What does 33.3' (recurring) x 3 equal?

Recently I confronted my flatmate with the age old question, “How much would you eat your own excrement for?”. He responded with “100 bucks”. After hearing his answer I immediately turned to my two other by standing flatmates and said “Cool, all we need is to put 33.3 recurring bucks in each”. Quickly added after two arrogant chuckles was this reply: “But that wouldn’t equal 100, it would equal 99.9 recurring”. Somewhat confused by the reply I left the room to contemplate and now, two weeks later, I just want some sort of solid answer.
How can 100 divided by 3 equal 33.3 recurring, yet 33.3 recurring times by 3 equals 99.9 recurring? I Have also been told that 99.9 recurring is so infinitely close to 100 that it is actually considered 100. However I just cannot accept that 99.9 recurring is 100, it is a number that is infinitely close to 100 but is not 100.

Death Ninja

Holy crap, don’t start or Phage will blow a gasket.

99.9 recurring is exactly equal to 100. Let me dig up the cite…it’s a wonderful read.

The Master speaks :

Here is the thread. It’s probably my favorite SDMB thread of all time. Alas, it was before my time so I couldn’t get in on it.

Oh yeah, welcome to the boards.

Yeah sorry guys, I did a search on the Archive but forgot to search the forums…

Im new here so I’m sure I’ll be forgiven…


Another Ninja in our midst, welcome.
Check out the many threads on this and similar questions in General Questions forum. Also look up stuph about Aleph null if you want your brain more thoroughly bombarded by interesting math.

(non-math guy walks into the thread): 100 bucks to eat his own poop! What a nutter!

Before you take up that bet, don’t forget to read the latest poop on poop.

The answer seems obvious.

100/3 = 33.333333… etc.

so 33.333333… etc. * 3 = 100.

.3… * 3 = 1. If you don’t understand what completeness has to do with this fact, don’t attempt to debate it.

I don’t know if this would help. But this made it easier for the primate that I am to accept that .999… = 1.
x = 0.999…
10x = 9.999…

10x-x = 9.999…-0.999…
9x = 9
x = 9/9 or 1

…get a new flatmate

Even if this hadn’t been answered before, methinks you picked the wrong forum.

Anduril, that was the same way a math teacher once demonstrated it in high school, but I’d forgotten it until then. Thanks

Exactly how much poop? A gram? One dumpload? That could be pretty small or really huge.

Sorry, I just made myself gag.

I don’t know, the thread I linked could qualify as a debate that’s great.

Just wait a few weeks. This’ll be on Fear Factor.

If you accept the fact that the fraction 1/3 is expressed in decimal form as 0.333… then the rest falls into place: 33 1/3 + 33 1/3 + 33 1/3 = 100.

Ok,… After reading the most (There’s alot there) of the other thread…

33.3 recurring times by 3 equals 100 because its simply a limition of decimal… Thats OK and makes perfect sense to me, but the whole thing that 99.9 recurring is actually 100 seems wrong to me… This is how I see it:

Its all about what context 99.9 recurring is being used in… For example 99.9 recurring is 100 in the 1/3 times by 3 in problem because of the problems with decimal, but the actual number 99.9 recurring is not 100. Its infinitely close to 100 but it never actually becomes 100 because infinity has no end…



You’re not understanding what the notation “99.999999…” means. You’re thinking that it means that you sit at your desk and continue to write down nines. And you’re thinking that at any point when we check on you, you’ve written a finite number of nines, so your number will be less than 100.

But that’s not what’s meant. The notation means that there are *already * and infinite number of nines there. And this number is exactly equal to 100.