Question

Express 2.07070707071... as a rational number, in the form pq where p and q are positive integers with no common factors.

Answer 1

$x=2.070707\ldots=2.\overline{07}$
$100x=207.070707\ldots=207.\overline{07}$
$100x-x=99x=205\implies x=\dfrac{205}{99}$