Question

What is the maximum number of digits that a decimal fraction with denominator 13 could have in a recurring block in theory?

Answer 1

12 ?

Answer 2

yeah that's the right ans. but why?

Answer 3

i think all we need to check is 1/13

Answer 4

as any other number will be decomposed into
N|13 = n+k*1/13
where n is any integer and 0<=k<=9, k is also integer

Answer 5

and its easy to show that addition of the repeating decimals of 1/13 cannot produce an extra digit in the pattern

Answer 6

i did 1/13 aswell and I figured the answer should have been 6, but the answer is supposed to be 12, I don't know why. I can take a wild guess and say that its 12 because from 1/13 to 12/13 there are twelve values in between? but like I said it's a wild guess, I have nothing to base it on, not to mention it doesn't make any sense.

Although there is a distinction between this question and the question following it, which says "How many digits does 1/13 actually have?" In which case the answer 6 is true