Does .9999999 Repeating = 1?

Asami Sato · December 10, 2014, 09:09:39 PM

The answer to this question alluded my creators, and now I must know.

rC · December 10, 2014, 09:10:34 PM

Of course not, two different numbers can't be equal.

R o c k e t · December 10, 2014, 09:10:38 PM

It is close, VERY close.
But no.

Unless you round it up of course.

Turkey · December 10, 2014, 09:11:18 PM

Oh my sweet lord jesus christ please don't do this.

Alternative Facts · December 10, 2014, 09:11:46 PM

Quote from: RC5908 on December 10, 2014, 09:10:34 PM

Of course not, two different numbers can't be equal.

50/50

Either they are equal, or they aren't.

rC · December 10, 2014, 09:11:57 PM

Quote from: H̲u̲r̲t̲f̲u̲l̲T̲u̲r̲k̲e̲y on December 10, 2014, 09:11:18 PM

Oh my sweet lord jesus christ please don't do this.

It's pretty much common knowledge that they aren't equal.

rC · December 10, 2014, 09:12:08 PM

Quote from: IcyWind on December 10, 2014, 09:11:46 PM

Quote from: RC5908 on December 10, 2014, 09:10:34 PM
Of course not, two different numbers can't be equal.

50/50

Either they are equal, or they aren't.

Exactly.

Jocephalopod · December 10, 2014, 09:12:19 PM

the answer is in this simple equation

Epsira · December 10, 2014, 09:13:56 PM

The number "0.9999..." can be "expanded" as:

0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

In other words, each term in this endless summation will have a "9" preceded by some number of zeroes. This may also be written as:

0.999... = 9/10 + (9/10)(1/10)^1 + (9/10)(1/10)^2 + (9/10)(1/10)^3 + ...

That is, this is an infinite geometric series with first term a = 9/10 and common ratio r = 1/10. Since the size of the common ratio r is less than 1, we can use the infinite-sum formula to find the value:

0.999... = (9/10)[1/(1 - 1/10)] = (9/10)(10/9) = 1

So the formula proves that 0.9999... = 1.

from Purplemath

Edit: Part of the answer didn't copy
http://www.purplemath.com/modules/howcan1.htm

Turkey · December 10, 2014, 09:15:23 PM

Quote from: RC5908 on December 10, 2014, 09:11:57 PM

Quote from: H̲u̲r̲t̲f̲u̲l̲T̲u̲r̲k̲e̲y on December 10, 2014, 09:11:18 PM
Oh my sweet lord jesus christ please don't do this.
It's pretty much common knowledge that they aren't equal.

rC · December 10, 2014, 09:16:36 PM

Quote from: H̲u̲r̲t̲f̲u̲l̲T̲u̲r̲k̲e̲y on December 10, 2014, 09:15:23 PM

Quote from: RC5908 on December 10, 2014, 09:11:57 PM
Quote from: H̲u̲r̲t̲f̲u̲l̲T̲u̲r̲k̲e̲y on December 10, 2014, 09:11:18 PM
Oh my sweet lord jesus christ please don't do this.
It's pretty much common knowledge that they aren't equal.

Are you trying to say that you know more about math than me, being in high school calculus?