Does 0.999... Equal 1?

[steven787]

dtewi said:

steven787 said:

twilit said:

dtewi said:
Yes, 0.999999999............... does equal 1.

Let's use a simple algebraeic equation.

Let c = 0.999...

10c= 9.9999.....

10c -c = 9

9c/9 = 1.

c = c

1 = 0.999...

If you knew the answer what was the point of this thread...

 

 

Wrong again, once you multiply c *10, theoretically at the end of the infinite 9's there would be a zero.  Which is why 9.... or 9-bar is not .9999999 infinite, it's a symbol for a number that can't be expressed in decimal terms.

 

Theoretically, if infinity has no end, how is there zero at the end of it?

 

 

Exactly. Which is why 1/3 can't be expressed as a decimal.

1/3 ~= .3-bar, it is not 1/3 = .3-bar.  Notice the ~, approximately.

Math is taught that way.  Through Tri you're told it's .33333.... because it's not necessary to confuse students with the concept to measure triangles.

In calc, they use them so they can be expressed graphically.  In Human terms, we would never be able to perceive the difference between 1/3 and .3333.....  but that doesn't mean they are equal.  They are not.  They are approximately equal.

In applied maths (physics, economics, statistics) you always clearly indicate the ~.

 

When you're a college junior taking advanced number theory, you will see more.  I think my previous posts explain it pretty simply though.  You're a smart kid, one day you'll be able to pass it on.

@kane, for now, leave it as 1-.9-bar, round, or approximate the return to a fraction 3(1/3).  If I saw it on a test, I would leave it as 1-.9bar