Nine tiles, each with a unique non$-$zero digit, are placed into a bag and shuffled. You pick four of them $($without replacement$)$ and they form a number in the order you drew them $($eg$.$ if you drew $2,3,1,7$ your number is $2317).$

$($a$)$ What is the expected value of the number you draw?

Hint: think recursively and also look ahead to what you will need in part $($b$).$

$($b$)$ Now you add a tenth tile with a decimal point into the bag, and repeat the experiment $($e$.$g$.,$ if you drew $3,.,1,6$ your number is $3\mathrm{.}16).$ What is the expected value of the number you draw?