I don't know the exact definition of % to double, cause I think it's useless, but how in the world would a $3.4 option with a delta of 0.97 double in value if the stock moves up by $1!?
I.e. we have an option price $3.4
Delta 0.97
stock @ 10.70.
10.70 to 11.70 is $1*0.97=$0.97...