text: # Homework Help: Statistical Physics: very large and very small numbers
  
  1. Jun 10, 2012
  
  ### PhysicsGirl90
  
  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?
  
  2. Jun 10, 2012
  
  ### BruceW
  
  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?
  
  3. Jun 10, 2012
  
  ### PhysicsGirl90
  
  They have a different base. So if we wanted to compare them we they would both have to have the same base.
  
  4. Jun 10, 2012
  
  ### BruceW
  
  exactly. So what can you do to get them both to have the same base?
  
  5. Jun 10, 2012
  
  ### PhysicsGirl90
  
  Thank you for your comment Bruce...i figured it out...convert (1/44) to a power of 10 and the rest follows easily.
  
  6. Jun 10, 2012
  
  ### PhysicsGirl90
  
  (1/44)^(10^5) = (10^log(1/44))^(10^5)...Thanks for helping me think it through.
  
  7. Jun 10, 2012
  
  ### BruceW
  
  yeah, no worries. Glad to have helped :)
explanation: The document is a forum thread discussing a statistical physics problem involving very large and very small numbers. It contains a math question and a series of responses leading to the solution of the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: # Homework Help: Statistical Physics: very large and very small numbers
  
  1. Jun 10, 2012
  
  ### PhysicsGirl90
  
  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?
  
  2. Jun 10, 2012
  
  ### BruceW
  
  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?
  
  3. Jun 10, 2012
  
  ### PhysicsGirl90
  
  They have a different base. So if we wanted to compare them we they would both have to have the same base.
  
  4. Jun 10, 2012
  
  ### BruceW
  
  exactly. So what can you do to get them both to have the same base?
  
  5. Jun 10, 2012
  
  ### PhysicsGirl90
  
  Thank you for your comment Bruce...i figured it out...convert (1/44) to a power of 10 and the rest follows easily.
  
  6. Jun 10, 2012
  
  ### PhysicsGirl90
  
  (1/44)^(10^5) = (10^log(1/44))^(10^5)...Thanks for helping me think it through.
  
  7. Jun 10, 2012
  
  ### BruceW
  
  yeah, no worries. Glad to have helped :)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum thread discussing a statistical physics problem involving very large and very small numbers. It contains a math question and a series of responses leading to the solution of the problem.
  
  Label: question-and-answer