## Question of the Week: what is 1/10 in decimals…. in base 3?

Posted by Michael Dickens on May 31, 2007

It might be 0.001111111111111 you get the idea. Not sure.

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Posted by Michael Dickens on May 31, 2007

It might be 0.001111111111111 you get the idea. Not sure.

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%d bloggers like this:

## bill said

It’s 1/101

## mtgap said

It’s 0.002200220022 etc.

But what is 1/2 in base 5? And what is 1/5 in base 2?

## Kelly Dickens said

By applying the division algorithm, I have calculated:

1/5 (in base2) = .00110011…

1/2 (in base 5) = .2222…

## Kelly Dickens said

By following the patterns, I see that, in “base 1”,

1 would be 1

2 would be 11

3 would be 111

and so on, since the positive powers of 1 are all equal to 1.

Representing non-integers (such as 1/10) poses a bit of a problem. A big one, really.

## Taylor said

I feel like an idiot

## mtgap said

Taylor, you’ll get it eventually.

## mtgap said

well since 10 is 1111111111, 1/10 would be .000000001 (with 8 zeros or 9?)