ok, i'm new here, so i thought i'd show you something neat

but first of all, my notation - when I mean a number is recurring (going on forever, the recurring part will be in bold.

(for example - 0.9 means 0.9999999... 0.42 means 0.4242424242... and 0.4567 means 0.4567567567...)

if you wish to express a number as a fraction, you can use this simple trick:
0.43 as a fraction:

first call the number I

so I = 0.43

therefore 100I = 43.43

if 100I - I = 99I,
and 100I - I = 43.43 - 0.43 = 43,
then 99I = 43

/99, and I = 43/99!

nice! well, here's the neat part: say we wanted to express 0.9

so,

0.9 as a fraction:

first call the number I

so I = 0.9

therefore 100I = 99.9

if 100I - I = 99I,
and 100I - I = 99.9 - 0.9 = 99,
then 99I = 99

/99, and I = 1

so 0.9 = 1



discuss.

Interesting problem we've got here. Right now I am trying to find a mistake, but here's some useful info:

If you want to display a number like this as a fraction, this is approx. how you do it. Depending on the number of digits that are repeating, (1,2,3) you divide the repeating number by the according number of nine's.

So, for 0.43434343... you get 43/99. For 0.55... it's 5/9. But this obviously can't be done fore 9, and I will find the mistake!

It's all to do with expressing recurring numbers as fractions - for example people often say 1/3 is 0.3, but if you multiply 0.3 by three, you get 0.9 whereas 1/3 multiplied by 3 is 1. so it is impossible to divide 1 by 3 in decimal form. yes?

There is but isn't a mistake there in his calculations....hehe



Your right, as well as wrong here also...I'll try to explain, but seeing as how I don't fully understand it I doubt I'll be able to explain it clearly.

As for the "repeating decimal" form of the fraction 1/3...there is a finite number of times that it repeats, theoretically. This is true of the repeating decimal pi but since we can't/haven't found the end of it yet we just "assume" that it has an end and therefore our calculations are correct. That is also the monkey wrench in the calculation that started this thread. I mean this for both sides of the conversation...its the proof that it is wrong...while at the same time proof that its correct...lol. At least as I understand it....

Ah, I have found the mistake! Actually, my friend told me (maths freak). You see, if we represent 0.999999.. as 1-0.000000..001, that is incorrect. We are playing with endless numbers, and therefore 0.0000..001 is equal to 10^(-infinity) - I hope you understand what wrote. And 10^(-inf) is equal to 0 (that's how it's defined in maths, as far as I understood it). That's why we can't represent 0.999.. that way. That's the error

And therefore if you multiply .9 by .9 therefore you get .18899989 some other b.s. lmao but yea this make no sense to me so can you please explain in retard terms lmao cuz im a bit lost...

Look at it this way. We can't represent 0.9999.. as 1-0.00000..00001 because 0.0000..0001 equals zero.

And here is why. Every 0.00..1 can be represented as 10^(-n), where n is some number. If we have infinite zero in this number, n must equal infinity. And 10^(-infinity) is actually zero.