Flaws in the decimal system.

[Josh]

Yes the decimal system has flaws. The reason I am posting this is because I just had a disagreement with a friend who has gone through Calculus 3 on this issue.

If you take 1/9 in decimal you get 0.1111 repeating for infinity.

To get 2/9 you add 1.9 to itself. 0.1111 repeating
+ 0.1111 repeating
0.22222 repeating (you add a 1 to every other 1)
By repeating this process and adding 0.11111 repeating to each one by the time you get to 9/9 the answer is 0.99999999999 repeating for infinity which does NOT equal 1 which it should equal.

The reason 1/9 equals 0.1111 repeating is shown in this picture. You keep puttin 9 into 10 which will result into putting 9 into 10 again which goes on forever. You will then have to add a 1 to each part of the decimal which is why after 9 times you get 0.999999999. It should be 1 though.

[Paul Miller]

We (And by we, I don't mean we, but the math people, which also doesn't include me) knew that already. Which is why the decimal system can only truly express a certain subset of all the numbers. There is a set for numbers like that..... irrational or something? Maybe that's for numbers like pi and this is something else... but the decimal system can't do all numbers. It could also be expressed in a decimal-like format if it were base 9, where it would simply be .1. No matter what base you choose, there will always be numbers like that.

[polobunny]

I agree, after carefully reading your post, the decimal system as it's flaws. But why this thread? Do you want us to stick with the old thing?
Nice drawing btw.

[Josh]

I have known all along. The reason I made it was for a chance for me to think about it more so I can explain it better and because I just had a disagreement with a friend over this who has taken a lot higher math then I.

[Winged 2.0]

:O WTF? I couldnt pay attention to that. I got lost somewhere in the 4th or 5th line. :\

[Isostealer]

:O WTF? I couldnt pay attention to that. I got lost somewhere in the 4th or 5th line. :\

You seem to get lost in a lot of things.

Can't we just all agree that 9 divided by 9 is 1. Math has always confused me when it comes to decimals and dividing, etc. No need to make it more complicated.

[GundamGuy]

My math teacher explaned this last year.. i dont rember how though i might dig through my notes... but i digress he said what you said but then proved that .9999999999 rep. is equal to 1. ergo 9/9 is 1.

[Winged 2.0]

I could probably figure it out if I gave it a chance. I never give math a chance unless I'm in school.

[crusher]

As long as I can add 34 with 35, the system is good. So run away kids.

[Ziegfried]

I seem to recall someone saying something like "9.9999999 does not equal 10, but 9.999... does" in some IRC channel sometime.



W2.0 is pretty dumb.

[MasJ]

The decimal system isn't flawed. It's the number 1/9. The number 1/9 is an approximation when it's divided. However, if you had divided it an infinite number of times and added them, you would've gotten 1. Infinity is a very large number so it's not possible to get it close to one, but the more times you divide it, the closer you'll get to one. At one point of time, you'll be so close to 1, that it won't matter whether it's 1 or 0.999999999999999999999999999999999999999999999999 999999999999

Also, all approximations work in the same way. 1/9 is an irrational number that is why it's decimal representation is an approximation. Rational numbers have to be terminating and non repeating. Whereas this one is non-terminating and repeating. Simply put, it's an approximation, same as 22/7 is.

I don't blame your friend for disagreeing with you. The number 1/9 is an approximation when expressed in decimals, so it's an irrational number. Those are exceptions under the decimal system. This also applies to 10/3, or 20/3 or any similar numbers.

[Gospel]

I rounded it to the nearest whole number.

Win.

EDIT:

Infinity is a very large number...

Hahaha.

[Dark Neighbour]

~1 or Approximately equal to 1. Problem solved!

[Xaenn]

Or you could just leave it in the form 1/9....

However it wouldn't really matter anyway in calculus because if you just solved the problem using limits...Basically you can get that number as close as you want to 1, so it sufficient to say it is 2. Especially in any real world application where it's impossible to have something that is infinately small...

[Roux!]

The decimal system isn't flawed. It's the number 1/9. The number 1/9 is an approximation when it's divided. However, if you had divided it an infinite number of times and added them, you would've gotten 1. Infinity is a very large number so it's not possible to get it close to one, but the more times you divide it, the closer you'll get to one. At one point of time, you'll be so close to 1, that it won't matter whether it's 1 or 0.999999999999999999999999999999999999999999999999 999999999999

Also, all approximations work in the same way. 1/9 is an irrational number that is why it's decimal representation is an approximation. Rational numbers have to be terminating and non repeating. Whereas this one is non-terminating and repeating. Simply put, it's an approximation, same as 22/7 is.

I don't blame your friend for disagreeing with you. The number 1/9 is an approximation when expressed in decimals, so it's an irrational number. Those are exceptions under the decimal system. This also applies to 10/3, or 20/3 or any similar numbers.

Agreed...

If you remembered your Calculus class, you'd know what a limit is...