HOW CAN I PROVE THAT 0,99999999.. equals 1??????

Question

The first to answers wins Best Answer (10 whole points)

h2 answered correctly! stop answering! he'll get his "best answer" first thing tomorrow!! thank you all

Yo answered very good to! sorry i ahve to giv eonly one best answer

Answer 1

Actually the above "proof" is misleading.

x=0.999...99

10x=9.999...90 (as anything x10 adds a zero to the end as the decimal place shifts, even if the number is infinite)

9x=10x-x
=9.999...90-0.999...99
=8.999...81

x=9x/9=8.999...81/9=0.999...99

Therefore 0.999...99 does not equal 1....mathematics isn't independent of logic. Beware of those who try to make it so.

Answer 2

OK, I give this question every year to my students. The answer is both it does equal 1 and it doesn't equal 1.

To a mathematician, it never will. In fact, it was a mathematician who proved that eventually it will be so close that we would no longer be able to detect the difference and can safely assume it is 1. This mathematician is Zeno of Alexandria. Now, here is what happened when he stated this. Two different groups formed those that called him a liar (Mathematicians) and those that called him a saint (Scientists). Every time I teach Significant Figures to my Chemistry students, the mathematicians call me a liar. Seriously, I have PhD's calling a foundation of mathematical science a lie.

Now, it depends who you are talking to.
Mathematicians - 0.999999999... will never be 1
Scientists - 0.999999999... aww, close enough... 1

Answer 3

It is a question of materiality. Let us assume that the .99999 equals a repeating non-ending numeral. The difference between .999999 ad infinium and 1 is so slight as to be non-existant...it is immaterial to the measurements in question.

If the .99999 DOES have an end, then the difference, when dealing with certain amounts, IS material and therefore it should be listed as the .99999

As for the mathematical formula that x=.999 and therefore 9x=10x-x and so 9x=9, and thusly x=1, this fails in the proof. 9x=/=9, with 9x equaling 8.9999999 ad infinium.

Answer 4

Look at it in terms of the sum of a geometric series:

0.99999...= 0.9+0.09+0.009+...
= 9.10^-1+9.10^-2+9.10^-3+...

So first term is a=9*10^-1, and the geometric ratio is r=10.^-1 (because you obtain the next term in the sequence by multiplying the previous one by 10^-1)

The sum of a geometric series is given by a/(1-r)
So S=9.10^-1/(1-10^-1)=9.10^-1/(9.10^-1)= 1.

So YES, 0.99999999.... is actually EQUAL to 1. (it's not a question of "rounding up")

Answer 5

When you add another "9", the value will advance towards 1. If you keep adding "9"s, they will never reach 1! However, if this is placed in an INFINITUM, it will theoreticaly equal 1.

I think this is the harder way to explain

Answer 6

It doesn't equal one, it CONVERGES to one. That is:
the series

(9 x 10^(-1)) + (9 x 10^(-2)) + ...+ (9 x 10^(-n))

converges to 1 as n goes to infinity.

You have to use some calculus.

Answer 7

0.33333333333... = 1/3
0.66666666666... = 2/3

Add both equations.

0.99999999999... = 3/3 = 1

(People that don't know that 0.9999999999... = 1 shouldn't be answering questions in the maths section.)

Answer 8

0.9999999999 is not equal 1. But if you buy a 1lb of chicken at the market and only get 0.99999999lb, would you complain the manager by wasting your time?

Answer 9

Actually it does = 1
Theoretically!!!!
Just define your Theory as to why it equals one and you have your answer. We have many theories in the world, does not mean they are True/False but, they give evidence that they are True.

Answer 10

0.99999999 is not equal to 1 see it 0.9999999999 which is less than < 1 if u show us how we might help u. or as someone here answered: if u round it up