Question

what is the smallest positive integer \(n\) such that out of the \(n\) unit fractions \(\frac{1}{k}\) where \(1\le k \le n\) exactly half the fractions give a terminating decimal/

Answer 1

someone posted this, not sure it is easy or hard i am up to 6

Answer 2

so if n=2 we have two fractions 1/1,1/2
Both of these terminate so that is more than half that give a terminating decimal

Answer 3

So based on my response this means I have the right interpretation?

Answer 4

ooho i think i got it!

Answer 5

Not the correct answer just correct interpretation..
I would think n would have to be even then.

Answer 6

i guess so i copied the question verbatim

Answer 7

n=2i
\[\frac{1}{1} ,\frac{1}{2}, \frac{1}{3}, \cdots, \frac{1}{2i-1}, \frac{1}{2i}\]
so we want half of these to terminate for some integer i

Answer 8

i made two lists until i got half and half
1, 1/2 1/4 1/5 1/8 1/10
1/3 1/6 1/7 1/9 1/11 1/12

Answer 9

too bad the asker has flown the coop

Answer 10

well look at you
you get a brownie and you can have one of my kitties

Answer 11

i have never kittled!

Answer 12

Hmm, neat problem :)

Answer 13

you should kittled! Kittling is the cutest.

Answer 14

I wonder if this was a number theory question or if it was a question that a math teacher came up with to test who knows what a terminating decimal is.

Answer 15

probably the latter
i have another one that i will post now
it is slightly more difficult but only slightly

Answer 16

I guess they would have to be able to read that which they probably wouldn't be able to.