1. ## extra credit help

i got a less-than-satisfactory grade on a test today(less than satisfactory in my parents eyes, at least, its an 80%...) and the teacher offered a 10% extra credit assignment for everyone.
ive done all of it, but there is one problem that is really getting me...
i wouldnt normally ask on such an assignment, but its all or nothing, and my calculator doesnt go high enough to figure it out for sure.
What fraction is exactly equal to .9(repeating)?
note: CANNOT be .9repeating over 1.

2. Originally Posted by Forkmaster
What fraction is exactly equal to .9(repeating)?
$\frac{1}{1}$
Normally I do not answer such questions.
But this one is really dumb.

$\begin{array}{rcl}
N & = & 0.9\bar 9 \\
10N & = & 9.9\bar 9 \\
9N & = & 9 \\
N & = & \frac{9}{9} = \frac{1}{1} \\
\end{array}$

3. we can't have anything over 1.

4. Originally Posted by Forkmaster
we can't have anything over 1.
Well O.K.
Use $\frac {9} {9}$

5. just say 1/3 = .3333...
so 1/1=3/3=1/3+1/3+1/3=.99999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 9999999999999999999999....999999999999999999999999 999999999999999999999999999999999...

okay fine (i said indirectly as in it follows--don't pay attention to this forkmaster, nothing was said, just go on with your life)

6. Originally Posted by jimmybuffet
haha plato you called a little kid "dumb" (indirectly) that's funny
No I did not. But I will ask if you can read.
I said that the problem is bumb.
I said nothing about the person who posted the questoin?

7. He said the question was dumb, not the OP (original poster).

8. you guys win. wait, did you guys read the original question? it says that it can't be (.999...)/1 but .99999....= 1, so it can't be 1/1, but 1/1= 9/9, so it can't be that either... hence, we failed to answer the question.

9. Originally Posted by jimmybuffet
you guys win. but really this question is worth 10 points? my kind of teacher
Look at this:
$\begin{array}{rcl}
N & = & 0.9\bar 9 \\
10N & = & 9.9\bar 9 \\
9N & = & 9 \\
N & = & \frac{9}{9} = \frac{1}{1} \\
\end{array}$

10. okay

11. the entire class tried various ones, ranging from 3/3 to 86/87..
none were correct. the teacher said that you must have it be exactly .9repeating, as in it wouldnt round to 1, which is almost impossible.. she also said that she has offered that EC question for 7 years in a row, and no one has ever gotten it right.

12. Originally Posted by Forkmaster
the entire class tried various ones, ranging from 3/3 to 86/87.. none were correct. the teacher said that you must have it be exactly .9repeating, as in it wouldnt round to 1, which is almost impossible.. she also said that she has offered that EC question for 7 years in a row, and no one has ever gotten it right.
Forkmaster, I truly do sympathize with you. It is tough to have an ignorant teacher.
If that is indeed her response, then she is mathematically ignorant.
Someone that uninformed will almost certainly be vindictive as well.
Ignorance makes nasty teachers. Believe me, having chaired a university mathematics department I know how minimally prepared people can and do take their inadequacies out on the students.

Here is my advice for you to do. Show you parents my response to this question and to this teacher. Ask them to complain to the educational authority in your school. I think any teacher such as this needs to be brought up short. To your parents I say: Please don’t let this matter go un-addressed.

13. i would do that if it was an actual assignment question, but it was an EC thing, and she said it must be exactly .9repeating without being a whole.. i dont think it needs to be brought to attention or anything like that

14. ## wow

forkmaster, your teacher must listen to reason or else!

the fact is that 1 = .9(repeating)
the users Plato and jimmybuffet both proved it, in different ways

again .9(repeating) is the same exact number as the number 1
that is, .9(repeating) is a whole number, so anything equal to it is a whole number

you can't have a fraction equal to 1 but not exactly .9(repeating)
any fraction equal to 1 is equal to .9999999999999999...

again, .99999999.... = 1
.99999999.... = 3/3
.99999999.... = 1/1
.99999999.... = 4/4
.99999999.... = (yourteacheriswrong)/(yourteacheriswrong)
.99999999.... = 9/9
.99999999.... = (.23)/(.23)
.99999999.... = (michael jordan)/(best basketball player ever)
.99999999.... = (charles barkley)/(coolest basket ball player ever)

provided of course that division is meaningful for the words too.

i hope it all works out... you're getting that 10% of your points, you could also give the fraction (1/1/1/1/1/1/1/1/1/.9(repeating)/1/1/1/1/1/1/1/1/1/1/1) / (1/1/1/1/1/1/1/1/1/1/1/1)

15. Originally Posted by Forkmaster
she said it must be exactly .9repeating without being a whole..
Well give her this even though you are Algbra II.
$0.\bar 9 = 9\sum\limits_{k = 1}^\infty {10^{ - k} }$