A certain number ends with the digit 2
. Moving the 2
from the end of the number to its front doubles it. Can you find this number?
(Hint: it's quite large)
We are looking for a number abcde...z2.
Let's consider the continued fraction n=0.abcde...z2abcde...z2...
It follows that n/10+0.2 = 0.2abcde...z2abcde...z2... = 2n as stated, and we get n=2/19=0.105263157894736842.