Does 0.999... equal 1?

Numbers are a fixed constant. They do not change value. 0.999... isn't 1.

"Because 1=.999... then 3/3=1=.999..."

1 is not .999..., stop throwing it in there. You can't divide 1 evenly by 3, so of course we will get .333... .666... .999...

When were done, we get .9999, so we round it to 1. Rounding is a function in math. Fractions are more accurate in this case because it represents the real value that we cannot determine using decimals.

Yes, why don't you read up on limitless.

 

You never need to round. It equals exactly. .333...(repeated) equals 1/3 exactly. The 3s go forever.

 

If two numbers are unequal, there is an infinite set of numbers "between" them.
If two numbers are equal, there is no number between them.

Answer my challenge, and you win. Find a number in between .9... and 1.

(If Shredder comes back - I'm reading up on infinitesimals. Apparently, it's impossible for them to be the difference between two standard numbers. So, one way or another, answer will be found though silly amounts of research.)

 

since i suck at maths. im not the best person to vote. but i still think it does.

 

Does 999 = 1000?

NO

It does not matter how many times you extend the 9's and 0's it will never work.

999999 does not = 1000000

 

It does actually.

If you extend the 9s and 0s on forever, then
9999999...=100000...
infinity = infinity

To address the posts above this - Annex didn't answer anything nicely, since he does not know the concept of base ten multiplication.

 

The 9s extend to infinity. They are not finite like 999999 and 1000000.
.9 ≠ 1
.99 ≠ 1
.999 ≠ 1
.9999 ≠ 1
.9999999999999999999999999999999999999999 ≠1
.999... = 1

 

Terrankiller / Tim Allen are right. .999999 is not 1.
Bad rounding skills doesn't make .999999 1.

 

If the 9s extended forever they would equal.

 

So if 999 went on infinitely, it'd be 1000?
(That's essentially what you're implying.)

 

nope it doesent =1 unless u round

 

999.9...=1000

This is what I am implying.
Something I came up with while stuck in traffic:
Use base 2
1=.11111111...
1=1/2+1/4+1/8+...+1/2^n

Still works.

 

My teacher tricked me with this -.- He asked if I wanted 100 Extra Credit Points, and who would turn that down? Obviously, I had to prove it, and I couldn't, but now I will and get that 100 Extra Credit point.

 

What does 7/17 equal? A fraction that goes on forever as a decimal. As such, it cannot be accurately expressed in decimal form. Just like 1/3. 0.333... may be EXTREMELY close to it, but it is not exactly 1/3. This is true for all numbers that don't terminate.

1/3+2/3=3/3=1
0.333...+0.666...=0.999... ≠ 1

Not all fractions can be expressed as decimals. We can just get really damn close. (And thus why my Pre-Calc teacher requires us to leave answers in improper fractions rather than as a decimal when applicable).

 

You CAN express all rational numbers with repeated decimals.
1/3 exactly equals .333... its just better practice to leave repeated decimals in fraction form. 7/17 equals .4117647058823529... exactly. Here is a simple algebraic proof:

 

Does 0.999... + 0.999... = 2? No.

 

Actually, that's wrong.

f(x) = 1/x CANNOT = 0
It can be an incredible small number, but can never reach zero.

That is what is taught in calculus courses.

 

The limit of 1/x as x approaches infinity is 0.

That is what is taught in calculus courses.