How to Compute Base 3 Floating Point Expansion of 1/4?

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Homework Help Overview

The discussion revolves around computing the base 3 floating point expansion of the fraction 1/4. Participants are exploring methods to perform this computation, particularly through the lens of geometric sequences and long division in base 3.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants have attempted to use geometric sequences and long division methods, questioning how to apply these concepts in base 3. There is a focus on the arithmetic involved in converting the fraction into its base 3 representation.

Discussion Status

Some participants have shared initial steps and are seeking further guidance on how to continue the computation. There is an ongoing exploration of the long division process in base 3, with no clear consensus yet on the next steps.

Contextual Notes

One participant points out a terminology issue regarding the term "decimal" in the context of base 3, suggesting that it should be referred to as "base 3 floating point" expansion instead.

hedipaldi
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Homework Statement



How to compute the base 3 decimal expansion of 1/4?

Homework Equations





The Attempt at a Solution


I tried sums of geometric sequences,but i need a clue for the computation.
 
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hedipaldi said:

Homework Statement



How to compute the base 3 decimal expansion of 1/4?

Homework Equations


The Attempt at a Solution


I tried sums of geometric sequences,but i need a clue for the computation.

You know how to find 1/4=0.25 in base 10 using long division, right? In base 3 that's 1/11. Do the same process, just do all the arithmetic in base 3.
 
So far i already got.How to proceed?
 
hedipaldi said:
So far i already got.How to proceed?

Just do it. 11 goes into 1 zero times. So you write down 0. and 'bring down' a 0. Now you've got 11 into 10. Still zero times. Answer so far 0.0, bring down another 0. Now you've got 11 into 100 in base 3. So what's the first nonzero digit in the expansion? Multiply subtract and keep going. I'm not really sure how else to explain it in words.
 
Thank's a lot.
 
Just as a nitpicking point, it is not correctly called base 3 DECIMAL expansion since "decimal" is specifically for the base 10 system. It is called "base 3 floating point" expansion.
 

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