Is 9 divide 9 equal to 1 because 1 divided 9 equals 0.1111 and 8 divide 9 equals 0.88888 therfore those two added equals 0.999999 not 1?

Answer 1

The last part of your question contains the mistake here. .9 repeating is, in fact, equal to one according to essentially all professional mathematicians.

There are tons of proofs on this topic, but I'll give a couple more basic ones since this doesn't seem to be intended as a necessarily rigorous question.

By definition: Real numbers must simply have a number (or really infinite numbers) between them. There is no number between .9 repeating and 1.

By definition: Two real numbers are the same if they subtract to equal 0. 1-.9 repeating is .000(infinite repeating zeroes)001. That number is provably smaller than any positive quantity and is obviously not negative. Not positive and not negative means 0, and thus 1 and .9 repeating are the same.

By Algebra: 1/9 = .1 repeating. 9 * 1/9 = 9 * .1 repeating. 9/9 = .9 repeating = 1. This must be true because we always modified each side of the equation in the same way, and the algebra is therefore sound.

In conclusion, 9/9 = 1 = 1/9 + 8/9 = .9 repeating.

Further proofs and background: http://en.wikipedia.org/wiki/0.999...