No, I'm glad you laid out the fairly simple math that lets one do these types of calculations quickly and fairly easily.

I just saw the opportunity to connect the two suggestions and thus 1) give people a quick intro to what Math::BigApprox is doing under the covers and 2) let the OP know that they don't have to do this by hand if this level of accuracy is acceptable.

Thanks for showing the math that I didn't have/take the time to. :)