At what point does a number such as 3.9999999 etc become 4?

Question

One would assume that there could be an infinite number of decimal places applied to the example given. But an infinite of 9's could never be represented and so surely this is a flaw with the decimal system? We don't usually think about it - we take it for granted but if one were to take a magnifying glass and delve deeper and deeper, one would find themselves drowning in 9's and never ever getting to the magical number four! It's a bizarre pitfall to fall into because it boggles the mind. Surely mathematics is all about working with finites and yet here is an example of an infinite that can never be solved with a finite number of decimal places.

It's simply absurd!

So our reaction to this problem is to pretend that it doesn't exist and only go as far as 2 or 3 decimal places before we bridge that gap. I know scientists go to about 10 decimal places but that is still side-stepping this small unsolvable conundrum!

Answer 1

Interesting question, but easily answered.

It depends entirely upon the level of exactness that the scientist/mathematician needs/wants.  

Consider the value for Pi.  The mathematical value never ends - so some scientists use 3.14, some use 3.1415, some go so far as to go 3.14158265...  and to "ball park" the value, some use a simple THREE.

When using complex math, the more exact you are, the more precise your answer will be.  If you round off a lot in the calculations, the answer can be skewed by quite a bit.  And this is the factor that scientists/mathematicians consider when deciding to use one, three or two-hundred decimal places.

Eventually, you just have to decide that, "Well, this is close enough for me!"

Answer 2

Wow, this is a very bizarre question! I guess you just use as many decimal places as you feel like.......................

Answer 3

Here's a nice little test to show you why scientists decided to round up such a number.

Start a set distant from a spot on the floor.

Now, move 1/2 of the way to that spot.

Repeat the process.

Repeat the process.

Keep repeating until you realize that you will have eventually reached that spot.

Another way of viewing the problem:

.99999 repeating = 1 - .00000repeating 1

Answer 4

The simple answer is never. 4 is a value of nothing more than and nothing less than 4 hence 3.anything is always going to be lower than 4 till the end of time

Answer 5

.9(recurring) is 1 - at least, algebra says it is.

x = .999...

10x = 9.999...

9x = 9

x = 1

Answer 6

if you add 1/9 and 8/9 you will get 1

but 1/9 is 0.1111111111......

and 8/9 is 0.8888888888.....

adding them together gives 0.9999999...  but we just said that this is equal to 1....  !

Answer 7

The answer to your question is never. but for practical purposes you can assume it is four and your margin of error would be negligible unless you are dealing in multi billions when you may have an error of nearly 1