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.
thanks in advance
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)
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.
I am not asking you to risk your grade by showing her my response.
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.
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)