I am aware that pennies only have a thin shell of copper. I still think that small amount of copper is worth more than 1/100th of a cent.
I was not aware you were referring to 1/100th of a cent as your post implies 1/100th of a dollar. In any case,
Coinflation.com gives a value of $0.0003686 for the copper, so 3.7% of a penny.