what is .999...+.111...?

Question

What does .9...+.1... equal? Is it 2.11..... on the principle of .9999...= 1? or is it something else?

Answer 1

I assume, by the ellipses, that you mean for these sequences to repeat themselves indefinitely. Then the sum is simply 1.111111... You can prove this to yourself by just summing the first few terms, or even formally take the sum of infinitely many terms (work from left to right and use induction to prove that the 1s you get are not provisional). But the easiest way to see this is to rewrite the numbers as fractions:

1+1/9 = 10/9 = 1.111111.....

Answer 2

.999+.111=1.11

On the idea of .99999...=1, that is ridiculous. All of the proof that have been done are so obviously wrong that its not even funny. First of all, you can use a number to which you kind of know. .999..... doesn't count. You need a finite number of digits to work with. .999........ IS NOT A NUMBER.

Furthermore, a variable cannot change when you want it to. It must always be the same. In this algebraic proof, the author adds a 9 at will:

If c = .999, 10c = 9.99, not 9.999. Therefore, 10c − c = 8.991, not 9.

Answer 3

nick 0.9999... (infinite number of nines) is a number, as much as 1/3 is a number (0.33333....) - even better 0.99999... = 1, as much as 0.3333333333... = 1/3

basically 1 - 0.999... = 0.000... (there is no 1 at the end as there is no end).

so 0.999 + 0.1111... = 1 + 0.1111... = 1.111...

Answer 4

0.1111... is the same as 1/9, while 0.9999... is the same as 1, so the answer is 10/9, or 1.1111...

Answer 5

No, it's 1.11. Ignore the decimal point and just add them.

Answer 6

.999
+.111
--------
1.110

Answer 7

.999
.111
_____
1.11

Answer 8

1.11............