Expert: Sherman D. - 6/22/2005

Question
ok if you look at a chart for the fractions of 9's;
1/9 = .1 repeating
2/9 = .2 repeating
3/9 = .3 repeating
so on and so forth. if you follow this pattern and you get to 9/9 should equal .9 repeating. but anyone knows that when the denominator and the numeratior are the same number it equals 1... does .9 equal 1. also when you add 1/3 and 2/3 going by a fraction you get 3/3 which equals 1. but when you go by decimals you get .9 repeating. how can this be? .9 repeating does not equal 1 because there is still that extremely small part missing. give me your feed back please

Answer
9/9 = .999999, however when you get to the end, you eventually will have to round the last number, because the calculator cannot keep going, so

9/9 = .999999
round the 9 at the end, and you get
9/9 = 1.000000, or just say 1

-----------------------------------------------------------

Also believe it or not (1/3) + (2/3) has been typed at this site often, and here is why (1/3) + (2/3) = (3/3) = 1
and .333333 + .666666 = 1

2 reasons
.3333 + .6666 = .9999 and same reason above, or

.6666 rounds to .6667 because you have to round the number next to last by adding 1 to it, because any number 5 and higher, you have to round the number before it to 1 more than it is, so

.3333 + .6666 becomes .3333 + .6667, and when you add those, you get 1.000 or just say 1.

another reason, even though .99999 repeats infinitely, when you finally reach infitity, you will still have to found the number before the last number to 1 more than it is, and when you say 9 + 1 you get 10, and you have to carry the 1 over and you get 9 + 1 over and over until you get 1.000000 with 0 repeating to infinity or just say 1.

-----------------------------------------------------------

Also for future knowledge, when you get to is, another popular question is

Why does x^0 = 1, and here is why
(x^n)/(x^n) = x^(n - n) = x^0 = 1
and as you know, a number divided by itself equals 1.

I know you didn't ask for me to give you that info. Lets just call it a bonus Q&A.