How really does 0.999... = 1? It just boggles my mind thinking about it.
0.999999999999999999999999999999999999999999...
2006-10-16 12:46:08 · 8 answers · asked by Mike S 2 in Science & Mathematics ➔ Mathematics
http://en.wikipedia.org/wiki/0.999... read for info
i still dont get it exactly
2006-10-16 12:52:37 · update #1
Look at this pattern:
0.11111... = 1/9
0.22222... = 2/9
0.33333... = 3/9 (or 1/3)
0.44444... = 4/9
0.55555... = 5/9
0.66666... = 6/9 (or 2/3)
0.77777... = 7/9
0.88888... = 8/9
0.99999... = 9/9 (or 1)
So 0.99999... = 1
It's not an approximation, it is another way to represent 1. It seems confusing, but it's no more confusing than saying 0.33333... = 1/3. That never ends, but it does equal a discrete 1/3 of something.
Also notice how 0.33333.... + 0.33333.... + 0.33333.... = 0.99999....
But 1/3 + 1/3 + 1/3 = 1
So again 0.99999... is the same as 1.
The reason it doesn't intuitively seem correct is that our mind has a hard time grasping infinity. However, if you can grasp that 0.333333... equals 1/3 (not almost 1/3), then you can grasp that 0.999999... equals 1 (not almost 1).
The people that mention "rounding" and "approximately" haven't grasped the concept yet. I think the conversion to fractions, makes things much more concrete to people so hopefully that will help you.
2006-10-16 13:23:23 · answer #1 · answered by Puzzling 7 · 4⤊ 0⤋
If you want a proof:
http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1
If you want an intuitive explanation....I wish I could help, but I can't. I'm sure it has to do with the nature of infinity, which defies intuition (at least my own).
2006-10-16 19:53:36 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Well, it's the sum of the infinite geometric series .9 + .09 + .009 + ... , which adds up to 1.
Another way to look at this is: You know 1/3 = .33333.... Given that, 1 = 3/3 = 3 * .33333... = .99999...
2006-10-16 19:56:22 · answer #3 · answered by Anonymous · 3⤊ 0⤋
greg g is so right since .9 is repeating and you want to make it a fraction than you do exactly what he did to get 1
2006-10-16 19:55:07 · answer #4 · answered by luvkitties 4 · 1⤊ 0⤋
.9999999999999999999999 doesn't equal one, it's simply just very close to it. That's why you round. Rounding is used for many things, mostly money. Gas for example. No one can actually pay $2.079 for a gallon of gas. But the company wants you to think of it as $2.07 instead of $2.08 so that you'll have a more positive reaction.
2006-10-16 19:50:09 · answer #5 · answered by Melissa S 2 · 0⤊ 8⤋
When you round up to the nearest whole number...
2006-10-16 19:48:15 · answer #6 · answered by Anonymous · 0⤊ 4⤋
It doesn't, dont panic, people just round up because their hands get tired writing all the nines.
2006-10-16 19:54:02 · answer #7 · answered by impeachrob 3 · 0⤊ 6⤋
x=.99999999...
10x=9.9999999
10x-x=9.9999999999...-.99999999999...
9x=9
x=1
2006-10-16 19:48:24 · answer #8 · answered by Greg G 5 · 0⤊ 0⤋