Lets say I have number in decimal form to the ten-thousands place $$p=0.abcd$$ and another number $$q=0.xyz$$ to the hundredth place. $$a.b,c,d,x,y,z$$ are all integers from 0 to 9, inclusive, except for z & d which can only range from 1 to 9, inclusive. If I want to know exactly where the decimal will lie in the multiplication of $$p*q$$ is there a formula I can employ?
Right now every time I multiply two decimals, I multiply $$abcd$$ and $$xyz$$ and then move the decimal point by the sum of number places d&z are away(so 7 moves to the eft). But this is all conditioned on the size of the number abcd*xyz yields. Is there a formula that can standardize this?