There are 15 zeros following the one in 1 quadrillion. There are three zeros per every thousand and six zeros per every million. A quadrillion is a thousand trillion, which means it has three zeros for the thousand plus 12 zeros for the trillion for a total of 15.
A billion is a thousand million, so it has three zeros for the thousand plus six zeros for the million for a total of nine zeros. A trillion is a million million, so it has six zeros for the million plus six more for the other million for a total of 12. The number googol has 100 zeros, and the number googolplex is a 1 with a googol of zeros.