Question

what is the 2013th digit after the decimal point in the decimal expansion of 8 /81?

Answer 1

observe: \(8/81=0.098765432098765\dots\)

Answer 2

It's rational so there's a repeating decimal expansion and we see every 9 digits it repeats \(098765432\)

Answer 3

Oh, I know how to find the answer now:)

Answer 4

... so all were interested in is the *remainder* of 2013 when divided by 9:$$2013\mod 9=6$$

Answer 5

can you find the 6th number in our pattern... ? :-)

Answer 6

5

Answer 7

Thanks:) You've helped a lot!

Answer 8

wait!

Answer 9

yes?

Answer 10

thanks then, and bye:)

Answer 11

nevermind you're fine :-)