A billion, in continental Europe is, a million squared ( 1,000,0002 = 1,000,000,000,000), but in the English speaking world, a billion is only a thousand million (1,000,000,000). numberphile goes into the beautiful, mathematical logic of the longer form (i.e. the continental system).
Of course, the “simplest” system, which avoids all the potential for miscommunication, is the standard scientific notation, where 1,000,000,000 is written as 1×109 (or just 109).