It occurred to me that since they're 1000 millimeters in a meter, picturing 1000 would be as simple as looking at the millimeters along the length of a meter rule. Now, if they're 1000 millimeters in a meter, it follows that they're 1000,000 square millimeters in a square meter. Just think about it for a while... Do you see them? (If you're having difficulty picturing all those little square millimeters, buy yourself some graph paper with with each unit in the grid measuring 1 square millimeter, which I believe is standard, and glue them together until you have a 1 square meter sheet. Presto! There's your 1000,000 squares.)
Unless you have some sort of 3D modeling software, this last step to 1 billion (1000,000,000) will require pure thought. Just picture a cubic meter. Why, it's easy: First we had the 1 dimensional meter with just length that contained 1000 millimeters. Then we had the 2 dimensional (consisting of both length and breadth) square meter that contained 1000,000 square millimeters. Now let's add some depth to that and think in 3 dimensions (that should be a piece o' cake to think about because that's the type of world we live in, baby). Picture a cubic meter. Now, in your mind's eye, look all those cubic millimeters! You guessed it - there are a billion of them. Can you see them?
Cool huh?
Wanna guess how long those cubic millimeters would stretch if laid out end to end? Off the top of my head, I figured 1 Kilometer. But then when I really thought about it, the answer was actually 1000 Km!

Now let's see if we can picture a trillion (1000,000,000,000).
