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

[hedipaldi]

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.

 

[Dick]

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.

 

[hedipaldi]

So far i already got.How to proceed?

 

[Dick]

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.

 

[hedipaldi]

Thank's a lot.

 

[phinds]

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.