convert (1/44) to a power of 10 and the rest follows easily.
 
(1/44)^(10^5) = (10^log(1/44))^(10^5)...Thanks for helping me think it through.
 
yeah, no worries. Glad to have helped :)
 

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