Jess and Brian are playing the following game: Jess thinks of a fraction, and Brian flips a coin. If the coin turns up heads, Jess multiplies the number she's thinking of by 5/6. If the coin turns up tails, she multiplies the number she's thinking of by 6/5. Brian flips the coin ten times, and after each flip Jess multiplies the number in her head by either 5/6 or 6/5, depending on the coin flip. The ten coin flips turn out to be: THTTHTHTTT, where H means 'heads' and T means 'tails.' What number is Jess thinking of at the end of the game if she starts out with the fraction 5/9?