Base 5 in real life

Will it ever be used in real life?

You know, I realised a couple of hours back that I use base 5 every now and then … when I’m counting things in (or as they pass me, or I collect them etc.).

You know that technique with a pencil, or a knife and a tree trunk, of counting things in blocks of 5? Four vertical strokes and then one that crosses through it. I can’t do it here, there’s no strikethrough format tool.

You end up with blocks of 5 and a few leftovers. Of course we’re very quick at converting the 5’s into base 10. Say we’ve counted 23 things (kids, sheep, spitfires, whatever). Oh, there’s four blocks of 5, that’s twenty … plus three, means there’s twenty three. etc.

In base 5 it is ever so quicker, four of them plus three is instantly recognisable as 43.

cheers

And my answer if the question is ‘what is a half in base five?’ is 0.222… recurring (arrived at by dividing 1 by 2 using long division rules modified to base five)…..I’ve never done bases before but if you multiply 0.22222…recurring by 2 you get 0.44444…recurring which approaches 1.0 in base five
An analogous ‘problem’ in base ten is dividing 1 by 3 when you get 0.33333 …recurring…the decimal version of a ‘third’….multiplying 0.33333….recurring by 3 you get 0.99999….recurring which approaches 1.0

(Edits due to thinking it out as I go)

Yep … I found that somewhere late last night … Google was my friend. Sort of.

That said, I don’t “get” it, proper like, just yet. There may be a delay before it sinks in. Or I may just get on with my life.

It’s all so much clearer if you watch this.

http://www.youtube.com/watch?v=DfCJgC2zezw

From about 2′ 25″ there is a demonstration of converting to Base 8, though it helps comprehension to watch the whole four minutes or so.

Moggy

Brilliant Moggy … I feel fine now.

I don’t mind showing my ignorance. Can someone offer me a short tutorial?

What is ‘learning bases’ ? What is ‘base 5’ ?

Is it perhaps a new name for something familiar ?

Yep. We use base 10 as our numbering system. We count 1-9 as discrete units all to themselves. When we get to one more than nine we call the next number 10 (being 1 x ten and 0 x units). Similarly 11 is 1 x ten plus 1 x a unit (one). And 12 is one ten and two units etc.

In base 5 our numbers would be built around multiples of 5 rather than 10. Our numbers would be 1, 2, 3, 4, 10, 11, 12, 13, 14, 20 etc.

10 is 1 x five plus 0 x units. 11 is 1 five plus 1 unit (6 in our decimal system).

Cheers D

Need a new number (or name for a number)

I think I’ve got my mind around this. Given there isn’t a 5 in base 5 there also can’t be a word (five) to name that non-existent number.

So would there need to be a number and word to describe the number that is a half in base five? As a fraction there is of course, “half”. But would there also have to be a number and word to label 0.25?

4?

Moggy

Hmmm. Where I’ve got to is …

You can have 1/2 as both 1 and 2 exist as numbers in base 5
But 0.5 is a decimal concept, it’s 5/10ths. 5 doesn’t exist in base 5, and the written 10 numeral is 5.

So I thought about approaching 0.5 from both directions. In base 10 (our regular number system) 0.4 is 2/5 and 0.6 is 3/5. In base 5 those numbers are 0.2 and 0.3 respectively.

So 0.5 (1/2) lies between 0.2 and 0.3, in fact logically it lies right in the middle of them, which is 0.25.

But can 0.25 exist in base 5? Answer = no. Because the 5 doesn’t exist. 0.25 is “nought point two ten” in base 5.

I think! Help!

0.5 in base 5 is surely 0.5 isn’t it?

I don’t know. I don’t think so. There isn’t a 5 in base 5. 5 is 10.

clue, it can’t be 0.25